拓扑排序

最新推荐文章于 2025-05-13 21:35:52 发布

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本文深入探讨了拓扑排序的概念，通过实例解析其算法流程，并提供了ACM竞赛中一道相关的题目链接，帮助读者更好地理解和运用拓扑排序。

原题链接：http://www.acmicpc.sdnu.edu.cn/problem/show/1031

#include <cstdio>
#include <algorithm>
#include <iostream>
#include <cmath>
#include <cstring>
#include <stack>
#include <queue>
#include <set>
#include <map>
#include <vector>
#include <ctype.h>
#include <deque>
using namespace std;
typedef long long ll;
typedef pair<int,int> P;
const int mod=998244353;
const ll inf=9999999999999;
#define mem(a,b) memset(a,b,sizeof(a))
#define IOS ios::sync_with_stdio(false);cin.tie(0)
#define mcy(a,b) memcpy(a,b,sizeof(a))
const int maxn=1e2+5;
struct node
{
    int v;
    int to;
}edge[maxn*2];
int n,m,a,b,tot,head[maxn],indegree[maxn],cpyindegree[maxn];
queue<int>ans;
void init()
{
    tot=0;
    mem(head,-1);
    mem(indegree,0);
}
void add(int u,int v)
{
    edge[++tot].v=v;
    edge[tot].to=head[u];
    head[u]=tot;
}
int topu(int number)
{
    while(!ans.empty())ans.pop();
    int sum=0,flag=0;
    queue<int>q;
    for(int i=0;i<number;++i)
    {
        cpyindegree[i]=indegree[i];
        if(indegree[i]==0)q.push(i);
    }
    while(!q.empty())
    {
        if(q.size()>=2)flag=1;
        int now=q.front();
        q.pop();
        sum++;
        ans.push(now);
        for(int i=head[now];~i;i=edge[i].to)
        {
            int v=edge[i].v;
            cpyindegree[v]--;
            if(cpyindegree[v]==0)q.push(v);
        }
    }
    if(sum<number)return -1;
    if(flag)return 0;
    return 1;
}
int main()
{
    while(~scanf("%d %d",&n,&m))
    {
        init();
        string s;
        if(n==0 && m==0)break;
        int error=-1,success=-1;
        for(int i=1;i<=m;++i)
        {
            cin >> s;
            if(error!=-1 || success!=-1)continue;
            a=s[0]-'A';
            b=s[2]-'A';
            if(s[1]=='<')
            {
                add(a,b);
                indegree[b]++;
            }
            else
            {
                add(b,a);
                indegree[a]++;
            }
            int flag=topu(n);
            if(flag==-1)error=i;
            if(flag==1)success=i;
        }
        if(error!=-1)
        {
            printf("Inconsistency found after %d relations.\n",error);
        }
        else if(success==-1)
            printf("Sorted sequence cannot be determined.\n");
        else
        {
            printf("Sorted sequence determined after %d relations: ",success);
            while(!ans.empty())
            {
                int answer=ans.front();
                ans.pop();
                char c=answer+'A';
                cout << c;
            }
            cout << ".\n";
        }

    }
    return 0;
}