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.

稍加改进变成一个简单版的迷宫问题。

public static void main(String[] args) { int[][] a = new int[][]{{1,1,0,0,0},{1,3,1,0,1},{1,1,4,1,1},{0,2,0,1,0},{0,1,1,1,1}}; search(a);}public static int search(int[][] a){if(a.length==0){return 0;}int r= a.length;int c= a[0].length;int[][] cost= new int[r][c];cost[0][0]=a[0][0];int flag=0;for (int i = 1; i < c; i++) {if(flag==1){cost[0][i]=Integer.MAX_VALUE;//表示此路不通}if(a[0][i]==0&&flag==0){cost[0][i]=Integer.MAX_VALUE;//表示此路不通flag=1;}if(flag==0){cost[0][i]=cost[0][i-1]+a[0][i];}}flag=0;for (int i = 1; i < r; i++) {if(flag==1){cost[i][0]=Integer.MAX_VALUE;}if(a[i][0]==0&&flag==0){cost[i][0]=Integer.MAX_VALUE;flag=1;}if(flag==0){cost[i][0]=cost[0][i-1]+a[i][0];}}for (int i =1 ; i < r; i++) {for (int j = 1; j < c; j++) {if(a[i][j]==0){cost[i][j]=Integer.MAX_VALUE;}else{if(cost[i-1][j]==Integer.MAX_VALUE&&cost[i][j-1]==Integer.MAX_VALUE){cost[i][j]=Integer.MAX_VALUE;}else{cost[i][j] = Math.min(cost[i-1][j], cost[i][j-1])+a[i][j];}}}}System.out.println(cost[r-1][c-1]);return cost[r-1][c-1];}