<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) {
        //T-O(n^2), S-O(n)
        std::vector<int> prev(s.size(), 0);
        int total = 0;
        for(int i=s.size()-1; i>=0; --i) {
            std::vector<int> curr(s.size(), 0);
            for(int j=i; j<s.size(); ++j) {
                if(i == j) curr[j] = 1;
                else if(i+1 == j) curr[j] = (s[i] == s[j]) ? 1 : 0;
                else curr[j] = (s[i] == s[j]) ? prev[j-1] : 0;

                total += curr[j];
            }
            prev = curr;
        }
        return total;
    }
};
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