65 lines
1.5 KiB
C++
65 lines
1.5 KiB
C++
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// Linear Time algorithms for longestPalindrome in a string problem. It is one of the standard algorithms but is not very intuitive.
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#include <vector>
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#include <iostream>
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#include <cstring>
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using namespace std;
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// Transform S into T.
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// For example, S = "abba", T = "^#a#b#b#a#$".
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// ^ and $ signs are sentinels appended to each end to avoid bounds checking
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string preProcess(string s) {
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int n = s.length();
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if (n == 0) return "^$";
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string ret = "^";
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for (int i = 0; i < n; i++)
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ret += "#" + s.substr(i, 1);
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ret += "#$";
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return ret;
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}
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string longestPalindrome(string s) {
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string T = preProcess(s);
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int n = T.length();
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int *P = new int[n];
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int C = 0, R = 0;
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for (int i = 1; i < n-1; i++) {
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int i_mirror = 2*C-i; // equals to i' = C - (i-C)
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P[i] = (R > i) ? min(R-i, P[i_mirror]) : 0;
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// Attempt to expand palindrome centered at i
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while (T[i + 1 + P[i]] == T[i - 1 - P[i]])
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P[i]++;
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// If palindrome centered at i expand past R,
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// adjust center based on expanded palindrome.
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if (i + P[i] > R) {
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C = i;
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R = i + P[i];
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}
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}
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// Find the maximum element in P.
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int maxLen = 0;
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int centerIndex = 0;
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for (int i = 1; i < n-1; i++) {
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if (P[i] > maxLen) {
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maxLen = P[i];
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centerIndex = i;
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}
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}
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delete[] P;
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return s.substr((centerIndex - 1 - maxLen)/2, maxLen);
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}
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int main() {
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string text = "babcbabcbaccba";
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std::cout << longestPalindrome(text)<< endl;
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}
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