64. Minimum Path Sum

    /*
     * 64. Minimum Path Sum
     * 12.20 by Mingyang 
     * 这道题目我完全使用的Unique Path的框架在构造的
     */
    public int minPathSum(int[][] grid) {
        int m = grid.length;
        int n = grid[0].length;
        int[][] dp = new int[m][n];
        dp[0][0] = grid[0][0];
        // 只有一行时，到终点每个格子只有一种走法
        for (int i = 1; i < n; i++)
            dp[0][i] = dp[0][i - 1] + grid[0][i];
        // 只有一列时，到终点每个格子只有一种走法
        for (int i = 1; i < m; i++)
            dp[i][0] = dp[i - 1][0] + grid[i][0];
        // for each body node, number of path = paths from top + paths from left
        for (int i = 1; i < m; i++) {
            for (int j = 1; j < n; j++) {
                dp[i][j] = Math.min(dp[i - 1][j], dp[i][j - 1]) + grid[i][j];
            }
        }
        return dp[m - 1][n - 1];
    }