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5.cpp
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5.cpp
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// 5. Longest Palindromic Substring
#include <iostream>
#include <vector>
#include <string>
using namespace std;
class Solution
{
public:
string longestPalindrome(string s)
// We define dp(i,j)
// dp(i,j) as following:
// dp[i,j] = 1 if i ==j
// = s[i] == s[j] if j = i+1
// = s[i] == s[j] && dp[i+1][j-1] if j>i+1
// dp(0,0) = True
{
int n = s.size();
if (n <= 1)
{
return s;
}
int start;
int max_length = 0;
vector<bool> row(n, false);
vector<vector<bool>> dp(n, row);
{
for (size_t i = 0; i < s.size(); i++)
{
dp[i][i] = true;
for (size_t j = 0; j < i; j++)
{
dp[j][i] = (s[i] == s[j]) and ((i - j == 1) or (dp[j + 1][i - 1]));
if (dp[j][i] and max_length < (i - j + 1))
{
max_length = i - j + 1;
start = j;
}
}
}
}
// corner case
if (max_length == 0)
{
return s.substr(start, 1);
}
return s.substr(start, max_length);
}
};
int main()
{
Solution s = Solution();
string t = "babad";
string r = s.longestPalindrome(t);
cout << t << "should be 'bab' : " << r << "\n"
<< endl;
t = "cbbd";
r = s.longestPalindrome(t);
cout << t << "should be 'bb' : " << r << "\n"
<< endl;
t = "ac";
r = s.longestPalindrome(t);
cout << t << "should be 'a' : " << r << "\n"
<< endl;
return 0;
}