<p>You are given a string <code>s</code>. You can convert <code>s</code> to a <span data-keyword="palindrome-string">palindrome</span> by adding characters in front of it.</p>

<p>Return <em>the shortest palindrome you can find by performing this transformation</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<pre><strong>Input:</strong> s = "aacecaaa"
<strong>Output:</strong> "aaacecaaa"
</pre><p><strong class="example">Example 2:</strong></p>
<pre><strong>Input:</strong> s = "abcd"
<strong>Output:</strong> "dcbabcd"
</pre>
<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>0 &lt;= s.length &lt;= 5 * 10<sup>4</sup></code></li>
	<li><code>s</code> consists of lowercase English letters only.</li>
</ul>

#include <string>
#include <algorithm>

class Solution {
public:
    std::string shortestPalindrome(const std::string& s) {
        unsigned d = 16777619; // Hash base
        unsigned h = 0; // Hash for the original string
        unsigned rh = 0; // Hash for the reversed string
        unsigned p = 1; // Power for the reversed hash
        unsigned maxLen = 0; // Maximum length of palindrome prefix

        // Compute hashes
        for (size_t i = 0; i < s.size(); ++i) {
            h = h * d + s[i];
            rh = rh + s[i] * p;
            p *= d;
            if (h == rh) {
                maxLen = i + 1; // Update the length of the palindrome prefix
            }
        }

        // Construct the shortest palindrome
        std::string suffix = s.substr(maxLen);
        std::reverse(suffix.begin(), suffix.end());
        return suffix + s;
    }
};

static const auto optimizeIO = []() {
    std::ios::sync_with_stdio(false);
    std::cin.tie(nullptr);
    std::cout.tie(nullptr);
    return 0;
}();

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