2013
11-13

# Labeling Balls

Windy has N balls of distinct weights from 1 unit to N units. Now he tries to label them with 1 to N in such a way that:

1. No two balls share the same label.
2. The labeling satisfies several constrains like “The ball labeled with a is lighter than the one labeled with b”.

Can you help windy to find a solution?

The first line of input is the number of test case. The first line of each test case contains two integers, N (1 ≤ N ≤ 200) and M (0 ≤ M ≤ 40,000). The next M line each contain two integers a and b indicating the ball labeled with a must be lighter than the one labeled with b. (1 ≤ a, bN) There is a blank line before each test case.

For each test case output on a single line the balls’ weights from label 1 to label N. If several solutions exist, you should output the one with the smallest weight for label 1, then with the smallest weight for label 2, then with the smallest weight for label 3 and so on… If no solution exists, output -1 instead.

5

4 0

4 1
1 1

4 2
1 2
2 1

4 1
2 1

4 1
3 2


1 2 3 4
-1
-1
2 1 3 4
1 3 2 4


/* @author: */
import java.util.Scanner;
import java.util.Arrays;
public class Main{
int degree[]=new int[210];
boolean visit[][]=new boolean[210][210];
int path[]=new int[210];
int n,m,t;

void topsort(){
for(int k=n;k>=1;k--){
int i=n;
while(i>=1 && degree[i]!=0) i--;
if(i< 1){ System.out.printf("-1\n"); return; }
degree[i]=-1;
path[i]=k;
for(int x=1;x<=n;x++) if(visit[x][i]) degree[x]--;
}
for(int j=1;j<=n;j++)  System.out.printf("%d ",path[j]);
System.out.printf("\n");
}

public void doit(){
Scanner sc=new Scanner(System.in);

int x,y;
t=sc.nextInt();
while((t--)!=0){
n=sc.nextInt();
m=sc.nextInt();
Arrays.fill(degree,0);
for(int i=0;i< visit.length;i++)
Arrays.fill(visit[i],false);
for(int i=1;i<=m;i++){
x=sc.nextInt();
y=sc.nextInt();
if(!visit[x][y]){
visit[x][y]=true;
degree[x]++;
}
}
topsort();
}
}
public static void main(String args[]){
Main m=new Main();
m.doit();
}
}

1. #!/usr/bin/env python
def cou(n):
arr =
i = 1
while(i<n):
arr.append(arr[i-1]+selfcount(i))
i+=1
return arr[n-1]

def selfcount(n):
count = 0
while(n):
if n%10 == 1:
count += 1
n /= 10
return count