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];
	}