P1347 排序

思路：每加一条边，更新结点数并做一次拓扑排序判断有没有环，并同时判断能不能唯一确定一个大小关系序列。

#include<iostream>
#include<vector>
#include<cstring>
#include<queue>
#include<cstdio>

using namespace std;

const int N = 27;

int n, m;
int st[N], in[N], backup[N];
int cur;
int g[N][N];
vector<char> res;
int flag;

int topsort(){
    memcpy(backup, in, sizeof in);
    
    queue<int> q;
    
    flag = 0;
    res.clear();
    
    int cnt = 0;
    for(int i = 1; i <= n; i ++)
        if(in[i] == 0 && st[i]){
            q.push(i);
            cnt ++;
        }
    
    
    if(cnt > 1) flag = 1;
        
    while(q.size()){
        int h = q.front();
        q.pop();
        
        res.push_back('A' + h - 1);
        
        int t = 0;
        for(int i = 1; i <= n; i ++){
            if(g[h][i]){
                in[i] --;
                if(in[i] == 0){
                    q.push(i);
                    t ++;
                    cnt ++;
                    if(t > 1) flag = 1;
                }
            }
        }
    }
    
    memcpy(in, backup, sizeof in);
    
    return cur == cnt;
}

int main(){
    cin >> n >> m;
    
    for(int i = 1; i <= m; i ++){
        char a, b, c;
        cin >> a >> b >> c;
        
        int av = a - 'A' + 1, cv = c - 'A' + 1;
        if(st[av] == 0) st[av] = 1, cur ++;
        if(st[cv] == 0) st[cv] = 1, cur ++;
        
        if(g[av][cv] == 0){
            g[av][cv] = 1;
            in[cv] ++;
        }
        
        int k = topsort();
        
        if(k && !flag && cur == n){
            printf("Sorted sequence determined after %d relations: ", i);
            for(int j = 0; j < res.size(); j ++) cout << res[j];
            cout << '.';
            return 0;
        }
        
        if(!k){
            printf("Inconsistency found after %d relations.", i);
            return 0;
        }
    }
    
    cout << "Sorted sequence cannot be determined.";
    
    return 0;
}