解决思路

二维动态规划

 public int minPathSum(int[][] grid) {
        int R = grid.length;
        int C = grid[0].length;
        int[][] dp = new int[R][C];
        for (int i = R - 1;i >= 0;i--){
            for (int j = C - 1;j >= 0;j--){
                if (i == R - 1 && j == C - 1)
                    dp[i][j] = grid[i][j];
                else if (i == R - 1 && j != C - 1)
                    dp[i][j] = dp[i][j + 1] + grid[i][j];
                else if (j == C - 1 && i != R - 1)
                    dp[i][j] = dp[i + 1][j] + grid[i][j];
                else
                    dp[i][j] = Math.min(dp[i + 1][j],dp[i][j + 1]) + grid[i][j];
            }
        }
        return dp[0][0];
    }

一维动态规划

 public int minPathSum(int[][] grid) {
       int[] dp = new int[grid[0].length];
       for (int i = grid.length - 1; i >= 0; i--) {
           for (int j = grid[0].length - 1; j >= 0; j--) {
               if(i == grid.length - 1 && j != grid[0].length - 1)
                   dp[j] = grid[i][j] +  dp[j + 1];
               else if(j == grid[0].length - 1 && i != grid.length - 1)
                   dp[j] = grid[i][j] + dp[j];
               else if(j != grid[0].length - 1 && i != grid.length - 1)
                   dp[j] = grid[i][j] + Math.min(dp[j], dp[j + 1]);
               else
                   dp[j] = grid[i][j];
           }
       }
       return dp[0];
   }

动态规划（不需要额外存储空间）

 public int minPathSum(int[][] grid) {
        for (int i = grid.length - 1; i >= 0; i--) {
            for (int j = grid[0].length - 1; j >= 0; j--) {
                if(i == grid.length - 1 && j != grid[0].length - 1)
                    grid[i][j] = grid[i][j] +  grid[i][j + 1];
                else if(j == grid[0].length - 1 && i != grid.length - 1)
                    grid[i][j] = grid[i][j] + grid[i + 1][j];
                else if(j != grid[0].length - 1 && i != grid.length - 1)
                    grid[i][j] = grid[i][j] + Math.min(grid[i + 1][j],grid[i][j + 1]);
            }
        }
        return grid[0][0];
    }