Given a string S, find the longest palindromic substring in S. You may assume that the maximum length of S is 1000, and there exists one unique longest palindromic substring.
原题
这题开始想用递归,没写出来,看了题解,原来可以用动态规划,但是用vector存储的时候会超时,需要优化下存储结构。
不太懂下面这种用递归做的方法?
#include <algorithm>
#include <iostream>
#include <map>
#include <string.h>
#include <string>
#include <vector>
using namespace std;
string find_palimdrom(string s, int left, int right) {
int n = s.size();
int l = left;
int r = right;
while (l >= 0 && r <= n - 1 && s[l] == s[r]) {
l--;
r++;
}
return s.substr(l + 1, r - l - 1);
}
string palimdrom_recursive_way(string s) {
if (s.size() <= 1)
return s;
string longest, str;
int n = s.size();
for (int i = 0; i < n; i++) {
str = find_palimdrom(s, i, i);
if (str.size() > longest.size())
longest = str;
str = find_palimdrom(s, i, i + 1);
if (str.size() > longest.size())
longest = str;
}
return longest;
}
//但是使用vector在leetcode上会超时
string palimdrom_DP_way(string s) {
int n = s.size();
if (n <= 1)
return s;
vector<vector<bool>> matrix(n, vector<bool>(n));
string longest;
for (int i = n - 1; i >= 0; i--) {
for (int j = i; j < n; j++) {
if (i == j || (j - i < 2 && s[i] == s[j]) ||
(s[i] == s[j] && matrix[i + 1][j - 1])) {
matrix[i][j] = true;
if (longest.size() < j - i + 1)
longest = s.substr(i, j - i + 1);
}
}
}
return longest;
}
//优化版:优化的存储方式
string palimdrom_DP_OP_way(string s) {
// Construct a matrix, and consdier matrix[j][i] as s[i] -> s[j] is Palindrome
// or not.
// ------^^^^^^
// NOTE: it's [j][i] not [i][j]
bool **matrix = new bool *[n];
int start, end;
for (int i = 0; i < n; i++) {
matrix[i] = new bool[i + 1];
memset(matrix[i], false, (i + 1) * sizeof(bool));
matrix[i][i] = true;
for (int j = 0; j < i; j++) {
if (i == j || (s[j] == s[i] && (i - j < 2 || matrix[i - 1][j + 1]))) {
matrix[i][j] = true;
if (len < i - j + 1) {
start = j;
len = i - j + 1;
}
}
}
}
for (int i = 0; i < n; i++) {
delete[] matrix[i];
}
delete[] matrix;
return s.substr(start, len);
}
int main() {
string s;
cin >> s;
// cout << palimdrom_recursive_way(s) << endl;
// cout << palimdrom_DP_way(s).size() << endl;
cout << palimdrom_recursive_way(s).size() << endl;
}