思路１：两层for循环 Ｏ（ｎ2）
class Solution:
def twoSum(self, nums, target):
res = []
for i in range(len(nums)):
for j in range(i+1, len(nums)):
if nums[i]+nums[j]==target:
res.extend([i, j])
break
print('==res:', res)
return res
nums = [2, 7, 6, 15]
target = 9
sol = Solution()
sol.twoSum(nums, target)
思路２：ｈａｓｈ
python代码
class Solution:
def twoSum(self, nums, target):
res_dict = {}
for i in range(len(nums)):
value = target - nums[i]
if value in res_dict:
return [res_dict[value], i]
res_dict[nums[i]] = i
print('==res_dict:', res_dict)
return [-1, -1]
nums = [2, 7, 6, 15]
target = 9
sol = Solution()
res = sol.twoSum(nums, target)
print('res:', res)
思路2:c++代码：
#include <string>
#include <iostream>
#include <vector>
#include <list>
#include <map>
#include <typeinfo>
using namespace std;
class Solution {
public:
vector<int> twoSum(vector<int>& nums, int target) {
map<int, int> dict_;
for(int k=0;k<nums.size();k++)
{
dict_[nums[k]] = k;
}
map <int,int>::iterator iter = dict_.begin();
for (;iter!=dict_.end();iter++)
{
if(dict_[target - iter->first])
{
// cout<<iter->second<<dict_[target - iter->first]<<endl;
return {iter->first,target - iter->first};
}
}
return {-1,-1};
}
};
int main()
{
vector<int> nums;
nums = {2,7,11,15};
int target = 9;
// nums = [2,7,11,15]
Solution sol;
vector<int> res;
res = sol.twoSum(nums,target);
for(int k=0;k<res.size();k++)
{
cout<<"==res[k]:"<<res[k]<<endl;
}
return 0;
}
方法1：利用字典
class Solution:
def twoSum(self, numbers: List[int], target: int) -> List[int]:
res_dict = {}
for i in range(len(numbers)):
value = target - numbers[i]
if value in res_dict:
return [res_dict[value]+1, i+1]
res_dict[numbers[i]] = i方法2：双指针
class Solution:
def twoSum(self, numbers, target):
left=0
right = len(numbers)-1
while left<right:
sum_= numbers[left]+numbers[right]
if sum_==target:
return [left+1, right+1]
elif sum_<target:
left+=1
else:
right-=1
return [-1, -1]
sol = Solution()
numbers = [2, 7, 11, 15]
target = 9
res = sol.twoSum(numbers,target)
print('res:',res)
ｃ++实现:
class Solution {
public:
vector<int> twoSum(vector<int>& numbers, int target) {
int n = numbers.size();
int l=0, r = n-1;
while(l < r){
if(numbers[l]+numbers[r] > target){
r -= 1;
}
else if(numbers[l] + numbers[r] == target){
return {l + 1, r + 1};
}
else{
l += 1;
}
}
return {-1, -1};
}
};2.两数相加
思路:开出一个head头,利用一个指针进行遍历,需要注意的是进位
# Definition for singly-linked list.
# class ListNode:
# def __init__(self, val=0, next=None):
# self.val = val
# self.next = next
class Solution:
def addTwoNumbers(self, l1: ListNode, l2: ListNode) -> ListNode:
head = ListNode(0)
new_node = head
carry = 0
while l1 and l2:
new_node.next =ListNode(l1.val+l2.val+carry)
carry = new_node.next.val//10
new_node.next.val = new_node.next.val%10
l1 = l1.next
l2= l2.next
new_node = new_node.next
# print(carry)
while l1:
new_node.next = ListNode(l1.val+carry)
carry = new_node.next.val//10
new_node.next.val = new_node.next.val%10
l1 = l1.next
new_node = new_node.next
while l2:
new_node.next = ListNode(l2.val+carry)
carry = new_node.next.val//10
new_node.next.val = new_node.next.val%10
l2 = l2.next
new_node = new_node.next
if carry:
new_node.next = ListNode(carry)
return head.nextc++实现:
/**
* Definition for singly-linked list.
* struct ListNode {
* int val;
* ListNode *next;
* ListNode() : val(0), next(nullptr) {}
* ListNode(int x) : val(x), next(nullptr) {}
* ListNode(int x, ListNode *next) : val(x), next(next) {}
* };
*/
class Solution {
public:
ListNode* addTwoNumbers(ListNode* l1, ListNode* l2) {
ListNode* head = new ListNode(0);
ListNode* new_head = head;
int carry = 0;
while(l1 && l2){
new_head->next = new ListNode(l1->val + l2->val + carry);
carry = new_head->next->val/10;
new_head->next->val = new_head->next->val%10;
new_head = new_head->next;
l1 = l1->next;
l2 = l2->next;
}
while(l1){
new_head->next = new ListNode(l1->val + carry);
carry = new_head->next->val/10;
new_head->next->val = new_head->next->val%10;
new_head = new_head->next;
l1 = l1->next;
}
while(l2){
new_head->next = new ListNode(l2->val + carry);
carry = new_head->next->val/10;
new_head->next->val = new_head->next->val%10;
new_head = new_head->next;
l2 = l2->next;
}
if(carry){
new_head->next = new ListNode(carry);
}
return head->next;
}
};
思路:滑动窗口，先往右拓展字典进行加1，发现大于1的在往左压缩 python代码
class Solution:
def lengthOfLongestSubstring(self, s):
n = len(s)
left = 0
right = 0
dict_= {}
res = 0
while right<n:#往右拓展
dict_[s[right]] = dict_.get(s[right], 0)+1#出现就加1
while dict_[s[right]]>1:#解决这种两个连续ww的问题"pwwkew" 再次出现往左压缩
dict_[s[left]]-=1
left+=1
res = max(res, right-left+1)
right+=1
return res
# s = "abcabcbb"
# s = "dvdf"
s = "pwwkew"
sol = Solution()
sol.lengthOfLongestSubstring(s)c++代码:
#include <string>
#include <iostream>
#include <vector>
#include <list>
#include <map>
#include <typeinfo>
using namespace std;
class Solution {
public:
int lengthOfLongestSubstring(string s) {
int left = 0, right = 0, res = 0;
unordered_map<char, int> dict_; //散列表实现 查找更高效
int length = s.size();
while(right < length){
dict_[s[right]]++;
while (dict_[s[right]] > 1){
dict_[s[left]]--;
left++;
}
right++;
res = max(right - left, res);
}
return res;
}
};
int main()
{
string s = "abcabc";
// Solution sol;
// int res;
// res= sol.lengthOfLongestSubstring(s);
int res;
Solution *sol = new Solution();
res = sol->lengthOfLongestSubstring(s);
delete sol;
sol = NULL;
cout<<"res:"<<res<<endl;
return 0;
}
思路:双指针，走完剩下的在进行合并 时间复杂度o(m+n) 空间复杂度0(m+n)
class Solution:
def findMedianSortedArrays(self, nums1, nums2):
res = []
i, j = 0, 0
m, n = len(nums1), len(nums2)
while i < m and j < n:
if nums1[i] < nums2[j]:
res.append(nums1[i])
i += 1
else:
res.append(nums2[j])
j += 1
print('==res:', res)
print('==i:', i)
print('==j:', j)
if i < m:
res.extend(nums1[i:])
if j < n:
res.extend(nums2[j:])
print('==res:', res)
if (m+n)%2==0:#偶数
return (res[(m+n)//2]+res[(m+n)//2-1])/2
else:#奇数
return res[(m+n)//2]
# nums1 = [1, 1, 3]
# nums2 = [2]
nums1 = [1,2]
nums2 = [3,4]
sol = Solution()
res = sol.findMedianSortedArrays(nums1, nums2)
print(res)c++实现:
class Solution {
public:
double findMedianSortedArrays(vector<int>& nums1, vector<int>& nums2) {
int m = nums1.size();
int n = nums2.size();
int i=0, j=0;
vector<double> res;
while(i<m && j<n){
if(nums1[i]<nums2[j]){
res.push_back(nums1[i]);
i++;
}
else{
res.push_back(nums2[j]);
j++;
}
}
while(i<m){
res.push_back(nums1[i]);
i++;
}
while(j<n){
res.push_back(nums2[j]);
j++;
}
// for(int i=0;i<res.size(); i++){
// cout<<"res:"<<res[i]<<endl;
// }
if((m+n)%2){
return res[(m+n)/2];
}
else{
return (res[(m+n)/2-1] + res[(m+n)/2])*1.0/2.;
}
return 0.;
}
};优化:双指针识别,不用开辟数组空间, 时间复杂度o((m+n)/2) 空间复杂度0(1)
class Solution {
public:
double findMedianSortedArrays(vector<int>& nums1, vector<int>& nums2) {
//双指针吧
int m = nums1.size();
int n = nums2.size();
int i=0, j=0;
float preNum = 0, current = 0;
while((i + j) <= (m + n)/2){
preNum = current;
if((j >= n) || (i < m && nums1[i] < nums2[j])){
current = nums1[i];
i++;
}
else{
current = nums2[j];
j++;
}
}
if((m + n)%2 == 0){
return (current + preNum) / 2;
}
else{
return current;
}
}
};5.最长回文子串
思路:中心枚举
class Solution:
def helper(self,left,right,s):
while left>=0 and right<len(s) and s[left]==s[right]:
left-=1
right+=1
if len(s[left+1:right])>len(self.res):
self.res = s[left+1:right]
def longestPalindrome(self, s: str) -> str:
self.res = ''
for i in range(len(s)):
self.helper(i,i,s)
self.helper(i,i+1,s)
return self.res
c++实现:
class Solution {
public:
string res;
void help(int left, int right, string& s){
while(left >= 0 && right < s.size() && s[left] == s[right]){
left--;
right++;
}
left++;
right--;
if(right - left + 1 > res.size()){
res = s.substr(left, right - left + 1);
}
}
string longestPalindrome(string s) {
if(s.size() <= 1){
return s;
}
for(int i=1; i<s.size(); i++){
help(i-1, i+1, s);
help(i-1, i, s);
}
return res;
}
};
求Max{(j-i) * Min( h(i), h(j) )},
思路：双指针
时间复杂度为 O(n)，空间复杂度为 O(1) 。
#解法2
class Solution:
def maxarea(self,height):
left=0
right=len(height)-1
max_area=0
while left<right:
max_area = max(max_area,(right - left) * min(height[left], height[right]))
if height[left]<height[right]:
left+=1
else:
right-=1
# index_i = left
# index_j=right
return max_area
s=Solution()
height=[2,8,1,5,9,3,4]
max_area=s.maxarea(height)
print(max_area)c++实现:
class Solution {
public:
int maxArea(vector<int>& height) {
int left = 0;
int right = height.size() - 1;
int max_area = 0;
while(left < right){
max_area = max(max_area, min(height[left], height[right])*(right - left));
if(height[left]<height[right]){
left++;
}
else{
right--;
}
}
return max_area;
}
};7.三数之和
思路1: 固定两数，寻找第三个数，两层循环，最复杂解法，列表比较大时，时间会很长
class Solution:
def threeSum(self, nums):
"""
:type nums: List[int]
:rtype: List[List[int]]
"""
result=[]
nums.sort()
length=len(nums)
for i in range(length-1):
for j in range(i+1,length):
if -(nums[i]+nums[j]) in nums[j+1:]:
tmp=[nums[i],nums[j],-(nums[i]+nums[j])]
if tmp not in result:
result.append(tmp)
return result思路2: 双指针，固定一个数，让其余两个数从第一个数+1和尾 向中间靠近，只需要循环一遍
# 双指针:排好序以后，双指针去寻找两数之和等于第一个
class Solution:
def threeSum(self, nums):
nums = sorted(nums)
res = []
n = len(nums)
print('==nums:', nums)
for i in range(n):
if i>0 and nums[i]==nums[i-1]:#去除相同的第一个数[-1, 0, 1, 2, -1, -4]
continue
start = i + 1
end = n - 1
# print('==start:', start)
# print('==end:', end)
while start < end:
if nums[i] + nums[start] + nums[end] == 0:
res.append([nums[i], nums[start], nums[end]])
start += 1
end -= 1
while start<end and nums[start]==nums[start-1]:# 首部出现连续两个数[-2, 0, 0, 2, 2]
start+=1
while start<end and nums[end]==nums[end+1]:# 尾部出现连续两个数[-2, 0, 0, 2, 2]
end-=1
elif (nums[i] + nums[start] + nums[end]) > 0:
end -= 1
else:
start += 1
print('==res:', res)
return res
# nums = [-1, 0, 1, 2, -1, -4]
nums = [-2, 0, 0, 2, 2]
sol = Solution()
sol.threeSum(nums)
c++实现:
class Solution {
public:
vector<vector<int>> threeSum(vector<int>& nums) {
vector<vector<int>> res;
sort(nums.begin(), nums.end());
int n = nums.size();
for(int i=0; i<n; i++){
if(i>0 && nums[i]==nums[i-1]){
continue;
}
int start = i + 1;
int end = n - 1;
while(start < end){
if(nums[i] + nums[start] + nums[end] == 0){
res.push_back({nums[i], nums[start], nums[end]});
start++;
end--;
while(start < end && nums[start]==nums[start-1]){
start++;
}
while(start < end && nums[end]==nums[end+1]){
end--;
}
}
else if((nums[i] + nums[start] + nums[end]) > 0){
end--;
}
else{
start++;
}
}
}
return res;
}
};思路3.利用两数之和
class Solution:
def twoSum(self, nums, target):
res_dict = {}
for i in range(len(nums)):
value = -target - nums[i]
if value in res_dict:
self.res.add((target, nums[i], value))
res_dict[nums[i]] = i
def threeSum(self, nums: List[int]) -> List[List[int]]:
self.res = set()
nums = sorted(nums)
for i in range(len(nums)):
if i>0 and nums[i] == nums[i-1]:
continue
self.twoSum(nums[i+1:], nums[i])
return list(self.res)
思路:也是双指针
class Solution(object):
def fourSum(self, nums, target):
"""
:type nums: List[int]
:type target: int
:rtype: List[List[int]]
"""
nums = sorted(nums)
ans = set()
for i in range(len(nums) - 3):#第一层循环到达三个数之前
for j in range(i + 1,len(nums) - 2):#最后两个数需要固定
start = j+1
end = len(nums)-1
while(start < end):
temp = nums[i] + nums[j] + nums[start] + nums[end]
if temp == target:
ans.add((nums[i], nums[j], nums[start], nums[end]))
start += 1
end -= 1
elif temp > target:
end -= 1
else:
start += 1
return list(ans)
思路:组合问题 用回溯
class Solution:
def backtrace(self, digits, track):
if len(digits) == 0:#满足终止条件
self.res.append(track)
return
for letter in self.phone[digits[0]]:# for循环去遍历选择条件
store = track#保存中间结果用于回溯
track += letter
self.backtrace(digits[1:], track)
track = store#恢复中间结果回溯
def letterCombinations(self, digits):
self.res = []
if len(digits) == 0:
return self.res
self.phone = {'2': ['a', 'b', 'c'],
'3': ['d', 'e', 'f'],
'4': ['g', 'h', 'i'],
'5': ['j', 'k', 'l'],
'6': ['m', 'n', 'o'],
'7': ['p', 'q', 'r', 's'],
'8': ['t', 'u', 'v'],
'9': ['w', 'x', 'y', 'z']}
self.backtrace(digits, track='')
print('==self.res:', self.res)
return self.res
digits = "23"
sol = Solution()
sol.letterCombinations(digits)
思路：找到链表长度，通过在头结点补充一个节点找到要删除的节点的上一个节点，然后在进行删除
方法１：循环
# Definition for singly-linked list.
# class ListNode:
# def __init__(self, val=0, next=None):
# self.val = val
# self.next = next
class Solution:
def removeNthFromEnd(self, head: ListNode, n: int) -> ListNode:
length = 0
node = head
#获取链表长度
while node:
length+=1
node= node.next
# print(length)
curr_length = 0
new_head = ListNode(0)
new_head.next = head
node2=new_head
stop_length = length - n
#循环走到要删除节点的前一个节点
while stop_length:
stop_length-=1
node2 = node2.next
#跳过要删除的节点即可
node2.next = node2.next.next
return new_head.next
方法２：递归
# Definition for singly-linked list.
# class ListNode:
# def __init__(self, val=0, next=None):
# self.val = val
# self.next = next
class Solution:
def __init__(self):
self.count = 0
def removeNthFromEnd(self, head: ListNode, n: int) -> ListNode:
if not head:
return head
head.next = self.removeNthFromEnd(head.next, n) # 递归调用
self.count += 1 # 回溯时进行节点计数
return head.next if self.count == n else head
方法3:双指针 推荐使用
fist 指针与second指针相隔n,这样first跑到尾部,second的下一个节点就是倒数第n个
# Definition for singly-linked list.
# class ListNode:
# def __init__(self, val=0, next=None):
# self.val = val
# self.next = next
class Solution:
# def __init__(self):
# self.count = 0
def removeNthFromEnd(self, head: ListNode, n: int) -> ListNode:
new_head = ListNode(0)
new_head.next = head
first = head
second = new_head
for i in range(n):
first = first.next
while first:
first = first.next
second = second.next
second.next = second.next.next
return new_head.nextc++实现:
/**
* Definition for singly-linked list.
* struct ListNode {
* int val;
* ListNode *next;
* ListNode() : val(0), next(nullptr) {}
* ListNode(int x) : val(x), next(nullptr) {}
* ListNode(int x, ListNode *next) : val(x), next(next) {}
* };
*/
class Solution {
public:
ListNode* removeNthFromEnd(ListNode* head, int n) {
ListNode* new_head = new ListNode(0);
new_head ->next = head;
ListNode* first = head;
ListNode* second = new_head;
for(int i=0;i<n;i++){
first = first->next;
}
while(first){
first = first->next;
second = second->next;
}
second->next = second->next->next;
return new_head->next;
}
};10.有效的括号
思路: 栈
class Solution:
def isValid(self, s: str) -> bool:
stack= []
dict_ = {
')':'(',
'}':'{',
']':'[',
}
for i in range(len(s)):
if s[i] in dict_.keys():
if len(stack) == 0 or stack[-1] != dict_[s[i]]:
return False
else:
stack.pop()
else:
stack.append(s[i])
return len(stack) == 0c++实现:
class Solution {
public:
bool isValid(string s) {
map<char, char> dict_;
dict_[']'] = '[';
dict_['}'] = '{';
dict_[')'] = '(';
vector<int> stack_;
for(int i = 0; i < s.size(); i++){
if(dict_.count(s[i]) > 0){
if(stack_.empty() || stack_.back() != dict_[s[i]]){
return false;
}
else{
stack_.pop_back();
}
}
else{
stack_.push_back(s[i]);
}
}
return stack_.empty();
}
};11.合并两个排序的链表
思路:引入一个指针头 python实现
# Definition for singly-linked list.
# class ListNode:
# def __init__(self, x):
# self.val = x
# self.next = None
class Solution:
def mergeTwoLists(self, l1: ListNode, l2: ListNode) -> ListNode:
head = ListNode(0)
node = head
while l1 and l2:
if l1.val < l2.val:
node.next = l1
l1 = l1.next
else:
node.next = l2
l2 = l2.next
node = node.next
if l1 is not None:
node.next= l1
if l2 is not None:
node.next= l2
return head.nextc++实现:
/**
* Definition for singly-linked list.
* struct ListNode {
* int val;
* ListNode *next;
* ListNode(int x) : val(x), next(NULL) {}
* };
*/
class Solution {
public:
ListNode* mergeTwoLists(ListNode* l1, ListNode* l2) {
ListNode* new_head = new ListNode(0);
ListNode* node = new_head;
while(l1!=NULL && l2 !=NULL){
if(l1->val<l2->val){
node->next = l1;
l1 = l1->next;
}
else{
node->next = l2;
l2 = l2->next;
}
node = node->next;
}
if (l1!=NULL){
node->next = l1;
}
if(l2!=NULL){
node->next = l2;
}
return new_head->next;
}
};12.括号生成
思路:回溯剪枝
1.左右括号插入数量不能超过n
2.左括号数量大于右括号，就可以插入右括号
# 回溯法:插入数量不超过n
# 可以插入 ） 的前提是 ( 的数量大于 ）
class Solution(object):
def generateParenthesis(self, n):
"""
:type n: int
:rtype: List[str]
"""
self.res = []
self.dfs(n, n, '')
return self.res
def dfs(self, left, right, track):
if left == 0 and right == 0: # 递归终止条件 左括号与右括号都用完
self.res.append(track)
return
if left > 0: # 左括号个数
store = track #
track += '('
self.dfs(left - 1, right, track)
track = store
if left < right: # 左括号个数大于右括号 此时可以添加右括号
# store = track
track += ')'
self.dfs(left, right - 1, track)
# track = store
n = 2
sol = Solution()
res = sol.generateParenthesis(n)
print(res)13.合并K个升序链表
思路1:上一题合并两个变成for循环顺序合并
# Definition for singly-linked list.
# class ListNode:
# def __init__(self, val=0, next=None):
# self.val = val
# self.next = next
class Solution:
def mergeTwo(self, l1, l2):
if l1 is None:
return l2
if l2 is None:
return l1
head = ListNode(0)
node = head
while l1 and l2:
if l1.val <l2.val:
node.next = l1
l1 = l1.next
else:
node.next = l2
l2 = l2.next
node = node.next
if l1:
node.next = l1
if l2:
node.next = l2
return head.next
def mergeKLists(self, lists: List[ListNode]) -> ListNode:
ans = None
for i in range(len(lists)):
ans = self.mergeTwo(ans,lists[i])
return ansc++:
/**
* Definition for singly-linked list.
* struct ListNode {
* int val;
* ListNode *next;
* ListNode() : val(0), next(nullptr) {}
* ListNode(int x) : val(x), next(nullptr) {}
* ListNode(int x, ListNode *next) : val(x), next(next) {}
* };
*/
class Solution {
public:
ListNode* mergtwo(ListNode* l1, ListNode* l2){
if(l1==nullptr){
return l2;
}
if(l2==nullptr){
return l1;
}
ListNode* new_head= new ListNode(0);
ListNode* node = new_head;
while(l1 && l2){
if(l1->val<l2->val){
node->next = l1;
l1= l1->next;
}
else{
node->next = l2;
l2= l2->next;
}
node = node->next;
}
if(l1){
node->next = l1;
}
if(l2){
node->next = l2;
}
return new_head->next;
}
ListNode* mergeKLists(vector<ListNode*>& lists) {
ListNode* res = nullptr;
for (int i=0;i<lists.size();i++){
res = mergtwo(res,lists[i]);
}
return res;
}
};思路2:分治归并１
# Definition for singly-linked list.
# class ListNode:
# def __init__(self, val=0, next=None):
# self.val = val
# self.next = next
class Solution:
def mergeTwo(self, l1, l2):
if l1 is None:
return l2
if l2 is None:
return l1
head = ListNode(0)
node = head
while l1 and l2:
if l1.val <l2.val:
node.next = l1
l1 = l1.next
else:
node.next = l2
l2 = l2.next
node = node.next
if l1:
node.next = l1
if l2:
node.next = l2
return head.next
def mergeSort(self, lists, left, right):
if left==right:
return lists[left]
middle = left + (right-left)//2
# print('== middle:', middle)
l1 = self.mergeSort(lists,left,middle)
# print('== l1:', l1)
l2 = self.mergeSort(lists,middle+1,right)
return self.mergeTwo(l1, l2)
def mergeKLists(self, lists: List[ListNode]) -> ListNode:
# print('==hahah')
if len(lists)==0:
return None
return self.mergeSort(lists,0,len(lists) - 1)c++实现:
/**
* Definition for singly-linked list.
* struct ListNode {
* int val;
* ListNode *next;
* ListNode() : val(0), next(nullptr) {}
* ListNode(int x) : val(x), next(nullptr) {}
* ListNode(int x, ListNode *next) : val(x), next(next) {}
* };
*/
class Solution {
public:
ListNode* mergetwo(ListNode* l1, ListNode* l2){
if(l1==nullptr){
return l2;
}
if(l2==nullptr){
return l1;
}
ListNode* new_head= new ListNode(0);
ListNode* node = new_head;
while(l1 && l2){
if(l1->val<l2->val){
node->next = l1;
l1= l1->next;
}
else{
node->next = l2;
l2= l2->next;
}
node = node->next;
}
if(l1){
node->next = l1;
}
if(l2){
node->next = l2;
}
return new_head->next;
}
ListNode* mergesort(vector<ListNode*>& lists,int left, int right){
if(left==right){
return lists[left];
}
int middle = left+(right -left)/2;
ListNode* l1 = mergesort(lists,left,middle);
ListNode* l2 = mergesort(lists,middle+1,right);
return mergetwo(l1,l2);
}
ListNode* mergeKLists(vector<ListNode*>& lists) {
// ListNode* res = nullptr;
// for (int i=0;i<lists.size();i++){
// res = mergtwo(res,lists[i]);
// }
// return res;
if (lists.size()==0){
return nullptr;
}
return mergesort(lists,0,lists.size()-1);
}
};思路3:分支归并２ 参考排序算法的归并排序 排序算法--（冒泡排序，插入排序，选择排序，归并排序，快速排序，桶排序，计数排序，基数排序）_智障变智能-优快云博客
class Solution:
def mergeTwo(self, l1, l2):
if l1 is None:
return l2
if l2 is None:
return l1
head = ListNode(0)
node = head
while l1 and l2:
if l1.val < l2.val:
node.next = l1
l1 = l1.next
else:
node.next = l2
l2 = l2.next
node = node.next
if l1:
node.next = l1
if l2:
node.next = l2
return head.next
def mergeSort(self, L):
if len(L) <= 1:
return L[0]
mid = len(L) // 2
l1 = self.mergeSort(L[:mid])
l2 = self.mergeSort(L[mid:])
return self.mergeTwo(l1, l2)
def mergeKLists(self, lists: List[ListNode]) -> ListNode:
if len(lists)==0:
return None
return self.mergeSort(lists)
思路：
1.要逆序找，这个时候的数最小;
2. 希望下一个数比当前数（递增的拐点）大,
3. 尽量大的幅度是最小的.
# 1.要逆序找，这个时候的数最小;
# 2. 希望下一个数比当前数（递增的拐点）大,
# 3. 尽量大的幅度是最小的
class Solution(object):
# 交换
def reverse(self, nums, left, right):
while left < right:
nums[left], nums[right] = nums[right], nums[left]
left += 1
right -= 1
return nums
def nextPermutation(self, nums):
"""
:type nums: List[int]
:rtype: None Do not return anything, modify nums in-place instead.
"""
# nums = [1, 2, 7, 4, 3, 1]
first_index = -1
second_index = -1
# 先找到逆序的峰值前的第一个点的索引first_index
for i in range(len(nums) - 2, -1, -1):
if nums[i] < nums[i + 1]:
first_index = i
break
print('==first_index:', first_index)
# 在找到稍微大于first_index的索引
for i in range(first_index, len(nums)):
if nums[i] > nums[first_index]:
second_index = i
print('==second_index:', second_index)
if first_index != -1: # 交换以后 对剩下的进行逆序
nums[first_index], nums[second_index] = nums[second_index], nums[first_index]
nums = self.reverse(nums, first_index + 1, len(nums) - 1)
else: # 说明全逆序
nums = self.reverse(nums, 0, len(nums) - 1)
return nums
# nums = [5, 4, 7, 5, 3, 2]
# nums = [1, 2, 7, 4, 3, 1]
# nums = [1, 2, 3, 8, 5, 7, 6]
nums = [1, 2, 3]
# nums = [3, 2, 1]
# nums=[-2,-1]
# nums=[0]
# nums=[2,2]
# nums=[4,10,4,3,8,9]
sol = Solution()
res = sol.nextPermutation(nums)
print('res:', res)
c++实现:
class Solution {
public:
void help(vector<int>& nums, int left, int right ){
while(left < right){
int temp = nums[left];
nums[left] = nums[right];
nums[right] = temp;
left++;
right--;
}
}
void nextPermutation(vector<int>& nums) {
int first_index = -1, second_index = -1;
int length = nums.size();
for (int i = length-2; i>=0; i--){
if(nums[i] < nums[i+1]){
first_index = i;
break;
}
}
if(first_index != -1){
for (int i = first_index + 1; i<length; i++){
if(nums[i] > nums[first_index]){
second_index = i;
}
}
}
if (first_index != -1){
int temp = nums[first_index];
nums[first_index] = nums[second_index];
nums[second_index] = temp;
help(nums, first_index + 1, length - 1);
}
else{
help(nums, 0, length - 1);
}
}
};14-2.下一个更大元素 III
思路:和上一题一样，只不过是将int转成string
class Solution:
def swap(self, list_str, left, right):
while left < right:
list_str[left], list_str[right] = list_str[right], list_str[left]
left += 1
right -= 1
return list_str
def nextGreaterElement(self, n: int) -> int:
list_n = list(str(n))
first_index = -1
for i in range(len(list_n) - 2, -1, -1):
if list_n[i] < list_n[i + 1]:
first_index = i
break
if first_index == -1:
return -1
second_index = -1
for i in range(first_index, len(list_n)):
if list_n[i] > list_n[first_index]:
second_index = i
list_n[first_index], list_n[second_index] = list_n[second_index], list_n[first_index]
list_n = self.swap(list_n, first_index + 1, len(list_n) - 1)
value = int(''.join(list_n))
if value < (1<<31):
return value
else:
return -1c++实现:
class Solution {
public:
void reverse(string& str_n, int left, int right){
while(left < right){
char temp = str_n[left];
str_n[left] = str_n[right];
str_n[right] = temp;
left++;
right--;
}
}
int nextGreaterElement(int n) {
string str_n = to_string(n);
int first_index = -1;
for(int i = str_n.size() - 2; i >= 0; i--){
if(str_n[i] < str_n[i+1]){
first_index = i;
break;
}
}
if(first_index == -1){
return -1;
}
int second_index = -1;
for(int i = first_index + 1; i < str_n.size(); i++){
if (str_n[i] > str_n[first_index]){
second_index = i;
}
}
char temp = str_n[first_index];
str_n[first_index] = str_n[second_index];
str_n[second_index] = temp;
reverse(str_n, first_index + 1, str_n.size() - 1);
long value = atol(str_n.c_str());
if(value > INT_MAX){
return -1;
}
else{
return value;
}
}
};15-1.给定一个只包括 '('，')'，'{'，'}'，'['，']' 的字符串，判断字符串是否有效。
思路：利用栈将括号左半部分先入栈，后半部分进行判断并匹配
class Solution:
def isValid(self, s):
stack= []
for i in range(len(s)):
if s[i] == '(' or s[i] == '[' or s[i] == '{':
stack.append(s[i])
elif len(stack) and s[i] == ']' and stack[-1] == '[':
stack.pop()
elif len(stack) and s[i] == ')' and stack[-1] == '(':
stack.pop()
elif len(stack) and s[i] == '}' and stack[-1] == '{':
stack.pop()
else:
return False
return len(stack)==0
sol = Solution()
s = '()'
# s = '()[]{}'
res = sol.isValid(s)
print('res:', res)
class Solution:
def isValid(self, s):
stack= []
dict_={')':'(',
']':'[',
'}':'{'
}
for i in range(len(s)):
if s[i] in dict_.keys():
if len(stack)==0 or stack[-1] != dict_[s[i]]:
return False
else:
stack.pop()
else:
stack.append(s[i])
return len(stack)==0
sol = Solution()
s = '()'
# s = '()[]{}'
res = sol.isValid(s)
print('res:', res)15-2：最长有效括号
思路:先利用栈存储相邻括号的索引，在用双指针做聚类class Solution:
def longestValidParentheses(self, s: str) -> int:
stack = []
res = []
for i in range(len(s)):
if s[i] == '(':
stack.append(i)
if stack and s[i] == ')':
res.append(stack.pop())
res.append(i)
print(res)
res = sorted(res)
left, right = 0, 0
# fin_res = []
ans = 0
while right < len(res):
right = left + 1
while right < len(res) and res[right] - res[right - 1] == 1:
right += 1
# fin_res.append([left, right-1])
ans = max(right - left, ans)
left = right
print(ans)
return ans
# s = "(()"
# s = "()(()"
# s = ")()())"
s = "()(())"
sol = Solution()
sol.longestValidParentheses(s)
思路：二分查找 利用二分法不断逼近目标数的索引
class Solution:
def searchInsert(self, nums: List[int], target: int) -> int:
#二分查找
left = 0
right = len(nums)-1
while left<=right:
middle = left + (right - left )//2
# print(middle)
if nums[middle]==target:
return middle
elif nums[middle]>target:
right = middle - 1
else:
left=middle+1
return left
思路1:双指针，时间复杂度O(n)
#O(n)
class Solution:
def searchRange(self, nums, target):
left,right = 0,len(nums)-1
while left < right:
if nums[left]==target and nums[right]==target:
return [left,right]
elif nums[left]<target:
left+=1
else:
right -= 1
return [-1,-1]
nums = [5,7,7,8,8,10]
target = 8
sol = Solution()
res = sol.searchRange(nums,target)
print(res)思路2:二分查找法，时间复杂度O(logn)
重点是找到左边界和右边界
class Solution:
def serachLeft(self, nums, target):
left, right = 0, len(nums) - 1
while left <= right:
middle = left + (right - left) // 2
if nums[middle] < target:
left = middle+1
else:
right = middle-1
return left
def serachRight(self, nums, target):
left, right = 0, len(nums) - 1
while left <= right:
middle = left + (right - left) // 2
if nums[middle] <= target:#加个等于符号 这样left就可以找到最后一个
left = middle + 1
else:
right = middle - 1
return left-1
def searchRange(self, nums, target):
left = self.serachLeft(nums, target)
# print('==left:', left)
right = self.serachRight(nums, target)
# print('==right:', right)
if left<=right:
return [left,right]
else:
return [-1, -1]
# nums = [5, 7, 7, 8, 8, 8]
nums = [5, 7, 7, 9, 9, 9]
target = 8
sol = Solution()
sol.searchRange(nums, target)
思路：判断中值和右值的关系来决定是否是有序的，通过缩短为有序数组 在进行二分法查找
class Solution:
def search(self, nums: List[int], target: int) -> int:
left,right=0,len(nums)-1
while left<=right:
middle = left + (right-left)//2
if nums[middle]==target:
return middle
if nums[middle]<nums[right]:#从ｍｉｄｄｌｅ到ｒｉｇｈｔ是有序的
if nums[middle]<target<=nums[right]:
left =middle+1
else:
right = middle-1
else:#从left到ｍｉｄｄｌｅ是有序的
if nums[left]<=target<nums[middle]:
right=middle-1
else:
left = middle+1
return -1
思路：判断左右两个子序 注意需要去重 避免对顺序造成的干扰
class Solution:
def search(self, nums: List[int], target: int) -> bool:
left,right = 0,len(nums)-1
while left<=right:
middle = left+(right-left)//2
if nums[middle]==target:
return True
if (nums[middle] == nums[left] == nums[right]):#去除边界重复值
left += 1
right -= 1
elif nums[middle]>=nums[left]:#left到middle有序
if nums[left]<=target<nums[middle]:
right = middle - 1
else:
left=middle+1
else:#middle 到right有序
# print('==hahhahha====')
# print('==left:', left)
# print('==middle:', middle)
if nums[middle]<target<=nums[right]:
left = middle + 1
else:
right = middle - 1
return False
思路：
class Solution:
def findMin(self, nums: List[int]) -> int:
# return min(numbers)
left, right = 0, len(nums) - 1
while left < right:
middle = left + (right - left) // 2
if nums[middle] < nums[right]:#说明middle是最小值右侧元素
right = middle
elif nums[middle] > nums[right]:#说明middle是最小值左侧元素
left = middle + 1
else:
right -= 1 #相当就没法判断 采取保守right-1即可
# print('==left:', left)
# print('===numbers[left]', numbers[left])
return nums[left]
思路：组合排列问题 回溯法
由于可以选2,2,3 不可以再选,3,2,2所以用view限定重复是不行的，还要加上start索引
class Solution:
def backtrace(self, candidates, target, start, track):
# #终止条件
if target == 0:
self.res.append(track)
return
for i in range(start, len(candidates)):
if candidates[i] > target:
continue
# if (i > 0 and candidates[i] == candidates[i - 1]):
# continue # 去掉重复的
store = track.copy()
track.append(candidates[i])#其中值满足选择条件
# print('==track.copy():', track.copy())
self.backtrace(candidates, target - candidates[i], i, track) # 回溯
track = store # 撤销选择
def combinationSum(self, candidates, target):
self.res = []
candidates = sorted(candidates)
self.backtrace(candidates, target, 0, track=[])
return self.res
# candidates = [2,3,6,7]
# target = 7
candidates = [2,3,5]
target = 8
sol = Solution()
res = sol.combinationSum(candidates, target)
print('res:', res)
c++实现:
class Solution {
public:
vector <vector<int>> res;
void backtrace(vector<int>& candidates, int target, int start, vector<int>& track){
if(target == 0){
res.push_back(track);
return;
}
for(int i = start; i < candidates.size(); i++){
if(candidates[i] > target){
continue;
}
track.push_back(candidates[i]);
backtrace(candidates, target - candidates[i], i, track);
track.pop_back();
}
}
vector<vector<int>> combinationSum(vector<int>& candidates, int target) {
vector<int> track;
backtrace(candidates, target, 0, track);
return res;
}
};
思路：注意与17-1的差别，不能重复选数字，故通过排序方便进行剪枝.
class Solution:
def backtrace(self, candidates, target, start, track):
# #终止条件
if target == 0:
self.res.append(track)
return
for i in range(start, len(candidates)):
if candidates[i] > target:
continue
if (i > start and candidates[i] == candidates[i - 1]):
continue # 去掉重复的
store = track.copy()
track.append(candidates[i])
# print('==track.copy():', track.copy())
self.backtrace(candidates, target - candidates[i], i + 1, track) # 回溯
track = store # 撤销选择
def combinationSum2(self, candidates: List[int], target: int) -> List[List[int]]:
self.res = []
candidates = sorted(candidates)
self.backtrace(candidates, target, 0, track=[])
return self.res
candidates = [10, 1, 2, 7, 6, 1, 5]
# candidates = [1, 7, 1]
target = 8
sol = Solution()
res = sol.combinationSum2(candidates, target)
print('res:', res)
c++实现:
class Solution {
public:
vector<vector<int>> res;
void backtrace(vector<int>& candidates, int target, int start, vector<int>& track){
if(target == 0){
res.push_back(track);
}
for(int i = start; i < candidates.size(); i++){
if(target < candidates[i]){
continue;
}
if(i > start && candidates[i] == candidates[i-1]){
continue;
}
track.push_back(candidates[i]);
backtrace(candidates, target - candidates[i], i + 1, track);
track.pop_back();
}
}
vector<vector<int>> combinationSum2(vector<int>& candidates, int target) {
sort(candidates.begin(), candidates.end());
vector<int> track;
backtrace(candidates, target, 0, track);
return res;
}
};
求Max{(j-i) * Min( h(i), h(j) )},
height=[2,8,1,5,9,3,4]
暴力法： 超出时间限制
#解法1
class Solution:
def maxarea(self,height):
max_area=0
for i in range(len(height)-1):
for j in range(i+1,len(height)):
if (j-i)*min(height[i],height[j])>max_area:
max_area=(j-i)*min(height[i],height[j])
index_i=i
index_j=j
return index_i,index_j,max_area
s=Solution()
height=[2,8,1,5,9,3,4]
i,j,max_area=s.maxarea(height)
print(i,j,max_area)分析:暴力法时间复杂度为O(n2),想想看，
-
如果 h(7) >= h(1)，我们还有必要再遍历h(6)，h(5)，...，h(2)吗，其实不用，这便是暴力算法的冗余之处，多做了很多次无用的遍历，i = 1这趟遍历中，最大面积一定为 (7-1) * h(1) ；
-
如果 h(7) < h(1)，我们再尝试h(6)，如果h(6)>=h(1)，那么在i = 1这趟遍历中的面积最大为(6-1) * h(1)，没必要再试h(5)了，依次这样下去。
动态规划:
-
面积最大值初始值设定 maxarea；
-
i, j 分别指向索引两头，动态交替地调整 i, j ，进而尝试取得较大的相对高度，这个调整的策略是关键，同时，更新目标函数即面积的最大值，如果大于maxarea，则更新；
-
直到 i > j 为止；
-
返回最大值法
时间复杂度为 O(n)，空间复杂度为 O(1) 。
#解法2
class Solution:
def maxarea(self,height):
left=0
right=len(height)-1
max_area=0
while left<right:
max_area = max(max_area,(right - left) * min(height[left], height[right]))
if height[left]<height[right]:
left+=1
else:
right-=1
# index_i = left
# index_j=right
return max_area
s=Solution()
height=[2,8,1,5,9,3,4]
max_area=s.maxarea(height)
print(max_area)18-2:接雨水
思路1.暴力法 对于i处能存的水，向右向左分别找到最大的值，在取这两值中的最小值减去此刻的值就是能存的水,超时O(n^2)
class Solution:
def trap(self, height):
res = 0
n = len(height)
for i in range(1, n):
print('==i:', i)
left_max, right_max = 0, 0
for j in range(i, -1, -1):#往左搜索
left_max = max(left_max, height[j])
for j in range(i, n):#往右搜索
right_max = max(right_max, height[j])
print('==left_max:', left_max)
print('==right_max:', right_max)
res +=min(right_max, left_max) - height[i]
print('res:', res)
return res
height = [0,1,0,2,1,0,1,3,2,1,2,1]
sol = Solution()
sol.trap(height)思路２.优化，双指针
#某个位置i处，它能存的水，取决于它左右两边(left_max,right_max)的最大值中较小的一个。
#对于位置left而言，它左边最大值一定是left_max，右边最大值“大于等于”right_max，
# 这时候，如果left_max<right_max成立，那么它就知道自己能存多少水了。
# 无论右边将来会不会出现更大的right_max，都不影响这个结果。
# 所以当left_max<right_max时，我们就希望去处理left下标，反之，我们希望去处理right下标。O(n)class Solution:
def trap(self, height):
left,right =0,len(height)-1
left_max,right_max =0,0
res = 0
while left<=right:
if left_max <right_max:
res+=max(0, left_max - height[left])
left_max = max(left_max, height[left])
left+=1
else:
res += max(0, right_max - height[right])
right_max = max(right_max, height[right])
right -= 1
print('==res:', res)
return res
height = [0,1,0,2,1,0,1,3,2,1,2,1]
sol = Solution()
sol.trap(height)c++实现:
class Solution {
public:
int trap(vector<int>& height) {
int left = 0, right = height.size() - 1;
int left_max = 0, right_max = 0;
int res = 0;
while(left <= right){
if(left_max < right_max){
res += max(0, left_max - height[left]);
left_max = max(height[left], left_max);
left++;
}
else{
res += max(0, right_max - height[right]);
right_max = max(height[right], right_max);
right--;
}
}
return res;
}
};思路3:动态规划
开出两个数组，一个用于统计坐边最大值，一个用于统计右边最大值，这样最终该点的雨水就是当前点的短板减去当前值。
class Solution:
def trap(self, height: List[int]) -> int:
length = len(height)
if length == 0:
return 0
left_max = [0 for i in range(length)]
left_max[0] = height[0]
right_max = [0 for i in range(length)]
right_max[-1] = height[-1]
for i in range(1, length):
left_max[i] = max(left_max[i-1], height[i])
for i in range(length-2, -1, -1):
right_max[i] = max(right_max[i + 1], height[i])
res = 0
for i in range(length):
res += min(left_max[i], right_max[i]) - height[i]
return resc++实现 :
class Solution {
public:
int trap(vector<int>& height) {
int res = 0;
int length = height.size();
if (length == 0){
return res;
}
vector<int> left_max(length, 0);
vector<int> right_max(length, 0);
left_max[0] = height[0];
right_max[length-1] = height[length-1];
for (int i=1; i<length; i++){
left_max[i] = max(left_max[i-1], height[i]);
}
for (int i=length-2; i>=0; i--){
right_max[i] = max(right_max[i+1], height[i]);
}
for (int i=0; i<length; i++){
res += min(right_max[i], left_max[i]) - height[i];
}
return res;
}
};
class Solution:
def backtrace(self, nums, view, track):
#终止条件
if len(track)==len(nums):
self.res.append(track)
return
for i in range(len(nums)):#满足选择条件
if view[i]:#出现元素跳过
continue
# if i>0 and nums[i] == nums[i-1] and view[i-1]==0:#重复元素跳过
# continue
store = track.copy()
track.append(nums[i])
print('track:', track)
view[i] = 1
self.backtrace(nums, view, track)
track = store# 撤销选择
view[i] = 0# 撤销选择
def permuteUnique(self, nums):
nums = sorted(nums)#排序方便剪枝
self.res = []
self.backtrace(nums, view=[0]*len(nums), track=[])
return self.res
nums = [1,2,3]
# nums = [1, 2, 3]
sol = Solution()
res=sol.permuteUnique(nums)
print('res:', res)
c++实现:
class Solution {
public:
vector<vector<int>> res;
void backtrace(vector<int>& view, vector<int>& track, vector<int>& nums){
if(track.size() == nums.size()){
res.push_back(track);
return ;
}
for(int i=0; i<nums.size(); i++){
if(view[i]){
continue;
}
track.push_back(nums[i]);
view[i] = 1;
backtrace(view, track, nums);
track.pop_back();
view[i] = 0;
}
}
vector<vector<int>> permute(vector<int>& nums) {
int size = nums.size();
vector<int> view(size, 0);
vector<int> track;
backtrace(view, track, nums);
return res;
}
};
思路：与上题相比要注意的是剪枝
class Solution:
def backtrace(self, nums, view, track):
#终止条件
if len(track)==len(nums):
self.res.append(track)
return
for i in range(len(nums)):#满足选择条件
if view[i]:#出现元素跳过
continue
if i>0 and nums[i] == nums[i-1] and view[i-1]==0:#重复元素跳过
continue
store = track.copy()
track.append(nums[i])
print('track:', track)
view[i] = 1
self.backtrace(nums, view, track)
track = store# 撤销选择
view[i] = 0# 撤销选择
def permuteUnique(self, nums):
nums = sorted(nums)#排序方便剪枝
self.res = []
self.backtrace(nums, view=[0]*len(nums), track=[])
return self.res
nums = [1, 1, 2]
# nums = [1, 2, 3]
sol = Solution()
res=sol.permuteUnique(nums)
print('res:', res)
c++实现:
class Solution {
public:
vector<vector<int>> res;
void backtrace(vector<int>& nums, vector<int>& view, vector<int>& track){
if(track.size() == nums.size()){
res.push_back(track);
return;
}
for(int i = 0; i < nums.size(); i++){
if(view[i]){
continue;
}
if(i > 0 && nums[i] == nums[i-1] && view[i-1] == 0){
continue;
}
view[i] = 1;
track.push_back(nums[i]);
backtrace(nums, view, track);
view[i] = 0;
track.pop_back();
}
}
vector<vector<int>> permuteUnique(vector<int>& nums) {
sort(nums.begin(), nums.end());
vector<int> view(nums.size(), 0);
vector<int> track;
backtrace(nums, view, track);
return res;
}
};19-3.有重复字符串的排列组合
解法二示意:
class Solution:
def help(self, S, view, track):
if len(S) == len(track):
self.res.append(track)
return
for i in range(len(S)):
if view[i]:#出现元素跳过
continue
if i>0 and S[i] == S[i-1] and view[i-1]==0:#重复字符剪枝
continue
store = track
track += S[i]
view[i] = 1
self.help(S, view, track)
track = store
view[i] = 0
def permutation(self, S: str) -> List[str]:
S = sorted(S)
self.res = []
self.help(S, [0]*len(S), '')
return self.res
19-4.二进制手表
可看成全排列找灯问题
class Solution:
def readBinaryWatch(self, num):
hash_code = {0:1, 1:2, 2:4, 3:8, 4:1, 5:2, 6:4, 7:8, 8:16, 9:32}
time_ = {'first':0, 'second':0}
res = []
def backtrace(num, start, time_):
if num == 0:#终止条件剩下0盏灯 此时保存结果
if (time_['first'] > 11 or time_['second'] > 59): #判断合法性
return
hour = str(time_['first'])
minute = str(time_['second'])
# print('==hour,minute:', hour, minute)
# if hour=='0' and minute=='8':
# assert 1==0
if len(minute) == 1:
minute = '0'+minute
res.append(hour+':'+minute)
return
for i in range(start, 10):#找出符合的
if (time_['first'] > 11 or time_['second'] > 59): # 判断合法性
continue
#保存状态 用于恢复
store = time_.copy()
if i<4:
time_['first'] += hash_code[i]#对小时数进行操作
else:
time_['second'] += hash_code[i]#对分钟数进行操作
#进入下一层，注意下一层的start是i+1，即从当前灯的下一盏开始
backtrace(num-1, i+1, time_)
time_ = store#恢复状态
backtrace(num, 0, time_)
return res
n = 1
sol = Solution()
res = sol.readBinaryWatch(n)
print('res:', res)
19-5.找子集(不含重复元素)
思路:回溯，注意的是选择过的数要跳过
#子集问题
class Solution:
def backtrace(self, nums, start, track):
print('==track:', track)
self.res.append(track.copy())#满足选择条件
print('==self.res:', self.res)
for i in range(start, len(nums)):
store = track.copy()
track.append(nums[i])#做选择
self.backtrace(nums, i+1, track)#回溯
track = store#撤销
def subsets(self, nums):
nums = sorted(nums)#排序 方便进行剪枝
self.res = []
self.backtrace(nums, start=0, track = [])
return self.res
nums = [1, 2, 3]
sol = Solution()
res = sol.subsets(nums)
print('res:', res)
可看出先找到最左边[]->[1]->[1,2]->[1,2,3]然后撤销选择回到上一层变成[]->[1]->[1,2]->[1,2,3]->[1,3],然后在上一层........
19-6.找子集(含重复元素)
思路：回溯注意与上一题的区别在于含有重复元素，需要过滤掉
class Solution:
def backtrace(self, nums, view, start, track):
self.res.append(track.copy())#满足选择条件
for i in range(start, len(nums)):
if view[i]:#出现元素跳过
continue
if i>0 and nums[i] == nums[i-1] and view[i-1]==0:#重复元素跳过
continue
store = track.copy()
track.append(nums[i])
view[i] = 1
self.backtrace(nums, view, i + 1, track)#回溯
track = store#撤销
view[i] = 0#撤销
def subsetsWithDup(self, nums):
nums = sorted(nums)#排序 方便进行剪枝
self.res = []
self.backtrace(nums, view=len(nums)*[0], start=0, track=[])
return self.res
nums = [1, 2, 2]
# nums = [1, 2, 3]
sol = Solution()
res = sol.subsetsWithDup(nums)
print('res:', res)c++实现:
class Solution {
public:
vector<vector<int>> res;
void backtrace(vector<int>& nums, vector<int>& view, int start, vector<int>& track){
res.push_back(track);
for(int i = start; i < nums.size(); i++){
if(view[i]){
continue;
}
if(i > 0 && nums[i] == nums[i - 1] && view[i-1] == 0){
continue;
}
track.push_back(nums[i]);
view[i] = 1;
backtrace(nums, view, i + 1, track);
view[i] = 0;
track.pop_back();
}
}
vector<vector<int>> subsetsWithDup(vector<int>& nums) {
sort(nums.begin(), nums.end());
int n = nums.size();
vector<int> view(n, 0);
vector<int> track;
backtrace(nums, view, 0, track);
return res;
}
};19-7.组合问题
例如输入n=4,k=2,输出[[1, 2], [1, 3], [1, 4], [2, 3], [2, 4], [3, 4]]
#组合问题
class Solution:
def readBinaryWatch(self, n, k):
res = []
track= []
if k<=0 or n<=0:
return res
def backtrace(n, k, start, track):
if len(track) == k:#终止条件 长度等于k
print('==track.copy():', track.copy())
res.append(track.copy())
print('==res:', res)
return
for i in range(start, n+1):#找出符合的 选择条件
#保存状态 用于恢复
store = track.copy()
track.append(i)
#进入下一层，注意下一层的start是i+1
backtrace(n, k, i+1, track)
track = store#恢复状态
backtrace(n, k, 1, track)
return res
n = 4
k = 2
sol = Solution()
res = sol.readBinaryWatch(n, k)
print('res:', res)
可看出k 限制了树的高度，n 限制了树的宽度，：先找到最左边[1,2]->[1,3]->[1,4]然后撤销选择回到上一层变成[1,2]->[1,3]->[1,4]->[2,3]->[2,4],然后在上一层........
思路1:
旋转后的倒数第几列是旋转前的正数第几行
m=[['a','b','c','d'],
['e','f','g','h'],
['i','j','k','l'],
['m','n','o','p']]
n=len(m)
res=[[0]*n for _ in range(n)]
print(res)
for i in range(n):
row=m[i]#第i行
print(row)
ncol=n-i-1#第n-i-1列
for j in range(len(row)):
res[j][ncol]=row[j]
print(res)
思路2：顺时针旋转90度==转置矩阵＋每一行逆序
class Solution:
def rotate(self, matrix: List[List[int]]) -> None:
"""
Do not return anything, modify matrix in-place instead.
"""
h = len(matrix)
w= len(matrix[0])
for i in range(h):
for j in range(i+1,w):
matrix[i][j],matrix[j][i] = matrix[j][i], matrix[i][j]
for i in range(h):
matrix[i]=matrix[i][::-1]
# print(matrix)
return matrix
c++实现:
class Solution {
public:
void rotate(vector<vector<int>>& matrix) {
int h = matrix.size();
int w = matrix[0].size();
for(int i = 0; i < h; i++){
for(int j = i + 1; j < w; j++){
int temp = matrix[i][j];
matrix[i][j] = matrix[j][i];
matrix[j][i] = temp;
}
}
for(int i = 0; i < h; i++){
int j = 0;
while(j < w/2){
int temp = matrix[i][j];
matrix[i][j] = matrix[i][w-j-1];
matrix[i][w-j-1] = temp;
j++;
}
}
return;
}
};21.字母异位词分组
思路１：对排序的字符进行hash表示，自然key值相同的就是异构词，用python字典
#hash
class Solution:
def groupAnagrams(self, strs):
dict_ = {}
for st in strs:
key = ''.join(sorted(st))
if key not in dict_:
dict_[key] = [st]
else:
dict_[key].append(st)
# print('==dict_:', dict_)
# print(list(dict_.values()))
return list(dict_.values())
strs = ["eat", "tea", "tan", "ate", "nat", "bat"]
sol = Solution()
sol.groupAnagrams(strs)思路2:hash,用collections.defaultdict
import collections
class Solution:
def groupAnagrams(self, strs):
mp = collections.defaultdict(list)
print('init mp:', mp)
for st in strs:
key = "".join(sorted(st))
mp[key]. append(st)
print('===mp',mp)
return mp
strs = ["eat", "tea", "tan", "ate", "nat", "bat"]
sol = Solution()
sol.groupAnagrams(strs)
1.修改nums
class Solution(object):
def maxSubArray(self, nums):
"""
:type nums: List[int]
:rtype: int
"""
for i in range(1,len(nums)):
nums[i]+=max(nums[i-1],0)
return max(nums)
a=[ 0, -2, 3, 5, -1, 2]
sol=Solution()
res=sol.maxSubArray(a)
print('res:',res)
2.借助一个变量
class Solution:
def maxSubArray(self, nums: List[int]) -> int:
value = nums[0]
res = nums[0]
for i in range(1, len(nums)):
value = max(nums[i], nums[i]+value)
res = max(res, value)
return resc++实现:
class Solution {
public:
int maxSubArray(vector<int>& nums) {
int length = nums.size();
if(length < 1){
return 0;
}
int value = nums[0];
int res = nums[0];
for(int i = 1; i < length; i++){
value = max(nums[i], nums[i] + value);
res = max(value, res);
}
return res;
}
};
方法1:贪心算法
思路:需要更新最长距离
class Solution:
def canJump(self, nums: List[int]) -> bool:
贪心算法
most_dis = 0
for i in range(len(nums)):
if i <= most_dis:
most_dis = max(most_dis, nums[i] + i)
if most_dis >= len(nums) - 1:
return True
return Falsec++实现:
class Solution {
public:
bool canJump(vector<int>& nums) {
int most_length = 0;
for(int i = 0; i < nums.size(); i++){
if(i <= most_length){
most_length = max(nums[i] + i, most_length);
}
if(most_length >= nums.size() - 1){
return true;
}
}
return false;方法2:动态规划 需要注意的是 需要实时更新距离
class Solution(object):
def canJump(self, nums):
"""
:type nums: List[int]
:rtype: bool
"""
opt = [False]*len(nums)
opt[0] = True
for i in range(1,len(nums)):
opt[i] = opt[i-1] and nums[i-1] > 0
nums[i] = max(nums[i], nums[i-1]-1)#更新nums 最大距离
return opt[-1]c++实现:
class Solution {
public:
bool canJump(vector<int>& nums) {
int n = nums.size();
vector<bool> opt(n, false);
opt[0] = true;
for(int i = 1; i < n; i++){
opt[i] = opt[i - 1] && nums[i-1] >= 1;
nums[i] = max(nums[i - 1] - 1, nums[i]);
}
return opt[n-1];
}
};
思路１：不断合并更新
class Solution:
def merge(self, intervals):
intervals = sorted(intervals, key=lambda x:(x[0], x[-1]))
index = 0
while index < len(intervals) - 1:
if intervals[index][-1] >= intervals[index + 1][0]:
intervals[index][-1] = max(intervals[index + 1][-1], intervals[index][-1])
intervals.pop(index + 1)
else:
index += 1
print('=intervals:', intervals)
return intervals
intervals = [[1, 3], [2, 6], [8, 10], [15, 18]]
# intervals = [[1,4],[0,4]]
sol = Solution()
sol.merge(intervals)思路２：开出新列表用于存储满足条件的数
class Solution:
def merge(self, intervals):
intervals= sorted(intervals,key= lambda x:(x[0],x[-1]))
print('==intervals:', intervals)
res = [intervals[0]]
for i in range(1, len(intervals)):
if intervals[i][0]<=res[-1][-1]:
res[-1][-1] = max(intervals[i][-1],res[-1][-1])
else:
res.append(intervals[i])
print('==res:', res)
return res
# intervals = [[1,3],[2,6],[8,10],[15,18]]
intervals = [[1,4],[2,3]]
sol = Solution()
sol.merge(intervals)
c++实现:
class Solution {
public:
vector<vector<int>> merge(vector<vector<int>>& intervals) {
if(intervals.size() == 0){
return {};
}
sort(intervals.begin(), intervals.end());
vector<vector<int>> merges={intervals[0]};
for(int i=1; i<intervals.size(); i++){
if(merges.back()[1] >= intervals[i][0]){
merges.back()[1] = max(intervals[i][1], merges.back()[1]);
}
else{
merges.push_back(intervals[i]);
}
}
return merges;
}
};25.不同路径
思路:动态规划 dp[i][j] = dp[i-1][j]+dp[i][j-1]
import numpy as np
#思路:dp[i][j] = dp[i-1][j]+dp[i][j-1]
class Solution:
def uniquePaths(self, m, n):
dp = [[0 for i in range(n)] for j in range(m)]
for i in range(m):
dp[i][0] = 1
for i in range(n):
dp[0][i] = 1
print('==np.array(dp):', np.array(dp))
for i in range(1,m):
for j in range(1,n):
dp[i][j] = dp[i-1][j]+dp[i][j-1]
print(np.array(dp))
return dp[-1][-1]
m = 3
n = 2
sol = Solution()
sol.uniquePaths(m, n)
c++实现:
class Solution {
public:
int uniquePaths(int m, int n) {
vector<vector<int>> dp(m, vector<int>(n, 0));
for(int i = 0; i < n; i++){
dp[0][i] = 1;
}
for(int i = 0; i < m; i++){
dp[i][0] = 1;
}
for(int i = 1; i < m; i++){
for(int j = 1; j < n; j++){
dp[i][j] = dp[i-1][j] + dp[i][j-1];
}
}
return dp[m - 1][n - 1];
}
};
26.最小路径和
思路:动态规划 dp[i][j] = min(dp[i-1][j],dp[i][j-1])+v[i][j]
import numpy as np
#dp[i][j] = min(dp[i-1][j],dp[i][j-1])+v[i][j]
class Solution:
def minPathSum(self, grid):
h = len(grid)
w = len(grid[0])
dp = [[0 for i in range(w)] for j in range(h)]
dp[0][0] = grid[0][0]
for i in range(1, h):
dp[i][0] = dp[i-1][0]+grid[i][0]
for i in range(1, w):
dp[0][i] = dp[0][i-1]+grid[0][i]
print('==np.array(dp):\n', np.array(dp))
for i in range(1, h):
for j in range(1, w):
dp[i][j] = min(dp[i-1][j],dp[i][j-1])+grid[i][j]
print('==np.array(dp):\n', np.array(dp))
return dp[-1][-1]
grid = [[1,3,1],[1,5,1],[4,2,1]]
sol = Solution()
sol.minPathSum(grid)
27.爬楼梯
思路1：dp
class Solution:
def climbStairs(self, n: int) -> int:
if n<3:
return n
dp = [0]*(n+1)
dp[1] = 1
dp[2] = 2
for i in range(3, n+1):
dp[i] = dp[i-1]+dp[i-2]
return dp[-1]思路2:变量
class Solution:
def climbStairs(self, n: int) -> int:
if n<3:
return n
a = 1
b = 2
for i in range(3, n+1):
a, b = b, a + b
return bc++实现:
class Solution {
public:
int climbStairs(int n) {
if(n < 3){
return n;
}
int a = 1, b = 2;
for(int i = 3; i < n+1; i++){
int temp = a;
a = b;
b += temp;
}
return b;
}
};28.编辑距离
编辑距离，又称Levenshtein距离（莱文斯坦距离也叫做Edit Distance），是指两个字串之间，由一个转成另一个所需的最少编辑操作次数，如果它们的距离越大，说明它们越是不同。许可的编辑操作包括将一个字符替换成另一个字符，插入一个字符，删除一个字符。
mat[i+1,j]+1表示增加操作
d[i,j+1]+1 表示删除操作
d[i,j]+temp表示替换操作,其中temp取0或1
import numpy as np
# 相等的情况dp[i][j] = min(dp[i-1][j-1], dp[i-1][j]+1, dp[i][j-1]+1)
# 不相等的情况dp[i][j] = min(dp[i-1][j-1]+1, dp[i-1][j]+1, dp[i][j-1]+1)
class Solution:
def minDistance(self, word1, word2):
dp = [[0 for i in range(len(word1) + 1)] for i in range(len(word2) + 1)]
for i in range(len(word1) + 1):
dp[0][i] = i
print('==np.array(dp):', np.array(dp))
for i in range(len(word2) + 1):
dp[i][0] = i
print('==np.array(dp):', np.array(dp))
for i in range(len(word2)):
for j in range(len(word1)):
if word2[i] == word1[j]:
dp[i+1][j+1] = dp[i][j]
else:
dp[i+1][j+1] = min(dp[i][j]+1, dp[i][j+1]+1, dp[i+1][j]+1)
print('==np.array(dp):', np.array(dp))
return dp[-1][-1]
word1 = "horse"
word2 = "ros"
sol = Solution()
sol.minDistance(word1, word2)
c++实现:
class Solution {
public:
int minDistance(string word1, string word2) {
int h = word1.size();
int w = word2.size();
vector<vector<int>> opt(h + 1, vector<int>(w + 1, 0));
for(int i = 0; i < h; i++){
opt[i + 1][0] = i + 1;
}
for(int j = 0; j < w; j++){
opt[0][j + 1] = j + 1;
}
for(int i = 0; i < h; i++){
for (int j = 0; j < w; j++){
if(word1[i] == word2[j]){
opt[i + 1][j + 1] = opt[i][j];
}
else{
opt[i + 1][j + 1] = min(opt[i][j] + 1, min(opt[i + 1][j] + 1, opt[i][j + 1] + 1));
}
}
}
return opt[h][w];
}
};
思路１:单指针法:先将0进行交换放在第一位,再将1进行交换放在0后面
# 单指针法:先将0进行交换放在第一位,再将1进行交换放在0后面
class Solution:
def sortColors(self, nums):
"""
Do not return anything, modify nums in-place instead.
"""
# 先将0进行交换放在第一位
start = 0
for i in range(len(nums)):
if nums[i] == 0:
nums[i], nums[start] = nums[start], nums[i]
start += 1
# 再将1进行交换放在0后面
for i in range(len(nums)):
if nums[i] == 1:
nums[i], nums[start] = nums[start], nums[i]
start += 1
print('==nums:', nums)
return nums
nums = [2, 0, 2, 1, 1, 0]
sol = Solution()
sol.sortColors(nums)
思路2:计数排序:对每种颜色进行计数,然后根据个数去修改nums数组
class Solution:
def sortColors(self, nums):
print('==nums:', nums)
count = [0] * 3
for i in range(len(nums)):
if nums[i] == 0:
count[0] += 1
elif nums[i] == 1:
count[1] += 1
else:
count[-1] += 1
print('==count:', count)
p = 0
for i in range(len(count)):
num = count[i]
while num>0:
nums[p] = i
num-=1
p += 1
print('==nums:', nums)
return nums
nums = [2, 0, 2, 1, 1, 0]
sol = Solution()
sol.sortColors(nums)
30-1.最小覆盖子串
思路:滑动窗口 左指针先不动，右指针遍历找到所有ｔ中出现的字符，左指针在移动缩小范围即可
class Solution:
def minWindow(self, s, t):
dict_ = {}
for i in t:
dict_[i] = dict_.get(i, 0)+1
print('dict_:', dict_)
n = len(s)
left, right = 0,0
remain=0
res = ''
minlen = float('inf')
while right<n:#向右边拓展
if s[right] in dict_:
if dict_[s[right]]>0:#大于0这个时候加才有效否则是重复字符
remain+=1
dict_[s[right]]-=1
while remain==len(t):#left 要拓展了 也就是左边要压缩
if (right - left)<minlen:
minlen = right-left
res = s[left:right+1]
print('==res:', res)
left+=1
if s[left-1] in dict_:#注意这里left已经加1了 要用前一个字符也就是s[left-1]
dict_[s[left - 1]] += 1
if dict_[s[left-1]]>0:#大于0这个时候减去才有效否则是重复字符
remain -= 1
right += 1#放后面进行向右拓展
print('==res:', res)
return res
s = "ADOBECODEBANC"
t = "ABC"
# s = "bba"
# t = "ab"
sol = Solution()
sol.minWindow(s, t)
30-2.字符串的排列
思路:滑动窗口，先向右扩张，在左边收缩 python代码
class Solution:
def checkInclusion(self, s1, s2):
dict_={}
for i in s1:
dict_[i] = dict_.get(i,0)+1
print('==dict_:',dict_)
left,right =0,0
length = 0
minlen = float('inf')
res = ''
while right<len(s2):# 向右拓展
if s2[right] in dict_:
if dict_[s2[right]]>0:#注意要进行判断避免重复字符
length+=1
dict_[s2[right]]-=1
while length==len(s1):#包含了子串啦 这个时候左边要压缩
if right-left+1==len(s1):#找最短的
return True
left+=1
if s2[left-1] in dict_:#注意left+1啦 所以要用left-1的字符判断是否出现在dict_中
dict_[s2[left - 1]] += 1
if dict_[s2[left-1]]>0:#避免重复字符造成的减法
length-=1
right+=1
return False
s1 = "ab"
s2 = "eidbaooo"
sol = Solution()
res= sol.checkInclusion(s1, s2)
print(res)
c++代码:
#include <string>
#include <iostream>
#include <vector>
#include <list>
#include <map>
using namespace std;
class Solution {
public:
bool checkInclusion(string s1, string s2) {
map<char,int> dict_;
for (int k=0;k<s1.size();k++)
{
dict_[s1[k]]++;
}
// map <char,int>::iterator itor = dict_.begin();
// //debug
// for(;itor!=dict_.end();itor++)
// {
// cout<<itor->first<<" "<<itor->second<<endl;
// }
int right=0;
int left=0;
int remain_legth =0;
while (right<s2.size())
{
if(dict_[s2[right]]>0)
{
remain_legth+=1;
}
dict_[s2[right]]-=1;
cout<<"remain_legth:"<<remain_legth<<endl;
while(remain_legth==s1.size())
{
cout<<"==right:"<<right<<endl;
cout<<"==left:"<<left<<endl;
if(right-left+1==s1.size())
{
return true;
}
left+=1;
dict_[s2[left-1]]+=1;
if (dict_[s2[left-1]]>0)
{
remain_legth-=1;
}
}
right+=1;
}
return false;
}
};
int main()
{
// string s1 = "ab";
// string s2 = "eidbaooo";
string s1 = "ab";
string s2 = "eidboaoo";
Solution sol;
bool res = sol.checkInclusion(s1, s2);
cout<<"res:"<<res<<endl;
return 0;
}30-3.找到字符串中所有字母异位词
思路1.hash 超时了
#超时间复杂度
class Solution:
def findAnagrams(self, s, p):
dict_ = {}
for str_ in p:
dict_[str_] = dict_.get(str_, 0)+1
print('==dict_:', dict_)
m = len(s)
n = len(p)
res = []
for i in range(m-n+1):
print('==s[i:n]:', s[i:i+n])
new_str = s[i:i + n]
new_dict = {}
for str_ in new_str:
if str_ not in dict_:
break
new_dict[str_] = new_dict.get(str_, 0)+1
if dict_ == new_dict:
res.append(i)
return res
s = "cbaebabacd"
p = "abc"
sol = Solution()
res = sol.findAnagrams(s, p)
print('==res:', res)
思路2.滑动窗口
class Solution:
def findAnagrams(self, s, p):
dict_ = {}
for i in p:
dict_[i] =dict_.get(i,0)+1
print(dict_)
length = 0
left,right = 0,0
res = []
while right<len(s):#往右拓展
if s[right] in dict_:
if dict_[s[right]]>0:#注意判断避免重复字符进行多次计数
length+=1
dict_[s[right]]-=1
while length==len(p):#往左压缩
if length==right-left+1:
res.append(left)
left+=1#往左压缩
#注意left进行了加1 要用left-1去修正dict
if s[left-1] in dict_:
dict_[s[left-1]]+=1
if dict_[s[left-1]]>0:#注意判断避免重复字符进行多次计数
length-=1
right+=1
print(res)
return res
s= "cbaebabacd"
p = "abc"
sol = Solution()
sol.findAnagrams(s, p)
30-4.无重复字符的最长子串
思路:滑动窗口，先往右拓展字典进行加1，发现大于1的在往左压缩 python代码
class Solution:
def lengthOfLongestSubstring(self, s):
n = len(s)
left = 0
right = 0
dict_= {}
res = 0
while right<n:#往右拓展
dict_[s[right]] = dict_.get(s[right], 0)+1#出现就加1
while dict_[s[right]]>1:#解决这种两个连续ww的问题"pwwkew" 再次出现往左压缩
dict_[s[left]]-=1
left+=1
res = max(res, right-left+1)
right+=1
return res
# s = "abcabcbb"
# s = "dvdf"
s = "pwwkew"
sol = Solution()
sol.lengthOfLongestSubstring(s)c++代码:
#include <string>
#include <iostream>
#include <vector>
#include <list>
#include <map>
#include <typeinfo>
using namespace std;
class Solution {
public:
int lengthOfLongestSubstring(string s) {
int left = 0;
int right = 0;
int res=0;
map <char, int> dict_;
while (right<s.size())
{
dict_[s[right]]+=1;
while (dict_[s[right]]>1)
{
dict_[s[left]]-=1;
left+=1;
}
// cout<<"dict_[s[right]]:"<<dict_[s[right]]<<endl;
// cout<<"right:"<<right<<endl;
// cout<<"left:"<<left<<endl;
res = max(res, right-left+1);
right+=1;
}
return res;
}
};
int main()
{
string s = "abcabc";
// Solution sol;
// int res;
// res= sol.lengthOfLongestSubstring(s);
int res;
Solution *sol = new Solution();
res = sol->lengthOfLongestSubstring(s);
delete sol;
sol = NULL;
cout<<"res:"<<res<<endl;
return 0;
}31.单词搜索
思路:与岛屿，水塘类似，只不过添加一个回溯的过程，直接修改board即可，回溯出来还原即可
class Solution:
def help(self, i, j, h, w, index):
if i<0 or j<0 or i>=h or j>=w or self.word[index] != self.board[i][j]:
return False
if index == len(self.word) - 1:
return True
self.board[i][j] = ''#说明board和word找到相同的 因为不能重复 修改一下borad
for direction in self.directions:
new_i, new_j = direction[0] + i, direction[1] + j
if self.help(new_i, new_j, h, w, index + 1):
return True
self.board[i][j] = self.word[index]#回溯出去需要还原
return False
def exist(self, board: List[List[str]], word: str) -> bool:
self.board = board
self.word = word
self.directions = [(-1, 0), (0, -1), (1, 0), (0, 1)]
h = len(board)
w = len(board[0])
for i in range(h):
for j in range(w):
if self.help(i, j, h, w, 0):
return True
return Falsec++实现:
class Solution {
public:
int h, w;
vector<vector<char>> board;
string word;
int directions[4][2] = {{-1, 0}, {1, 0}, {0, -1}, {0, 1}};
bool help(int i, int j, int index){
if(i < 0 || j < 0 || i > h - 1 || j > w - 1 || this->word[index] != this->board[i][j]){
return false;
}
if(index == this->word.size() - 1){
return true;
}
this->board[i][j] = '#';
for(int k = 0; k < sizeof(directions) / sizeof(directions[0]); k++){
if(help(directions[k][0] + i, directions[k][1] + j, index + 1)){
return true;
}
}
this->board[i][j] = this->word[index];
return false;
}
bool exist(vector<vector<char>>& board, string word) {
this->h = board.size();
this->w = board[0].size();
this->board = board;
this->word = word;
for(int i = 0; i < this->h; i++){
for(int j = 0; j < this->w; j++){
if(help(i, j, 0)){
return true;
}
}
}
return false;
}
};
思路１:暴力枚举，直接向左右扩撒直到找到小于heights[i]的点
超时：
class Solution:
def largestRectangleArea(self, heights):
res = 0
for i in range(len(heights)):
# print('==i:', i)
left_i = i
right_i = i
# print(stack)
while left_i >= 0 and heights[left_i] >= heights[i]:
left_i-=1
while right_i<len(heights) and heights[right_i] >= heights[i]:
right_i+=1
# print('==left_i,right_i:', left_i,right_i)
res = max(res, (right_i - left_i - 1)*heights[i])
return res
heights = [2,1,5,6,2,3]
# heights = [0,9]
# heights = [2,0,2]
# heights = [4,2,0,3,2,4,3,4]
sol = Solution()
sol.largestRectangleArea(heights)思路２:单调递增栈
#单调递增栈 将依次增加的值放入栈中，出现小于栈的值则进行出栈计算面积
class Solution:
def largestRectangleArea(self, heights):
stack = []
heights = [0] + heights + [0]
res = 0
for i in range(len(heights)):
while stack and heights[stack[-1]] > heights[i]:
# print('heights', heights)
print('===i:', i)
print('==stack:', stack)
tmp = stack.pop()
print('==tmp:', tmp)
width = (i - stack[-1] - 1)
res = max(res, width * heights[tmp])
print('==res:', res)
stack.append(i)
return res
heights = [2,1,5,6,2,3]
# heights = [0,9]
# heights = [2,0,2]
# heights = [4,2,0,3,2,4,3,4]
sol = Solution()
sol.largestRectangleArea(heights)
c++实现:
class Solution {
public:
int largestRectangleArea(vector<int>& heights) {
heights.push_back(0);
heights.insert(heights.begin(), 0);
vector<int> stack;
int max_area = 0;
for(int i = 0; i < heights.size(); i++){
while(!stack.empty() && heights[i] < heights[stack.back()]){
int index = stack.back();
stack.pop_back();
int width = i - 1 - stack.back();
int height = heights[index];
max_area = max(max_area, width * height);
}
stack.push_back(i);
}
return max_area;
}
};
33.最大矩形
思路1:动态规划 获取最长宽度
if 0, dp[i][j]=1
if 1, dp[i][j]=dp[i][j-1]+1
找到右下角在往上去找到高度和最小宽度即可求矩形面积
import numpy as np
class Solution:
def maximalRectangle(self, matrix):
print('==np.array(matrix):\n', np.array(matrix))
h = len(matrix)
if h==0:
return 0
w= len(matrix[0])
dp = [[0 for i in range(w)] for i in range(h)]
# print('==np.array(dp):', np.array(dp))
max_area = 0
for i in range(h):
for j in range(w):
if j>0 and matrix[i][j]=='1':
dp[i][j] = dp[i][j-1]+1
elif j == 0:
dp[i][j] = int(matrix[i][j])
else:
pass
width = dp[i][j]
for k in range(i,-1,-1):
height = i-k+1
width = min(width, dp[k][j])
max_area = max(max_area, height*width)
print('==np.array(dp):\n', np.array(dp))
print('===max_area:', max_area)
return max_area
# matrix = [["1","0","1","0","0"],
# ["1","0","1","1","1"],
# ["1","1","1","1","1"],
# ["1","0","0","1","0"]]
matrix = [["0", "0", "0"],
["1", "1", "1"]]
sol = Solution()
sol.maximalRectangle(matrix)
思路２，采用单调递增栈，也就是139.柱状图中最大的矩形，那么构造出高度列表即可以求出最大面积，如下图所示，橙色就是每一行需要抓换的高度列表
import numpy as np
#
class Solution:
def largestRectangleArea(self, heights):
stack = []
heights = [0] + heights + [0]
res = 0
for i in range(len(heights)):
while stack and heights[stack[-1]] > heights[i]:
index = stack.pop()
width = i - stack[-1] - 1
res = max(res, width * heights[index])
stack.append(i)
return res
def maximalRectangle(self, matrix):
if not matrix: return 0
print('==np.array(matrix):\n', np.array(matrix))
h = len(matrix)
w = len(matrix[0])
heights = [0] * w
max_area = 0
for i in range(h):
for j in range(w):
if matrix[i][j] == '1':
heights[j] += 1
else:
heights[j] = 0
print('==heights:', heights)
max_area = max(max_area, self.largestRectangleArea(heights))
print('==max_area:', max_area)
return max_area
# matrix = [["1", "0", "1", "0", "0"],
# ["1", "0", "1", "1", "1"],
# ["1", "1", "1", "1", "1"], ["1", "0", "0", "1", "0"]]
# matrix = [["1"]]
# matrix = [["1", "1"]]
# matrix = [["0", "0", "0"],
# ["1", "1", "1"]]
matrix = [["0","1"],
["1","0"]]
sol = Solution()
sol.maximalRectangle(matrix)
34.中序遍历
思路１：递归法
# Definition for a binary tree node.
# class TreeNode:
# def __init__(self, val=0, left=None, right=None):
# self.val = val
# self.left = left
# self.right = right
class Solution:
def helper(self, node):
if node is not None:
self.helper(node.left)
self.res.append(node.val)
self.helper(node.right)
def inorderTraversal(self, root: TreeNode) -> List[int]:
self.res = []
self.helper(root)
return self.res
c++实现:
/**
* Definition for a binary tree node.
* struct TreeNode {
* int val;
* TreeNode *left;
* TreeNode *right;
* TreeNode() : val(0), left(nullptr), right(nullptr) {}
* TreeNode(int x) : val(x), left(nullptr), right(nullptr) {}
* TreeNode(int x, TreeNode *left, TreeNode *right) : val(x), left(left), right(right) {}
* };
*/
class Solution {
public:
vector<int>res;
void help(TreeNode* node){
if(node){
help(node->left);
res.push_back(node->val);
help(node->right);
}
}
vector<int> inorderTraversal(TreeNode* root) {
help(root);
return res;
}
};思路2.栈（迭代法）
# Definition for a binary tree node.
# class TreeNode(object):
# def __init__(self, val=0, left=None, right=None):
# self.val = val
# self.left = left
# self.right = right
class Solution(object):
def inorderTraversal(self, root):
"""
:type root: TreeNode
:rtype: List[int]
"""
stack = []
node = root
output = []
if root == None:
return output
while node or stack: # 如果node和aStack都是空的，说明全查完了。
while node: # 如果node是空的，说明左边没子节点了。
stack.append(node)
node = node.left
node = stack.pop() # 左边没子节点了就输出栈顶的节点值，然后从它右边的子节点继续。
output.append(node.val)
node = node.right
return output
35-1.不同的二叉搜索树
思路:卡塔兰数
将 1⋯(i−1) 序列作为左子树，将 (i+1)⋯n 序列作为右子树。接着我们可以按照同样的方式递归构建左子树和右子树。
在上述构建的过程中，由于根的值不同，因此我们能保证每棵二叉搜索树是唯一的.也就得到卡塔兰数
class Solution(object):
def numTrees(self, n):
"""
:type n: int
:rtype: int
"""
#状态方程 和G(j-1) * G(n-j)
dp = [0]*(n+1)
#0 1树都为1
dp[0], dp[1] = 1, 1
for i in range(2,n+1):
for j in range(1,i+1):
dp[i] += dp[j-1]*dp[i-j]
# print('==dp:', dp)
return dp[-1]c++实现:
class Solution {
public:
int numTrees(int n) {
vector<int> res(n+1,0);
res[0] = 1;
res[1] = 1;
for (int i=2;i<n+1;i++){
for (int j=1;j<i+1;j++){
res[i] += res[j-1] * res[i-j];
}
}
return res[n];
}
};35-2.不同的二叉搜索树 II
思路:
# Definition for a binary tree node.
# class TreeNode(object):
# def __init__(self, val=0, left=None, right=None):
# self.val = val
# self.left = left
# self.right = right
class Solution(object):
def generateTrees(self, n):
"""
:type n: int
:rtype: List[TreeNode]
"""
if n==0:
return []
def build_tree(left,right):
if left > right:#递归终止条件 如果左边计数大于右边 说明要返回空值
return [None]
all_trees = []
for i in range(left, right+1):
left_trees = build_tree(left, i-1)
right_trees = build_tree(i+1, right)
for l in left_trees:#遍历可能的左子树
for r in right_trees:#遍历可能的右子树
cur_tree = TreeNode(i)#根节点
cur_tree.left= l
cur_tree.right = r
all_trees.append(cur_tree)
return all_trees
res = build_tree(1,n)
return res
思路1:递归处理右子树节点和 左子树节点的值和上下界限的大小
# Definition for a binary tree node.
# class TreeNode(object):
# def __init__(self, x):
# self.val = x
# self.left = None
# self.right = None
class Solution(object):
def isValidBST(self, root):
"""
:type root: TreeNode
:rtype: bool
"""
def helper(node, lower=float('-inf'), upper=float('inf')):
if node is None:#递归终止条件 节点为None
return True
val = node.val#获取节点值
#如果节点值大于上界或者小于下界 ,返回false
if val >= upper or val <= lower :
return False
#递归右子树 对于右子树 具备下界
if not helper(node.right, val, upper):
return False
#递归左子树 对于左子树 具备上界
if not helper(node.left, lower, val):
return False
return True
return helper(root)c++实现:
/**
* Definition for a binary tree node.
* struct TreeNode {
* int val;
* TreeNode *left;
* TreeNode *right;
* TreeNode() : val(0), left(nullptr), right(nullptr) {}
* TreeNode(int x) : val(x), left(nullptr), right(nullptr) {}
* TreeNode(int x, TreeNode *left, TreeNode *right) : val(x), left(left), right(right) {}
* };
*/
class Solution {
public:
bool help(TreeNode* node, long long lower,long long upper){
if(node == nullptr){
return true;
}
if(node->val <= lower || node->val >= upper){
return false;
}
if(!help(node->right, node->val, upper)){
return false;
}
if(!help(node->left, lower, node->val)){
return false;
}
return true;
}
bool isValidBST(TreeNode* root) {
if(root == nullptr){
return true;
}
return help(root, LONG_MIN, LONG_MAX);
}
};
思路2 :利用中序遍历的特点,遍历左子树和根节点,如果值不满足二叉搜索数特点就返回false.
# Definition for a binary tree node.
# class TreeNode(object):
# def __init__(self, x):
# self.val = x
# self.left = None
# self.right = None
class Solution(object):
def isValidBST(self, root):
stack = []
node = root
inorder_value = float('-inf')
while stack or node:#出栈终止条件
while node:#进栈
stack.append(node)
node = node.left
node = stack.pop()#左节点
# 如果中序遍历得到的节点的值小于等于前一个 inorder_value，说明不是二叉搜索树
if node.val <=inorder_value:
return False
inorder_value = node.val
node=node.right
return True
思路3:递归实现中序遍历 左 跟 右 也就是遍历的后一个节点值要大于上一个 否则不满足二叉搜索树特点
# Definition for a binary tree node.
# class TreeNode:
# def __init__(self, val=0, left=None, right=None):
# self.val = val
# self.left = left
# self.right = right
#中序遍历 左跟右
class Solution:
def __init__(self):
self.pre = float('-inf')
def isValidBST(self, root: TreeNode) -> bool:
if root is None:
return True
if not self.isValidBST(root.left):#先访问左子树
return False
if root.val<=self.pre:#在访问当前节点
return False;
print('==before self.pre:',self.pre)
self.pre = root.val
print('==after self.pre:',self.pre)
return self.isValidBST(root.right)#在访问右子树
37.对称二叉树
1.解法1 bfs 对每个节点的左子树和右子树进行判断相等
# Definition for a binary tree node.
# class TreeNode:
# def __init__(self, x):
# self.val = x
# self.left = None
# self.right = None
class Solution:
def isSymmetric(self, root: TreeNode) -> bool:
def check(t1,t2):
if t1==None and t2==None:
return True
if t1==None or t2==None:
return False
if (t1.val != t2.val):
return False
return check(t1.left,t2.right) and check(t1.right,t2.left)
return check(root,root)
c++实现:
/**
* Definition for a binary tree node.
* struct TreeNode {
* int val;
* TreeNode *left;
* TreeNode *right;
* TreeNode() : val(0), left(nullptr), right(nullptr) {}
* TreeNode(int x) : val(x), left(nullptr), right(nullptr) {}
* TreeNode(int x, TreeNode *left, TreeNode *right) : val(x), left(left), right(right) {}
* };
*/
class Solution {
public:
bool dfs(TreeNode* t1, TreeNode* t2){
if(t1==nullptr && t2==nullptr){
return true;
}
if(t1==nullptr || t2==nullptr){
return false;
}
return dfs(t1->left,t2->right) && dfs(t1->right,t2->left);
}
bool isSymmetric(TreeNode* root) {
return dfs(root, root);
}
};2.解法2 dfs ，首先对根节点左子树进行前序遍历并存储值，对根节点右子树的右分支进行遍历在对左分支进行遍历并存储值，最后比较两个列表的值。
# Definition for a binary tree node.
# class TreeNode:
# def __init__(self, x):
# self.val = x
# self.left = None
# self.right = None
class Solution:
def isSymmetric(self, root: TreeNode) -> bool:
if root==None:
return True
def leftsearch(t1, left):
if t1==None:
left.append(None)
else:
left.append(t1.val)
leftsearch(t1.left,left)
leftsearch(t1.right,left)
def rightsearch(t2, right):
if t2==None:
right.append(None)
else:
right.append(t2.val)
rightsearch(t2.right,right)
rightsearch(t2.left,right)
left = []
right = []
leftsearch(root.left, left)
rightsearch(root.right, right)
if left==right:
return True
else:
return False
38. 二叉树的层序遍历
# Definition for a binary tree node.
# class TreeNode:
# def __init__(self, x):
# self.val = x
# self.left = None
# self.right = None
class Solution:
def levelOrder(self, root: TreeNode) -> List[List[int]]:
res = []
if root is None:
return res
quene = [root]
while quene:
temp = []
for i in range(len(quene)):
node = quene.pop(0)
temp.append(node.val)
if node.left:
quene.append(node.left)
if node.right:
quene.append(node.right)
res.append(temp)
return res39.二叉树的最大深度
# Definition for a binary tree node.
# class TreeNode:
# def __init__(self, x):
# self.val = x
# self.left = None
# self.right = None
class Solution:
def maxDepth(self, root: TreeNode) -> int:
if root is None:
return 0
return max(self.maxDepth(root.left),self.maxDepth(root.right))+140-1.从前序与中序遍历序列构造二叉树
思路：
终止条件:前序或中序数组为空．
根据前序数组第一个元素，拼出根节点，再将前序数组和中序数组分成两半，递归的处理前序数组左边和中序数组左边，递归的处理前序数组右边和中序数组右边。
# Definition for a binary tree node.
# class TreeNode:
# def __init__(self, x):
# self.val = x
# self.left = None
# self.right = None
class Solution:
def buildTree(self, preorder: List[int], inorder: List[int]) -> TreeNode:
# 递归终止条件 前序遍历节点数或中序遍历节点数为０
if len(preorder)==0 or len(inorder)==0:
return None
root = TreeNode(preorder[0])#根据前序遍历特点创建根节点
#再根据中序遍历特点用根节点找出左右子树的分界点
mid_index = inorder.index(preorder[0])
#再利用中序遍历和前序遍历的左子树节点个数相等特点 构造根节点左子树
root.left = self.buildTree(preorder[1:mid_index+1],inorder[:mid_index])
#再利用中序遍历和前序遍历的右子树节点个数相等特点 构造根节点右子树
root.right = self.buildTree(preorder[mid_index+1:],inorder[mid_index+1:])
return root
c++实现:
/**
* Definition for a binary tree node.
* struct TreeNode {
* int val;
* TreeNode *left;
* TreeNode *right;
* TreeNode() : val(0), left(nullptr), right(nullptr) {}
* TreeNode(int x) : val(x), left(nullptr), right(nullptr) {}
* TreeNode(int x, TreeNode *left, TreeNode *right) : val(x), left(left), right(right) {}
* };
*/
class Solution {
public:
TreeNode* buildTree(vector<int>& preorder, vector<int>& inorder) {
if(preorder.empty() || preorder.empty()) {
return nullptr;
}
TreeNode* root = new TreeNode(preorder[0]);
int root_value = preorder[0];
int middle = 0;
for (int i=0;i<inorder.size();i++){
if(inorder[i]==root_value){
middle = i;
break;
}
}
vector<int> leftInorder(inorder.begin(), inorder.begin() + middle);
vector<int> rightInorder(inorder.begin() + middle + 1, inorder.end());
vector<int> leftPreorder(preorder.begin()+1, preorder.begin() + middle+1);
vector<int> rightPreorder(preorder.begin() + middle + 1, preorder.end());
root->left = buildTree(leftPreorder,leftInorder);
root->right = buildTree(rightPreorder,rightInorder);
return root;
}
};40-2.从中序与后序遍历序列构造二叉树
思路：和上一题类似
# Definition for a binary tree node.
# class TreeNode:
# def __init__(self, x):
# self.val = x
# self.left = None
# self.right = None
class Solution:
def buildTree(self, inorder: List[int], postorder: List[int]) -> TreeNode:
#递归终止条件
if len(inorder)==0 or len(postorder)==0:
return None
#创建根节点
root = TreeNode(postorder[-1])
#根据中序遍历获取分离点
mid_index = inorder.index(postorder[-1])
# print('==mid_index:',mid_index)
#获取左子树
root.left = self.buildTree(inorder[:mid_index],postorder[:mid_index])
#获取右子树
root.right = self.buildTree(inorder[mid_index+1:],postorder[mid_index:-1])
return root
c++实现:
/**
* Definition for a binary tree node.
* struct TreeNode {
* int val;
* TreeNode *left;
* TreeNode *right;
* TreeNode() : val(0), left(nullptr), right(nullptr) {}
* TreeNode(int x) : val(x), left(nullptr), right(nullptr) {}
* TreeNode(int x, TreeNode *left, TreeNode *right) : val(x), left(left), right(right) {}
* };
*/
class Solution {
public:
TreeNode* buildTree(vector<int>& inorder, vector<int>& postorder) {
if(inorder.empty() || postorder.empty()){
return nullptr;
}
TreeNode* root = new TreeNode(postorder[postorder.size()-1]);
int root_value = postorder[postorder.size()-1];
int middle = 0;
for (int i=0; i<inorder.size(); i++){
if(inorder[i] == root_value){
middle = i;
break;
}
}
// cout<<"===middle:"<<middle<<endl;
vector<int> left_inorder(inorder.begin(), inorder.begin() + middle);
vector<int> right_inorder(inorder.begin() + middle + 1, inorder.end());
vector<int> left_postorder(postorder.begin(), postorder.begin() + middle);
vector<int> right_postorder(postorder.begin() + middle, postorder.end() - 1);
root->left = buildTree(left_inorder, left_postorder);
root->right = buildTree(right_inorder, right_postorder);
return root;
}
};由上面两题可知对于前序遍历：跟左右，中序遍历：左跟右，后序遍历左右跟；
采前序遍历和中序遍历，中序遍历和后序遍历都能通过根节点分离出左右，而前序遍历和后序遍历就不能，故而后者无法恢复出二叉树．
41.二叉树展开为链表
思路:可看出是根据前序遍历的节点统统放在右子树上
# Definition for a binary tree node.
# class TreeNode:
# def __init__(self, val=0, left=None, right=None):
# self.val = val
# self.left = left
# self.right = right
class Solution:
def help(self, node):
if node is not None:
self.res.append(node)
self.help(node.left)
self.help(node.right)
def flatten(self, root: TreeNode) -> None:
"""
Do not return anything, modify root in-place instead.
"""
self.res = []
self.help(root)
# print(self.res)
length = len(self.res)
for i in range(1,length):
pre,cur = self.res[i-1],self.res[i]
pre.left = None
pre.right = cur
return rootc++实现:
/**
* Definition for a binary tree node.
* struct TreeNode {
* int val;
* TreeNode *left;
* TreeNode *right;
* TreeNode() : val(0), left(nullptr), right(nullptr) {}
* TreeNode(int x) : val(x), left(nullptr), right(nullptr) {}
* TreeNode(int x, TreeNode *left, TreeNode *right) : val(x), left(left), right(right) {}
* };
*/
class Solution {
public:
vector<TreeNode* >res;
void help(TreeNode* node){
if(node){
res.push_back(node);
help(node->left);
help(node->right);
}
}
void flatten(TreeNode* root) {
help(root);
for(int i=1;i<res.size();i++){
TreeNode* pre = res[i-1];
TreeNode* cur = res[i];
pre->left = nullptr;
pre->right = cur;
}
// return root;
}
};
思路１：动态规划用来存储最小和最大值之间差距
状态转移方程 不卖或者卖 opt[i] = max(opt[i-1], prices[i]-min_price)
class Solution:
def maxProfit(self, prices: List[int]) -> int:
if len(prices) <= 1:
return 0
opt = len(prices)*[0]
min_price = prices[0]
for i in range(1, len(prices)):
if prices[i]<min_price:
min_price = prices[i]
opt[i] = max(opt[i-1], prices[i]-min_price)
# print('opt:', opt)
return opt[-1]思路２：就是存储最小最大值的差值即可
class Solution:
def maxProfit(self, prices: List[int]) -> int:
#dp[i] = max(dp[i-1],prices[i] - minprice)
if len(prices)<=0:
return 0
# dp = len(prices)*[0]
minprice = prices[0]
res = 0
for i in range(1,len(prices)):
if prices[i]<minprice:
minprice = prices[i]
# dp[i] = max(dp[i-1], prices[i]-minprice)
res = max(res, prices[i]-minprice)
# print(dp)
return res思路3:利用单调递增栈，找到元素小于栈顶的，则更新此时的最大利润， 对于一直递增的要特意在prices增加一个负数 作为递增拐点
class Solution:
def maxProfit(self, prices):
if len(prices)<=1:
return 0
stack = []
res = 0
prices.append(-1)
# print('==prices:', prices)
for i in range(len(prices)):
while stack and prices[i] <= prices[stack[-1]]:
print('==stack:', stack)
res = max(res, prices[stack[-1]]-prices[stack[0]])
print('==res:', res)
stack.pop()
stack.append(i)
# print('==stack:', stack)
return res
prices = [7,1,5,3,6,4]
# prices = [1,2]
sol = Solution()
sol.maxProfit(prices)
class Solution {
public:
int maxProfit(vector<int>& prices) {
if(prices.size() <= 1){
return 0;
}
vector<int> stack;
int max_profit = 0;
prices.push_back(-1);
for(int i = 0; i < prices.size(); i++){
while(!stack.empty() && prices[i] < prices[stack[stack.size() - 1]]){
max_profit = max(max_profit, prices[stack[stack.size() - 1]] - prices[stack[0]]);
stack.pop_back();
}
stack.push_back(i);
}
return max_profit;
}
};
思路1：与上一题差异在于对次数没有限制，所以采用贪心算法，一直累加
class Solution:
def maxProfit(self, prices):
if len(prices)<=1:
return 0
# opt = len(prices)*[0]
res = 0
for i in range(1,len(prices)):
if prices[i]>prices[i-1]:
res+=prices[i]- prices[i-1]
print('===res:', res)
return res
prices = [7,1,5,3,6,4]
sol = Solution()
sol.maxProfit(prices)class Solution:
def maxProfit(self, prices: List[int]) -> int:
if len(prices)<=1:
return 0
# opt = len(prices)*[0]
res = 0
for i in range(1,len(prices)):
if prices[i]>prices[i-1]:
res+=prices[i]- prices[i-1]
# print('===res:', res)
return res思路2:dp解法
dp存储有无的利润
今天无股票：1.昨天就没有，今天不操作; 2.昨天有，今天卖了
今天有股票:1.昨天有，今天不操作; 2.昨天无，今天买
1代表有 0代表无
dp[i][0] =max(dp[i-1][0],dp[i-1][1]+prices[i])
dp[i][1] =max(dp[i-1][1],dp[i-1][0]-prices[i])
class Solution:
def maxProfit(self, prices):
# res = 0
# for i in range(1, len(prices)):
# if prices[i]>prices[i-1]:
# res +=prices[i] - prices[i-1]
# return res
n = len(prices)
dp = [[0 for i in range(2)] for i in range(n)]
print('==dp:', dp)
dp[0][1] = -prices[0]
for i in range(1, n):
dp[i][0] = max(dp[i - 1][0], dp[i - 1][1] + prices[i])
dp[i][1] = max(dp[i - 1][1], dp[i - 1][0] - prices[i])
print('==dp:', dp)
return dp[-1][0]#返回没有的最大利润
prices = [7, 1, 5, 3, 6, 4]
sol = Solution()
sol.maxProfit(prices)
class Solution {
public:
int maxProfit(vector<int>& prices) {
int n = prices.size();
if(n <= 1){
return 0;
}
vector<vector<int>> dp(n, vector<int>(2, 0));
//dp[i][0] = max(dp[i-1][0], dp[i-1][1] + prices[i])
//dp[i][1] = max(dp[i-1][1], dp[i-1][0] - prices[i])
//dp[0][1] = -prices[0]
dp[0][1] = -prices[0];
for(int i = 1; i < n; i++){
dp[i][0] = max(dp[i-1][0], dp[i-1][1] + prices[i]);
dp[i][1] = max(dp[i-1][1], dp[i-1][0] - prices[i]);
}
return max(dp[n-1][0], dp[n-1][1]);
}
};
dp解法: dp存储有无的利润
今天无股票：1.昨天就没有，今天不操作; 2.昨天有，今天卖了 在减去费用
今天有股票:1.昨天有，今天不操作; 2.昨天无，今天买
1代表有 0代表无
dp[i][0] =max(dp[i-1][0],dp[i-1][1]+prices[i]-fee)
dp[i][1] =max(dp[i-1][1],dp[i-1][0]-prices[i])
class Solution:
def maxProfit(self, prices, fee):
dp = [[0 for i in range(2)] for i in range(len(prices))]
dp[0][1] = -prices[0]
for i in range(1, len(prices)):
dp[i][0] = max(dp[i - 1][0], dp[i - 1][1] + prices[i] - fee)
dp[i][1] = max(dp[i-1][1], dp[i-1][0]-prices[i])
print('==dp:', dp)
return dp[-1][0]
prices = [1, 3, 2, 8, 4, 9]
fee = 2
sol = Solution()
sol.maxProfit(prices, fee)
思路:和上一题不用的是增加了冷冻期，故状态方程dp[i]不在由dp[i-1]来，而是dp[i-2]来的
今天无股票：1.昨天就没有，今天不操作; 2.昨天有，今天卖了
今天有股票:1.昨天有，今天不操作; 2.昨天是冷冻期，前天卖出,今天买
1代表有 0代表无
dp[i][0] =max(dp[i-1][0],dp[i-1][1]+prices[i])
dp[i][1] =max(dp[i-1][1],dp[i-2][0]-prices[i])
class Solution:
def maxProfit(self, prices):
if len(prices) <= 1:
return 0
dp = [[0 for i in range(2)] for i in range(len(prices))]
print('==dp:', dp)
dp[0][1] = -prices[0]
dp[1][0] = max(dp[1 - 1][0], dp[1 - 1][1] + prices[1])
dp[1][1] = max(dp[1-1][1], -prices[1])
for i in range(2, len(prices)):
dp[i][0] = max(dp[i - 1][0], dp[i - 1][1] + prices[i])
dp[i][1] = max(dp[i - 1][1], dp[i - 2][0] - prices[i])
print('==dp:', dp)
return dp[-1][0]#返回没有的最大利润
prices = [1, 2, 3, 0, 2]
sol = Solution()
sol.maxProfit(prices)
#dp[i][j][0] 不持有利润
#dp[i][j][1] 持有的利润
# i代表天数,j代表买入次数
#昨天可能持有也可能没有持有,昨天持有今天卖了dp[i-1][j][1]+prices[i],昨天没有dp[i-1][j][0]
#dp[i][j][0] = max(dp[i-1][j][0],dp[i-1][j][1]+prices[i])
#昨天持有也可能没有持有,昨天持有dp[i-1][j][1],昨天没有持有dp[i-1][j-1][0]-prices[i]
#dp[i][j][1] = max(dp[i-1][j][1], dp[i-1][j-1][0]-prices[i])
class Solution:
def maxProfit(self, prices):
#k代表交易次数,本题为0,1,2
n = len(prices)
k = 2
dp = [[[0, 0] for i in range(k+1)] for _ in range(n)]
for i in range(n):#边界条件1:第i天不买入是否持有的利润
dp[i][0][0] = 0
dp[i][0][1] = float('-inf')#用负无穷代表不可能
# print(dp)
for j in range(1, k+1):#边界条件2:第0天买入是否持有的利润
dp[0][j][0] = 0
dp[0][j][1] = -prices[0]
for i in range(1, n):
for j in range(1,k+1):
dp[i][j][0] = max(dp[i - 1][j][0], dp[i - 1][j][1] + prices[i])
dp[i][j][1] = max(dp[i - 1][j][1], dp[i - 1][j - 1][0] - prices[i])
return dp[-1][-1][0]
prices = [3,3,5,0,0,3,1,4]
sol = Solution()
sol.maxProfit(prices)
43.二叉树中的最大路径和
递归 主要是要找准递归终止条件和递归出口,终止条件就是节点为none自然返回值为0, 递归出口就是节点本身值+max(左节点增益值，右节点增益值)
# Definition for a binary tree node.
# class TreeNode:
# def __init__(self, val=0, left=None, right=None):
# self.val = val
# self.left = left
# self.right = right
class Solution:
def helper(self, node):
if node is None:
return 0
left_gain = self.helper(node.left)
right_gain = self.helper(node.right)
self.max_gain = max(self.max_gain,left_gain+right_gain+node.val)
return max(node.val+left_gain,node.val+right_gain,0)
def maxPathSum(self, root: TreeNode) -> int:
self.max_gain = float('-inf')
self.helper(root)
return self.max_gainc++实现:
/**
* Definition for a binary tree node.
* struct TreeNode {
* int val;
* TreeNode *left;
* TreeNode *right;
* TreeNode() : val(0), left(nullptr), right(nullptr) {}
* TreeNode(int x) : val(x), left(nullptr), right(nullptr) {}
* TreeNode(int x, TreeNode *left, TreeNode *right) : val(x), left(left), right(right) {}
* };
*/
class Solution {
public:
int max_value=INT_MIN;
int helper(TreeNode *node){
if(!node){
return 0;
}
int left_gain = helper(node->left);
int right_gain = helper(node->right);
max_value = max(max_value, node->val+left_gain+right_gain);
return max(max(node->val+left_gain,0),node->val+right_gain);
}
int maxPathSum(TreeNode* root) {
helper(root);
return max_value;
}
};44.最长连续序列
class Solution:
def longestConsecutive(self, nums):
longest_length = 0
num_set = set(nums)#set 比list 快几十倍
print('==num_set:', num_set)
temp = 1
for num in num_set:
if num - 1 in num_set:#如果有小于的就跳过
continue
else:
while num+1 in num_set:#如果有大于的就一直不停更新+1 寻找长度
temp += 1
num += 1
longest_length = max(longest_length, temp)
temp = 1#寻找完结束以后 在初始化为１
print('==longest_length:', longest_length)
return longest_length
nums = [100,4,200,1,3,2,2]
sol = Solution()
sol.longestConsecutive(nums)
1,给定一个非空整数数组，除了某个元素只出现一次以外，其余每个元素均出现两次。找出那个只出现了一次的元素。
思路:利用异或,相同为0,不同为1
#方法1
a=[4,1,2,2,1]
b=set(a)
print(b)
print(2*sum(b)-sum(a))
#方法2：
a=[4,1,1]
res=0
for i in a:
res^=i
print('res=',res)
#方法3：
a=[4,1,2,1,2]
from functools import reduce
b=reduce(lambda x,y:x^y,a)
print('b=',b)45-2.只出现一次的数字 II
给定一个非空整数数组，除了某个元素只出现一次以外，其余每个元素均出现了三次。找出那个只出现了一次的元素。
思路:0与任何数异或为该数,两个相同的数异或为0,需要两个位运算符来存储单次和三次出现的值
class Solution:
def singleNumber(self, nums: List[int]) -> int:
# return (3 * sum(set(nums)) - sum(nums)) // 2
seen_once = seen_twice = 0
for num in nums:
seen_once = ~seen_twice & (seen_once ^ num)
seen_twice = ~seen_once & (seen_twice ^ num)
return seen_once46-1. 单词拆分
思路１:动态规划
#动态规划 dp[i]表示 s 的前 i 位是否可以用 wordDict 中的单词表示,
#
class Solution:
def wordBreak(self, s, wordDict):
n = len(s)
dp = [False] * (n + 1)
dp[0] = True
for i in range(n):
for j in range(i+1, n+1):
if dp[i] and (s[i:j] in wordDict):
dp[j] = True
print('==dp:', dp)
return dp[-1]
s = "leetcode"
wordDict = ["leet", "code"]
sol = Solution()
res= sol.wordBreak(s, wordDict)
print('==res:', res)
c++实现:
class Solution {
public:
bool wordBreak(string s, vector<string>& wordDict) {
int n = s.size();
unordered_set<string> wordDictSet;
for (auto word: wordDict) {
wordDictSet.insert(word);
}
vector<bool> dp(n+1, false);
dp[0] = true;
for(int i = 0; i < n; i++){
for(int j = i+1; j < n+1; j++){
if(dp[i] && wordDictSet.find(s.substr(i, j - i)) != wordDictSet.end()) {
// cout<<"s.substr(i, j - i):"<<s.substr(i, j - i)<<endl;
dp[j] = true;
}
}
}
return dp[n];
}
};思路2：回溯加缓存
#递归 lru_cache用于缓存 将数据缓存下来 加快后续的数据获取 相同参数调用时直接返回上一次的结果
import functools
class Solution:
@functools.lru_cache()
def helper(self, s):
if len(s) == 0:
return True
res = False
for i in range(1, len(s)+1):
if s[:i] in self.wordDict:
res = self.helper(s[i:]) or res
return res
def wordBreak(self, s, wordDict):
self.wordDict = wordDict
return self.helper(s)
s = "leetcode"
wordDict = ["leet", "code"]
# s = "aaaaaaa"
# wordDict = ["aaaa", "aaa"]
# s= "aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaab"
# wordDict = ["a","aa","aaa","aaaa","aaaaa","aaaaaa","aaaaaaa","aaaaaaaa","aaaaaaaaa","aaaaaaaaaa"]
sol = Solution()
res= sol.wordBreak(s, wordDict)
print('==res:', res)
思路：递归
class Solution:
def helper(self, s, wordDict, memo):
if s in memo:#递归终止条件
return memo[s]
if s=='':#递归终止条件
return []
res = []
for word in wordDict:
if not s.startswith(word):
continue
if len(word)==len(s):#匹配上刚好相等
res.append(word)
else:#匹配上 但是字符还没到最后
rest = self.helper(s[len(word):], wordDict, memo)
for tmp in rest:
tmp = word+ " "+ tmp
res.append(tmp)
print('==res:', res)
print('==memo:', memo)
memo[s] = res
return res
def wordBreak(self, s, wordDict):
if s=='':
return []
return self.helper(s, wordDict, memo={})
s = "catsanddog"
wordDict = ["and", "cat", "cats", "sand", "dog"]
# s = "cat"
# wordDict = ["cat"]
sol = Solution()
res = sol.wordBreak(s, wordDict)
print(res)
# Definition for singly-linked list.
# class ListNode:
# def __init__(self, x):
# self.val = x
# self.next = None
class Solution:
def hasCycle(self, head: ListNode) -> bool:
#快慢指针 人追人
slow,fast = head,head
while fast:
if fast and fast.next:
slow = slow.next
fast=fast.next.next
else:
return False
if slow==fast:
return True
return Falsec++实现:
/**
* Definition for singly-linked list.
* struct ListNode {
* int val;
* ListNode *next;
* ListNode(int x) : val(x), next(NULL) {}
* };
*/
class Solution {
public:
bool hasCycle(ListNode *head) {
ListNode* slow = head;
ListNode* fast = head;
while(fast){
if(fast && fast->next){
slow = slow->next;
fast = fast->next->next;
}
else{
return false;
}
if(slow==fast){
return true;
}
}
return false;
}
};47-2.给定一个有环链表，实现一个算法返回环路的开头节点。
假设有两个指针，分别为快慢指针fast和slow, 快指针每次走两步，慢指针每次前进一步，如果有环则两个指针必定相遇；
反证法：假设快指针真的 越过 了慢指针，且快指针处于位置 i+1，而慢指针处于位置 i，那么在前一步，快指针处于位置 i-1，慢指针也处于位置 i-1，它们相遇了。
A:链表起点
B:环起点
C:相遇点
X:环起点到相遇点距离
Y:链表起点到环起点距离
R：环的长度
S:第一次相遇时走过的路程
1.慢指针slow第一次相遇走过的路程 S1 = Y + X;（11）
快指针fast第一次相遇走过的路程 S2=2S1 = Y + X + NR;（2）
说明：快指针的速度是慢指针的两倍，相同时间内路程应该是慢指针的两倍，Y + X + NR是因为快指针可能经过N圈后两者才相遇；
把（1）式代入（2）式得：Y = NR -X;
2..在将慢指针回到A点，满指针和快指针同时走，在B点相遇，此处就是环节点.
# Definition for singly-linked list.
# class ListNode:
# def __init__(self, x):
# self.val = x
# self.next = None
class Solution:
def detectCycle(self, head: ListNode) -> ListNode:
slow = head
fast = head;
while fast:
if fast and fast.next:
slow = slow.next
fast = fast.next.next
else:
return None
if slow==fast:
break
if fast ==None or fast.next==None:
return None
slow= head
while slow!=fast:
slow = slow.next
fast = fast.next
return slowc++实现:
/**
* Definition for singly-linked list.
* struct ListNode {
* int val;
* ListNode *next;
* ListNode(int x) : val(x), next(NULL) {}
* };
*/
class Solution {
public:
ListNode *detectCycle(ListNode *head) {
ListNode* slow = head;
ListNode* fast = head;
while(fast){
if(fast && fast->next){
slow = slow->next;
fast = fast->next->next;
}
else{
return NULL;
}
if(slow==fast){
break;
}
}
if(!fast || !fast->next){
return NULL;
}
slow = head;
while(slow!=fast){
slow = slow->next;
fast = fast->next;
}
return slow;
}
};47-3.链表相交
如这题应该是比较明显的双指针题，要是能实现一种算法让两个指针分别从A和B点往C点走，两个指针分别走到C后，又各自从另外一个指针的起点，也就是A指针第二次走从B点开始走，B指针同理，这样，A指针走的路径长度 AO + OC + BO 必定等于B指针走的路径长度 BO + OC + AO，这也就意味着这两个指针第二轮走必定会在O点相遇，相遇后也即到达了退出循环的条件，代码如下：
# Definition for singly-linked list.
# class ListNode:
# def __init__(self, x):
# self.val = x
# self.next = None
class Solution:
def getIntersectionNode(self, headA: ListNode, headB: ListNode) -> ListNode:
index_a = headA
index_b = headB
while index_a !=index_b:
if index_a !=None:
index_a = index_a.next
else:
index_a = headB
if index_b != None:
index_b = index_b.next
else:
index_b = headA
return index_a
c++实现:
/**
* Definition for singly-linked list.
* struct ListNode {
* int val;
* ListNode *next;
* ListNode(int x) : val(x), next(NULL) {}
* };
*/
class Solution {
public:
ListNode *getIntersectionNode(ListNode *headA, ListNode *headB) {
ListNode* node_A = headA;
ListNode* node_B = headB;
while(node_A!=node_B){
if(node_A!=NULL){
node_A=node_A->next;
}
else{
node_A = headB;
}
if(node_B!=NULL){
node_B=node_B->next;
}
else{
node_B = headA;
}
}
return node_A;
}
};48.LRU 缓存机制
class DLinkedNode:
def __init__(self, key=0, value=0):
self.key = key
self.value = value
self.prev = None
self.next = None
class LRUCache:
def __init__(self, capacity):
self.cache = dict()
# 使用伪头部和伪尾部节点
self.head = DLinkedNode()
self.tail = DLinkedNode()
self.head.next = self.tail
self.tail.prev = self.head
self.capacity = capacity
self.size = 0
def get(self, key):
if key not in self.cache:
return -1
# 如果 key 存在，先通过哈希表定位，再移到头部
node = self.cache[key]
self.moveToHead(node)
return node.value
def put(self, key, value):
if key not in self.cache:
# 如果 key 不存在，创建一个新的节点
node = DLinkedNode(key, value)
# 添加进哈希表
self.cache[key] = node
# 添加至双向链表的头部
self.addToHead(node)
self.size += 1
if self.size > self.capacity:
# 如果超出容量，删除双向链表的尾部节点
removed = self.removeTail()
# 删除哈希表中对应的项
self.cache.pop(removed.key)
self.size -= 1
else:
# 如果 key 存在，先通过哈希表定位，再修改 value，并移到头部
node = self.cache[key]
node.value = value
self.moveToHead(node)
def addToHead(self, node):
node.prev = self.head
node.next = self.head.next
self.head.next.prev = node
self.head.next = node
def removeNode(self, node):
node.prev.next = node.next
node.next.prev = node.prev
def moveToHead(self, node):
self.removeNode(node)
self.addToHead(node)
def removeTail(self):
node = self.tail.prev
self.removeNode(node)
return node
sol = LRUCache(2)
sol.put(1, 1)
res = sol.get(1)
print('==res:', res)49.排序链表
思路1:归并排序 先通过快慢指针找到中心点 进行截断以后一直递归拆开 在进行合并即可
python代码:
# Definition for singly-linked list.
# class ListNode:
# def __init__(self, val=0, next=None):
# self.val = val
# self.next = next
class Solution:
def merge(self, left, right):
res = ListNode(0)
temp = res
while left and right:
if left.val < right.val:
temp.next, left = left, left.next
else:
temp.next, right = right, right.next
temp = temp.next
temp.next = left if left else right
return res.next
def sortList(self, head: ListNode) -> ListNode:
if head is None or head.next is None:
return head
#快慢指针找到链表中心点
slow, fast = head, head.next
while fast and fast.next:
fast, slow = fast.next.next, slow.next
mid, slow.next = slow.next, None#将找到的中心点进行截断故 slow.next = None
left, right = self.sortList(head), self.sortList(mid)#递归一直进行拆分
return self.merge(left, right)#合并操作
c++代码:
/**
* Definition for singly-linked list.
* struct ListNode {
* int val;
* ListNode *next;
* ListNode() : val(0), next(nullptr) {}
* ListNode(int x) : val(x), next(nullptr) {}
* ListNode(int x, ListNode *next) : val(x), next(next) {}
* };
*/
class Solution {
public:
ListNode* mergetwo(ListNode* l1,ListNode* l2){
ListNode* new_head = new ListNode(0);
ListNode* node = new_head;
while(l1 && l2){
if(l1->val<l2->val){
node->next = l1;
l1 = l1->next;
}
else{
node->next = l2;
l2 = l2->next;
}
node = node->next;
}
if(l1){
node->next = l1;
}
if(l2){
node->next = l2;
}
return new_head->next;
}
ListNode* sortList(ListNode* head) {
if(head==nullptr || head->next==nullptr){
return head;
}
ListNode* slow = head;
ListNode* fast = head->next;
while(fast && fast->next){
slow = slow->next;
fast = fast->next->next;
}
ListNode* middle = slow->next;
slow->next = nullptr;
ListNode* l1 = sortList(head);
ListNode* l2 = sortList(middle);
return mergetwo(l1,l2);
}
};思路2:合并也是递归
# Definition for singly-linked list.
# class ListNode:
# def __init__(self, val=0, next=None):
# self.val = val
# self.next = next
class Solution:
# def merge(self, left, right):
# res = ListNode(0)
# temp = res
# while left and right:
# if left.val < right.val:
# temp.next, left = left, left.next
# else:
# temp.next, right = right, right.next
# temp = temp.next
# temp.next = left if left else right
# return res.next
def merge(self,left,right):
if left is None:
return right
if right is None:
return left
if left.val < right.val:
left.next = self.merge(left.next, right)
return left
else:
right.next = self.merge(left, right.next)
return right
def sortList(self, head: ListNode) -> ListNode:
if head is None or head.next is None:
return head
#快慢指针找到链表中心点
slow, fast = head, head.next
while fast and fast.next:
fast, slow = fast.next.next, slow.next
mid, slow.next = slow.next, None#将找到的中心点进行截断故 slow.next = None
left, right = self.sortList(head), self.sortList(mid)#递归一直进行拆分
return self.merge(left, right)#合并操作
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