<p>Given a string <code>s</code>, return <em>the longest</em> <span data-keyword="palindromic-string"><em>palindromic</em></span> <span data-keyword="substring-nonempty"><em>substring</em></span> in <code>s</code>.</p>

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

<pre>
<strong>Input:</strong> s = &quot;babad&quot;
<strong>Output:</strong> &quot;bab&quot;
<strong>Explanation:</strong> &quot;aba&quot; is also a valid answer.
</pre>

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

<pre>
<strong>Input:</strong> s = &quot;cbbd&quot;
<strong>Output:</strong> &quot;bb&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> consist of only digits and English letters.</li>
</ul>

class Solution {
public:
    string longestPalindrome(string s) {
        uint32_t startIndex = 0;
        uint32_t endIndex = 0;
        for (uint32_t i=0; i<s.size(); i++) {
            for (uint32_t j=i; j<s.size(); j++) {
                if (isPalindrome(s, i, j)) {
                    const auto candidateLength = j - i;
                    const auto longestLength = endIndex - startIndex;
                    if (candidateLength > longestLength) {
                        startIndex = i;
                        endIndex = j;
                    }
                }
            }
        }

        std::string result;
        for (uint32_t i=startIndex; i<=endIndex; i++) {
            result += s[i];
        }

        return result;
    }

private:
    std::unordered_set<uint64_t> knownPalindromes;

    bool isPalindrome(const string& str, uint32_t startIndex, uint32_t endIndex) {
        const auto key = cacheKey(startIndex, endIndex);
        if (startIndex == endIndex) {
            return true;
        } else if (knownPalindromes.contains(key)) {
            return true;
        } else if (str[startIndex] == str[endIndex]) {
            const auto result = (endIndex > startIndex + 1)
                ? isPalindrome(str, startIndex+1, endIndex-1)
                : true;
            if (result) {
                knownPalindromes.insert(key);
            }

            return result;
        } else {
            return false;
        }
    }

    uint64_t cacheKey(uint32_t startIndex, uint32_t endIndex) {
        return (static_cast<uint64_t>(startIndex) << 32) | endIndex;
    }
};
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