POJ 3687 Labeling Balls

Description

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:

No two balls share the same label.
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?

Input

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, b ≤
N) There is a blank line before each test case.

Output

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.

Sample Input

5

4 0

4 1
1 1

4 2
1 2
2 1

4 1
2 1

Sample Output

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

思路：刚开始看这个题当成了简单的拓扑排序，后来发现是我想的太简单了。

10 5
4 1
8 1
7 8
4 1
2 8

5 1 6 2 7 8 3 4 9 10

参考这个样例就可以发现问题所在。

正确的做法是每次找到入度的所有点中，index最大的一个并加到排列中。然后更新其他点的入度。可以用优先队列做，也可以直接每次都直接找。

代码：

#include<algorithm>
#include<iostream>
#include<cstdio>
#include<cstring>
#include<climits>
#include<cstdlib>
#include<cmath>
#include<queue>
using namespace std;
typedef long long LL;
const int MAXN=410;

int G[MAXN][MAXN];
int in[MAXN];
int weight[MAXN];
int n;
bool toposort()
{
for(int i=n;i>=1;i--)
{
int k;
for(k=n;k>=1;k--)
if(in[k]==0)
{
weight[k]=i;
in[k]--;
break;
}
if(k<1) return false;
for(int j=1;j<=n;j++)
if(G[k][j])
in[j]--;
}
return true;
}
int main()
{
#ifdef LOCAL
freopen("in.txt","rb",stdin);
//freopen("out.txt","wb",stdout);
#endif
int tt;
scanf("%d",&tt);
while(tt--)
{
int m;
scanf("%d%d",&n,&m);
memset(G,0,sizeof(G));
memset(in,0,sizeof(in));
for(int i=1;i<=m;i++)
{
int u,v;
scanf("%d%d",&u,&v);
if(!G[v][u])
{
in[u]++;
G[v][u]=1;
}
}
if(toposort())
{
for(int i=1;i<=n;i++)
{
if(i!=n) printf("%d ",weight[i]);
else printf("%d\n",weight[i]);
}
}
else printf("-1\n");
}
return 0;
}