WEI-CHENG CHEN

說明：

他依樣是往右往下走，然後要一找最短值

解法：二維 DP

class Solution {
public:
    int minPathSum(vector<vector<int>>& grid) {
        int m = grid.size(), n = grid[0].size();
        vector<vector<int>> v(m, vector<int>(n,0));
        v[0][0] = grid[0][0];

        for (int i = 1; i < m; ++i) {
            v[i][0] = v[i-1][0] + grid[i][0];
        }
        for (int j = 1; j < n; ++j) {
            v[0][j] = v[0][j-1] + grid[0][j];
        }
        for (int i = 1; i < m; ++i) {
            for (int j = 1; j < n; ++j) {
                v[i][j] = min(v[i-1][j], v[i][j-1]) + grid[i][j];
            }
        }
        return v[m-1][n-1];
    }
};

解法：一維 DP

class Solution {
public:
    int minPathSum(vector<vector<int>>& grid) {
        int m = grid.size(), n = grid[0].size();
        vector<int> dp(n, 0);
        dp[0] = grid[0][0];

        // 跑row=1(把值填進去)
        for(int i=1;i<n;i++){
            dp[i] = dp[i-1] + grid[0][i];
        }

        for(int i=1;i<m;i++){
            dp[0] = dp[0] + grid[i][0];
            for(int j=1;j<n;j++){
                dp[j] = min(dp[j], dp[j-1]) + grid[i][j];
            }
        }
        return dp[n-1];
    }
};