ORIGIN

LeetCode 5. Longest Palindromic Substring

2023-03-16

ACM DP Brute Force Center Expand 3 mins565 words

Problem Description

https://leetcode.com/problems/longest-palindromic-substring/

Brute Force

Loop for each possible substring, check if its a palindromic string, But it is not suitable for this problem, it will get TLE.

Code

class Solution {
public:
    string longestPalindrome(string s) {
        int maxLen = 1;
        int left = 0;
        for(int i = 0; i < s.length() - 1; i ++) {
            for(int j = i  + 1; j < s.length(); j ++) {
                int len = (j - i + 1);
                if(len > maxLen && isPalindromic(s, i, j)) {
                    maxLen = len;
                    left = i;
                }
            }
        }
        return s.substr(left, maxLen);
    }
    bool isPalindromic(string s, int left, int right) {
        while(left < right) {
            if(s[left] != s[right]) {
                return false;
            }
            left ++, right --;
        }
        return true;
    }
};

Center Expand

Palindromic string has two situations:

the center is a character
the center is the gap between two character

So we loop each index to check the two situations by expanding the index from the centers to see how long can is the palindromic string

Code

class Solution {
public:
    string longestPalindrome(string s) {
        if(s.length() < 2) return s;
        int maxLen = 1;
        int left = 0;
        for(int i = 0; i < s.length() - 1; i ++) {
            int len1 = centerExpand(s, i, i);
            int len2 = centerExpand(s, i, i + 1);
            int maxn = max(len1, len2);
            if(maxn > maxLen) {
                maxLen = maxn;
                left = i - (maxLen - 1) / 2;
            }
        }
        return s.substr(left, maxLen);
    }
    int centerExpand(string s, int left, int right) {
        while(left >= 0 and right < s.length() and s[left] == s[right]) {
            left --;
            right ++;
        }
        return right - left - 1;
    } 
};

DP

There is a regular pattern: if the string s is a palindromic string, then after removing the head and tail character, the rest string is still a palindromic string.

We use dp[i][j] to represents if the the substring s[i, j] a palindromic string.

So, dp[i][j] is based on s[i] == s[j] && dp[i+1][j-1]

And the i+1 , j-1 must be form a legal string, so j-1 - (i+1) >= 2 => j - i >= 3

First, the diagonal means the character itself, so it should be true;

	0	1	2	3	4
0	true
1		true
2			true
3				true
4					true

So we can just fill the form, fill them by column, and in each column fill in ascending order. ( babab )

	0	1	2	3	4
0	true	false	true	false
1		true	false	true
2			true	false
3				true
4					true

Code

class Solution {
public:
    string longestPalindrome(string s) {
        if(s.length() < 2) return s;
        int maxLen = 1;
        int left = 0;
        int len = s.length();
        vector<vector<bool>> dp(len, vector<bool>(len));
        for(int i = 0; i < len; i ++) dp[i][i] = true;
        for(int j = 1; j < len; j ++) {
            for(int i = 0; i < j; i ++) {
                if(s[i] != s[j]) {
                    dp[i][j] = false;
                    continue;
                }
                if(j - i < 3) {
                    dp[i][j] = true;
                } else {
                    dp[i][j] = dp[i+1][j-1];
                }
                if(dp[i][j] && j - i + 1 > maxLen) {
                    maxLen = j - i + 1;
                    left = i;
                }
            }
        }
        return s.substr(left, maxLen);
    }
};