120_minimumTotal.txt

class Solution {
public:
    int minimumTotal(vector<vector<int>>& triangle) {
        //经典动态规划
        int n = triangle.size();
        vector<vector<int>> dp(n, vector<int>(n));
        dp[0][0] = triangle[0][0];
        for(int i = 1;i<n;++i){
            dp[i][0] = dp[i-1][0] + triangle[i][0];//该行最左侧
            for(int j = 1;j < i;++j){
                dp[i][j] = min(dp[i-1][j-1], dp[i-1][j]) + triangle[i][j];
            }
            dp[i][i] = dp[i-1][i-1] + triangle[i][i];//该行最右侧
        }
        return *min_element(dp[n-1].begin(),dp[n-1].end());
    }
};

class Solution {
public:
    int minimumTotal(vector<vector<int>>& triangle) {
        //经典动态规划,空间优化
        int n = triangle.size();
        vector<int> f(n);
        f[0] = triangle[0][0];
        for (int i = 1; i < n; ++i){
            f[i] = f[i - 1] + triangle[i][i];
            for (int j = i - 1; j > 0; --j) {
                f[j] = min(f[j - 1], f[j]) + triangle[i][j];
            }
            f[0] += triangle[i][0];
        }
        return *min_element(f.begin(), f.end());
    }
};