<p>Given a string <code>s</code>, return <em>the number of <strong>palindromic substrings</strong> in it</em>.</p>

<p>A string is a <strong>palindrome</strong> when it reads the same backward as forward.</p>

<p>A <strong>substring</strong> is a contiguous sequence of characters within the string.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> s = &quot;abc&quot;
<strong>Output:</strong> 3
<strong>Explanation:</strong> Three palindromic strings: &quot;a&quot;, &quot;b&quot;, &quot;c&quot;.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> s = &quot;aaa&quot;
<strong>Output:</strong> 6
<strong>Explanation:</strong> Six palindromic strings: &quot;a&quot;, &quot;a&quot;, &quot;a&quot;, &quot;aa&quot;, &quot;aa&quot;, &quot;aaa&quot;.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= s.length &lt;= 1000</code></li>
	<li><code>s</code> consists of lowercase English letters.</li>
</ul>

class Solution {
public:
    int countSubstrings(string s) {
        int len=s.length();
        vector<vector<bool>>dp(len,vector<bool>(len,false));
        vector<vector<int>>count_dp(len,vector<int>(len,0));
        for(int i=0;i<len;i++){
            dp[i][i]=true;
            count_dp[i][i]=1;
        }
        for(int i=0;i<len-1;i++){
            count_dp[i][i+1]=2;
            if(s[i]==s[i+1]){
                dp[i][i+1]=true;
                count_dp[i][i+1]+=1;
            }
        }
        for(int gap=3;gap<=len;gap++){
            for(int i=0;i<=len-gap;i++){
                int start=i;
                int end=i+gap-1;
                count_dp[start][end]=count_dp[start+1][end]+count_dp[start][end-1]
                                        -count_dp[start+1][end-1];
                if(s[start]==s[end] && dp[start+1][end-1]){
                    count_dp[start][end]+=1;
                    dp[start][end]=true;
                }
            }
        }
        return count_dp[0][len-1];
    }
};

// class Solution {
// public:
//     int countSubstrings(string s) {
//         int len=s.length();
//         vector<vector<bool>>dp(len,vector<bool>(len,false));
//         vector<vector<int>>count_dp(len,vector<int>(len,0));
//         for(int i=0;i<len;i++){
//             dp[i][i]=true;
//             count_dp[i][i]=1;
//         }
//         for(int gap=1;gap<len;gap++){
//             for(int i=0;i<len-gap;i++){
//                 int start=i;
//                 int end=i+gap;
//                 count_dp[start][end]=count_dp[start+1][end]+count_dp[start][end-1]-count_dp[start+1][end-1];
//                 if(s[start]==s[end] && ((start+1==end) || dp[start+1][end-1])){
//                     count_dp[start][end]+=1;
//                     dp[start][end]=true;
//                 }
//             }
//         }
//         for(int i=0;i<len;i++){
//             for(int j=0;j<len;j++){
//                 cout<<count_dp[i][j]<<" ";
//             }
//             cout<<endl;
//         }
//         return count_dp[0][len-1];
//     }
// };
38911