Minimum Path Sum

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.

 

 1 public class Solution {

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

 3         // Start typing your Java solution below

 4         // DO NOT write main() function

 5         //[m,n] = (m,n) + min([m-1,n],[m,n-1])

 6         //only can move right or down

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

 8         int m = grid.length;

 9         int n = grid[0].length;

10         int[][] map = new int[m][n];

11         for(int i = 0; i < m; i ++){

12             map[i][0] = grid[i][0];

13             if(i > 0) map[i][0] += map[i - 1][0];

14         }

15         for(int j = 1; j < n; j ++){

16             map[0][j] = map[0][j - 1] + grid[0][j];

17         }

18         for(int i = 1; i < m; i ++){

19             for(int j = 1; j < n; j ++){

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

21             }

22         }

23         return map[m - 1][n - 1];

24     }

25 }

 第二遍：

 1 public class Solution {

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

 3         // Start typing your Java solution below

 4         // DO NOT write main() function

 5         //[m,n] = (m,n) + min([m-1,n],[m,n-1])

 6         //only can move right or down

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

 8         int m = grid.length;

 9         int n = grid[0].length;

10         int[][] map = new int[m][n];

11         for(int i = 0; i < m; i ++){

12             for(int j = 0; j < n; j ++){

13                 map[i][j] = grid[i][j];

14                 if(i > 0 && j > 0) map[i][j] += Math.min(map[i - 1][j], map[i][j - 1]);

15                 else if(i > 0) map[i][j] += map[i - 1][j];

16                 else if(j > 0) map[i][j] += map[i][j - 1];

17             }

18         }

19         return map[m - 1][n - 1];

20     }

21 }

 第三遍：

 1 public class Solution {

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

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

 4         int m = grid.length, n = grid[0].length;

 5         int[][] result = new int[m][n];

 6         result[0][0] = grid[0][0];

 7         for(int i = 0; i < m; i ++)

 8             for(int j = 0; j < n; j ++)

 9                 if(i != 0 || j != 0){

10                     int aa = i > 0 ? result[i - 1][j] : Integer.MAX_VALUE;

11                     int bb = j > 0 ? result[i][j - 1] : Integer.MAX_VALUE;

12                     result[i][j] = Math.min(aa, bb) + grid[i][j];

13                 }

14         return result[m - 1][n - 1];

15     }

16 }