<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 isPalindromic(string& str, unordered_map<string, int>& cache) {
        auto iter = cache.find(str);
        if(cache.end() != iter) {
            return iter->second;
        }
        for(int i=0;i!=str.size()/2;++i) {
            if(str[i] != str[str.size()-1-i]) {
                cache[str] = 0;
                return 0;
            }
        }
        cache[str] = 1;
        return 1;
    }
    int dfs(string& s, string& temp, int index, unordered_map<string, int>& cache) {
        if(index >= s.size()) {
            return 0;
        }
        temp += s[index];
        return isPalindromic(temp, cache) + dfs(s, temp, index+1, cache);
    }
    int countSubstrings(string s) {
        int ans = 0;
        unordered_map<string, int> cache{};
        for(int i=0;i!=s.size();++i) {
            string temp{};
            ans += dfs(s, temp, i, cache);
        }
        return ans;
    }
};
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