120. 三角形最小路径和

//看成一个下三角形
class Solution 
{
public:
    int minimumTotal(vector<vector<int>>& triangle) 
    {
        int n = triangle.size();
        int res = INT_MAX;
        vector<vector<int>> dp(n,vector<int>(n,0));
        
        dp[0][0] = triangle[0][0];//初始化
        for(int i = 1;i < n;i ++) dp[i][0] = dp[i - 1][0] + triangle[i][0];    //初始化第一列
        for(int j = 1;j < n;j ++) dp[j][j] = dp[j - 1][j - 1] + triangle[j][j];//初始化主对角线

        for(int i = 2;i <= n - 1;i ++)
        {
            for(int j = 1;j < i; j++) dp[i][j] = triangle[i][j] + min(dp[i - 1][j],dp[i - 1][j - 1]);
        }

        for(int j = 0;j < n;j ++) res = min(res,dp[n - 1][j]);//最后一行求最小值
        return res;
    }
};