不知道又犯了什么弱智错，求大佬指教 Orz

#include <iostream>
#include <cstring>
#include <stdio.h>
#include <string>
using namespace std;
const int S = 55;
int n, f[S][S];
string a;
int main() {
	memset(f, 0x3f, sizeof(f));
	cin >> a;
	n = a.size();
	a = ' ' + a;
	for (int i = 1; i <= n; i++) {
		f[i][i] = 1;
	}
	for (int l = 2; l <= n; l++) {
		for (int i = 1; i <= n; i++) {
			int j = i + l - 1;
			if (a[i] == a[j]) {
				f[i][j] = min(f[i + 1][j], f[i][j - 1]);
			}
			for (int k = i; k <= j - 1; k++) {
				f[i][j] = min(f[i][j], f[i][k] + f[k + 1][j]);
			}
		}
	}
	printf("%d", f[1][n]);
	return 0;
}