64. Minimum Path Sum

 只初始化（0,0）

class Solution {
public:
    int minPathSum(vector<vector<int>>& grid) {
        int height = grid.size();
        int width = grid[0].size();
        vector<vector<int>> result(height,vector<int>(width));
        result[0][0] = grid[0][0];
        for(int i = 0;i < height;i++){
            for(int j = 0;j < width;j++){
                if(i != 0 && j != 0)
                    result[i][j] = min(result[i][j-1],result[i-1][j]) + grid[i][j];
                else if(i == 0)
                    result[i][j] = result[i][j-1] + grid[i][j];
                else
                    result[i][j] = result[i-1][j] + grid[i][j];
            }
        }
        return result[height-1][width-1];
    }
};

 初始化第一行，第一列

class Solution {
public:
    int minPathSum(vector<vector<int>>& grid) {
        int length = grid.size();
        if(length <= 0)
            return 0;
        int width = grid[0].size();
        vector<vector<int>> result(length,vector<int>(width));
        result[0][0] = grid[0][0];
        for(int i = 1;i < width;i++)
            result[0][i] = result[0][i-1] + grid[0][i];
        for(int j = 1;j < length;j++)
            result[j][0] = result[j-1][0] + grid[j][0];
        for(int i = 1;i < length;i++){
            for(int j = 1;j < width;j++){
                result[i][j] = min(result[i-1][j],result[i][j-1]) + grid[i][j];
            }
        }
        return result[length-1][width-1];
    }
};