class Solution {
public:
	int minCut(string s) {
		//先求解小段的子序列
		vector<vector<int>> dp(s.length(), vector<int>(s.length()));  //存放最小切割數
		vector<vector<bool>> p(s.length(), vector<bool>(s.length(), false));  //存放是否是迴文
		for (int t = 0;t <= s.length();t++) {
			for (int i = 0, j = t;j<s.length();i++, j++) {
				dp[i][j] = compCut(i, j, s, p, dp);
			}
		}
		return dp[0][s.length() - 1];
	}

	// 狀態轉移方程的實現
	int compCut(int i, int j, string &s, vector<vector<bool>> &p, vector<vector<int>> &dp) {
		if (s[i] == s[j] && (j - i < 2 || p[i + 1][j - 1])) {
			p[i][j] = true;
			return 0;
		}
		int min = s.length();
		for (int k = i; k < j; ++k) {
			int a = dp[i][k];
			int b = dp[k + 1][j];
			a = a + b + 1;
			min = min<a ? min : a;
		}
		return min;
	}
};


/*
class Solution {
public:
	int minCut(string s) {
		vector<int> dp(s.length() + 1);
		vector<vector<bool>> p(s.length(), vector<bool>(s.length(), false));
		dp[s.length()] = -1;//確保dp[s.length()-1]=0
		for (int i = s.length() - 1; i >= 0; --i) {
			//下面i==j時肯定是迴文，一定會被替換掉，所以不用去初始化為s.length()-i-1
			dp[i] = INT_MAX;  
			for (int j = i; j < s.length(); ++j) {
				if (s[i] == s[j] && (j - i < 2 || p[i+1][j-1])) {
					dp[i] = min(dp[i], dp[j + 1] + 1);
					p[i][j] = true;
				}
			}
		}
		return dp[0];
	}
};
*/