70. 爬楼梯
解法一、dp
class Solution {
public int climbStairs(int n) {
int[] dp = new int[n+1];
dp[0] = 1;
dp[1] = 1;
for(int i = 2;i <= n;i++){
dp[i] = dp[i-1] + dp[i-2];
}
return dp[n];
}
}118. 杨辉三角
解法一、dp
class Solution {
public List<List<Integer>> generate(int numRows) {
int[][] num = new int[numRows][numRows];
num[0][0] = 1;
List<List<Integer>> res = new LinkedList<>();
List<Integer> t = new LinkedList<>();
t.add(1);
res.add(t);
for(int i = 1;i < numRows;i++){
num[i][0] = 1;
num[i][i] = 1;
t = new LinkedList<>();
t.add(1);
for(int j = 1;j < i;j++){
num[i][j] = num[i-1][j-1] + num[i-1][j];
t.add(num[i][j]);
}
t.add(1);
res.add(t);
}
return res;
}
}198. 打家劫舍
解法一、dp
状态转移方程：偷了上一个或者偷了这个与上上个
class Solution {
public int rob(int[] nums) {
int n = nums.length;
int[] dp = new int[n];
dp[0] = nums[0];
for(int i = 1;i < n;i++){
dp[i] = i > 1 ? Math.max(dp[i-1],dp[i-2] + nums[i]) : Math.max(dp[i-1],nums[i]);
}
return dp[n-1];
}
}279. 完全平方数
解法一
class Solution {
public int numSquares(int n) {
int[] dp = new int[n + 1];
Arrays.fill(dp, Integer.MAX_VALUE);
dp[0] = 0;
for (int i = 1; i * i <= n; i++) {
int square = i * i;
for (int j = square; j <= n; j++) {
dp[j] = Math.min(dp[j], dp[j - square] + 1);
}
}
return dp[n];
}
}
322. 零钱兑换
解法一、多数组
class Solution {
public int coinChange(int[] coins, int amount) {
int n = coins.length;
int[][] dp = new int[n+1][amount+1];
Arrays.fill(dp[0],Integer.MAX_VALUE / 2);
dp[0][0] = 0;
for(int i = 0;i < n;i++){
for(int j = 0;j <= amount;j++){
if(j < coins[i]){
dp[i+1][j] = dp[i][j];
}else{
dp[i+1][j] = Math.min(dp[i][j],dp[i+1][j - coins[i]]+1);
}
}
}
return dp[n][amount] >= Integer.MAX_VALUE/2 ? -1 : dp[n][amount];
}
}解法二、双数组
class Solution {
public int coinChange(int[] coins, int amount) {
int n = coins.length;
int[][] dp = new int[2][amount+1];
Arrays.fill(dp[0],Integer.MAX_VALUE / 2);
dp[0][0] = 0;
for(int i = 0;i < n;i++){
for(int j = 0;j <= amount;j++){
if(j < coins[i]){
dp[(i+1)%2][j] = dp[i%2][j];
}else{
dp[(i+1)%2][j] = Math.min(dp[i%2][j],dp[(i+1)%2][j - coins[i]]+1);
}
}
}
return dp[n%2][amount] >= Integer.MAX_VALUE/2 ? -1 : dp[n%2][amount];
}
}解法三、单数组
class Solution {
public int coinChange(int[] coins, int amount) {
int n = coins.length;
int[] dp = new int[amount+1];
Arrays.fill(dp,Integer.MAX_VALUE / 2);
dp[0] = 0;
for(int i = 0;i < n;i++){
for(int j = coins[i];j <=amount;j++){
if(j >= coins[i]){
dp[j] = Math.min(dp[j],dp[j - coins[i]]+1);
}
}
}
return dp[amount] >= Integer.MAX_VALUE/2 ? -1 : dp[amount];
}
}139. 单词拆分
解法一、
dp[j]的含义：0-j可以拆分并且从wordDict找到
class Solution {
public boolean wordBreak(String s, List<String> wordDict) {
int n = s.length();
boolean[] dp = new boolean[n+1];
dp[0] = true;
for(int i = 0;i < n;i++){
for(int j = i+1;j <= n;j++){
if(dp[i] && isE(s.substring(i,j),wordDict)){
dp[j]= true;
}
}
}
return dp[n];
}
private boolean isE(String s,List<String> wordDict){
for(String tmp : wordDict){
if(s.equals(tmp))return true;
}
return false;
}
}300. 最长递增子序列
解法一
class Solution {
public int lengthOfLIS(int[] nums) {
int n = nums.length;
int[] dp = new int[n];
int ans = 0;
for(int i = 0;i < n;i++){
for(int j = 0;j < i;j++){
if(nums[j] < nums[i]){
dp[i] = Math.max(dp[j],dp[i]);
}
}
ans = Math.max(ans,++dp[i]);
}
return ans;
}
}152. 乘积最大子数组
解法一
class Solution {
public int maxProduct(int[] nums) {
int n = nums.length;
int ans = nums[0];
int[] fMax = new int[n];
int[] fMin = new int[n];
fMin[0] = fMax[0] = nums[0];
for(int i = 1;i < n;i++){
fMax[i] = Math.max(Math.max(fMax[i - 1] * nums[i], fMin[i - 1] * nums[i]), nums[i]);
fMin[i] = Math.min(Math.min(fMax[i - 1] * nums[i], fMin[i - 1] * nums[i]), nums[i]);
ans = Math.max(fMax[i],ans);
}
return ans;
}
}32. 最长有效括号
解法一
class Solution {
public int longestValidParentheses(String s) {
int n = s.length(),ans = 0;
char[] c = s.toCharArray();
int[] dp = new int[n];
//dp[i][j] = 从i到j的括号有效
for(int i = 1;i < n;i++){
if(c[i] == ')'){
if(c[i-1] == '('){
dp[i] = 2;
if(i-2 > 0)dp[i]+=dp[i-2];
}
if(c[i-1] == ')' && i - dp[i-1] - 1 >= 0 && c[i - dp[i-1] - 1] == '(' ){
dp[i] = dp[i-1] + 2;
if(i - dp[i-1] - 2 >0)dp[i]+=dp[i - dp[i-1] - 2];
}
}
ans = Math.max(ans,dp[i]);
}
return ans;
}
}62. 不同路径
解法一
class Solution {
public int uniquePaths(int m, int n) {
int[][] dp = new int[m+1][n+1];
dp[0][1] = 1;
for(int i = 0;i < m;i++){
for(int j = 0;j < n;j++){
dp[i+1][j+1] = dp[i+1][j] + dp[i][j+1];
}
}
return dp[m][n];
}
}64. 最小路径和
解法一、
class Solution {
public int minPathSum(int[][] grid) {
int m = grid.length,n = grid[0].length;
int [][] dp = new int[m][n];
dp[0][0] = grid[0][0];
for(int i = 1;i < m;i++){
dp[i][0] = dp[i-1][0] + grid[i][0];
}
for(int j = 1;j < n;j++){
dp[0][j] = dp[0][j-1] + grid[0][j];
}
for(int i = 1;i < m;i++){
for(int j = 1;j < n;j++){
dp[i][j] = Math.min(dp[i-1][j],dp[i][j-1] )+ grid[i][j];
}
}
return dp[m-1][n-1];
}
}5. 最长回文子串
解法一
class Solution {
public String longestPalindrome(String s) {
char[] c = s.toCharArray();
int n = c.length;
int begin = 0, end = 0;
boolean[][] dp = new boolean[n][n];
for(int i = 0 ;i < n;i++){
for(int j = i;j >=0;j--){
if(c[i]==c[j] && (i - j <= 1 || dp[i-1][j+1] )){
dp[i][j] = true;
if(i - j > end - begin){
begin = j;
end = i;
}
}
}
}
return s.substring(begin,end+1);
}
}1143. 最长公共子序列
解法一
class Solution {
public int longestCommonSubsequence(String text1, String text2) {
int m = text1.length(),n = text2.length();
int[][] dp = new int [m+1][n+1];
for(int i = 0; i < m;i++){
for(int j = 0; j < n;j++){
if(text1.charAt(i) == text2.charAt(j)){
dp[i+1][j+1] = dp[i][j] + 1 ;
}else{
dp[i+1][j+1] = Math.max(dp[i][j+1], dp[i+1][j]);
}
}
}
return dp[m][n];
}
}72. 编辑距离
解法一、
class Solution {
public int minDistance(String word1, String word2) {
int m = word1.length(),n = word2.length();
int[][] dp = new int[m+1][n+1];
for(int i = 0;i <= m;i++){
dp[i][0] = i;
}
for(int j = 0;j <= n;j++){
dp[0][j] = j;
}
for(int i = 0;i < m;i++){
for(int j = 0;j < n;j++){
dp[0][j+1] = j+1;
if(word1.charAt(i) == word2.charAt(j)){
dp[i+1][j+1] = dp[i][j];
}else{
dp[i+1][j+1] = Math.min(Math.min(dp[i][j+1],dp[i+1][j]),dp[i][j])+1;
}
}
}
return dp[m][n];
}
}
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