## Problem

Problem ID: 647

Title: Palindromic Substrings

Difficulty: Medium

Description: Given a string s, return the number of palindromic substrings in it.

A string is a palindrome when it reads the same backward as forward.

A substring is a contiguous sequence of characters within the string.

## Thoughts

I initially went with the solution of maintaining a forward and backward deque. For each index we will treat it as the head and keep traversing the characters and check if it is palindrome but checking if both deque are equal. However, I failed to realise that comparing deque is a O(N) operation and my solution would result in O(N^3) time complexity.

Take aways:

• Comparing equality of data structure is O(N) operation
• A string is a palindrome if and only if the inner substring is a palindrome
• When dealing with a palindrome, a string of different parity (even/odd) in length should be dealt differently.

## Solution

If a string is a palindrome, then its inner string(exclude start and end) must be a palindrome as well. A tricky edge case to take note is that the base case is when the string is of size 2.

### Implementation

class Solution {
public:
int countSubstrings(string s) {
int ans = 0;
int n = s.size();
vector<vector<bool>> dp(n, vector<bool>(n+1, false));
for (int i = 0; i < n ;i++) {

dp[i][1] = true;
ans++;
}
for (int i = 0; i < n-1; i++) {
if (s[i] == s[i+1]) {
ans++;
dp[i][2] = true;
}

}
for (int length = 3; length <= n; length++) {
for (int start = 0; start < n; start++) {
if (start + length > n) continue;
int end = start + length -1;
int inner_start = start+1;
int inner_length = length -2;
if (s[start] != s[end]) continue;
if (!dp[inner_start][inner_length]) continue;
ans++;
dp[start][length] = true;
}
}
return ans;
}
};