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];
}