拓扑排序（栈）——POJ 1094

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Sorting It All Out
Crawling in process...Crawling failedTime
Limit:1000MS Memory Limit:10000KB 64bit IO Format:%I64d & %I64u
SubmitStatus

Description

An ascending sorted sequence of distinct values is one in which some form of a less-than operator is used to order the elements from smallest to largest. For example, the sorted sequence A, B, C, D implies that A < B, B < C and
C < D. in this problem, we will give you a set of relations of the form A < B and ask you to determine whether a sorted order has been specified or not.

Input

Input consists of multiple problem instances. Each instance starts with a line containing two positive integers n and m. the first value indicated the number of objects to sort, where 2 <= n <= 26. The objects to be sorted will
be the first n characters of the uppercase alphabet. The second value m indicates the number of relations of the form A < B which will be given in this problem instance. Next will be m lines, each containing one such relation consisting of three characters:
an uppercase letter, the character "<" and a second uppercase letter. No letter will be outside the range of the first n letters of the alphabet. Values of n = m = 0 indicate end of input.

Output

For each problem instance, output consists of one line. This line should be one of the following three:

Sorted sequence determined after xxx relations: yyy...y.

Sorted sequence cannot be determined.

Inconsistency found after xxx relations.

where xxx is the number of relations processed at the time either a sorted sequence is determined or an inconsistency is found, whichever comes first, and yyy...y is the sorted, ascending sequence.

Sample Input

4 6
A<B
A<C
B<C
C<D
B<D
A<B
3 2
A<B
B<A
26 1
A<Z
0 0

Sample Output

Sorted sequence determined after 4 relations: ABCD.
Inconsistency found after 2 relations.
Sorted sequence cannot be determined.

#include <cstdio>
#include <cstring>
#include <queue>
#include <iostream>
using namespace std;
const int INF=1<<30;
const int MAXN=7500+10;
int n,m;
int G[30][30];
int in[30];
int out[30];
int in1[30];
int topo[30];
int countt;

int toposort()
{
	memset(topo,-1,sizeof(topo));
	memset(in1,0,sizeof(in1));
	memcpy(in1,in,sizeof(in));
	queue<int>q;
	int t=0,qin=0;
	for(int u=0; u<n; u++){
		if(!in[u] && out[u]) q.push(u);
		if(in[u] || out[u]) t++;
	}
	countt=0;
	while(!q.empty())
	{
		if(q.size()>1) qin=1;
		int u=q.front();
		q.pop();
		topo[countt++]=u;
		for(int v=0; v<n; v++){
			if(G[u][v]) in1[v]--;
			if(G[u][v] && !in1[v]) q.push(v);
		}
	}
	if(countt!=t) return 0;//有环
	if(t!=n) return 1;//边没有连完
	if(t==n && qin) return 2;//大小不确定
	if(t==n && !qin) return 3;//大小确定
}

int main()
{
    //freopen("in.txt","r",stdin);
	while(cin>>n>>m, n+m)
	{
		memset(G,0,sizeof(G));
		memset(in,0,sizeof(in));
		int i,j,ok=-1;
		int num1,num2;
		for(i=0; i<m; i++){
			char ch1,ch2,ch3;
			cin>>ch1>>ch2>>ch3;
			//cout<<ch1<<" "<<ch3<<endl;
			int a=ch1-'A';
			int b=ch3-'A';
			G[a][b]=1;
			in[b]++;
			out[a]++;
			if(ok==0 || ok==3) continue;
			ok=toposort();
			if(ok==0) num1=i+1;
			if(ok==3) num2=i+1;
		}
		if(!ok) cout<<"Inconsistency found after "<<num1<<" relations."<<endl;
		else if(ok==3) {
			cout<<"Sorted sequence determined after "<<num2<<" relations: ";
			for(i=0; i<countt; i++)
				cout<<char(topo[i]+'A');
			cout<<"."<<endl;
		}
		else cout<<"Sorted sequence cannot be determined."<<endl;
	}
    return 0;
}

另附拓扑排序DFS版

bool dfs(int u)
{
	c[c]=-1;
	for(int v=0; v<n; v++){
		if(G[u][v]){
			if(c[v]<0) return false;//存在有向环，退出
			else if(!c[v] && !dfs(v)) return false;//后面的节点存在有向环，退出；
		}
	}
	c[u]=1; topo[--t]=u;
	return true;
}

bool toposort()
{
	t=n;
	memset(c,0,sizeof(c));
	for(int u=0; u<n; u++)
	{
		if(!c[u]){
			if(!dfs(u)) return false;
		}
	}
	return true;
}