Minimum Path Sum

標籤：

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.

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

 1 public class Solution { 2     /** 3      * @param grid: a list of lists of integers. 4      * @return: An integer, minimizes the sum of all numbers along its path 5      */ 6     public int minPathSum(int[][] grid) { 7         if (grid == null) return 0; 8          9         // initialize the first row10         int [][] min = new int[grid.length][grid[0].length];11         12         min[0][0] = grid[0][0];13         14         for (int i = 1; i < grid[0].length; i++) {15             min[0][i] = min[0][i - 1] + grid[0][i];16         }17         18         for (int i = 1; i < grid.length; i++) {19             min[i][0] = min[i - 1][0] + grid[i][0];20         }21         22         for (int i = 1; i < grid.length; i++) {23             for (int j = 1; j < grid[0].length; j++) {24                 min[i][j] = (int)Math.min(min[i - 1][j], min[i][j - 1]) + grid[i][j];25             }26         }27         28         return min[grid.length - 1][grid[0].length - 1];29     }30 }

 

Minimum Path Sum