Minimum Path Sum——LeetCode

Given a m x n grid filled with non-negative numbers, find a path from top left to bottom right which minimizes the sum of all numbers along its path.

Note: You can only move either down or right at any point in time.

 

题目大意：给定一个m*n矩阵，都是非负数字，找到一条路径从左上角到右下角路径和最小，路径只能向右或向下走。

解题思路：基础dp题，用一个二维数组记录到当前位置最小路径和，取决于当前位置的左边和上边的最小路径和，注意处理矩阵最左边和最上边的。

    public int minPathSum(int[][] grid) {

        if (grid == null || grid[0].length == 0)

            return 0;

        int rowLen = grid.length;

        int colLen = grid[0].length;

        int[][] sum = new int[rowLen][colLen];

        sum[0][0] = grid[0][0];

        for (int i = 0; i < rowLen; i++) {

            for (int j = 0; j < colLen; j++) {

                if (i > 0 && j > 0)

                    sum[i][j] = Math.min(sum[i - 1][j], sum[i][j - 1]) + grid[i][j];

                else if (i == 0 && j > 0) {

                    sum[i][j] = sum[i][j - 1] + grid[i][j];

                } else if (i > 0 && j == 0) {

                    sum[i][j] = sum[i - 1][j] + grid[i][j];

                }

            }

        }

        return sum[rowLen - 1][colLen - 1];

    }