P1347 排序 · znzryb

## 思路讲解

图论建模，拓扑排序。

拓扑排序的代码（使用BFS kahn‘s算法），通过判断q的大小可以知道其是不是严格的（该题目要求严格的顺序）。

```cpp
ll trop(const vector<ll> &a,ll siz){
	vector<ll> op=a;
	Ans.clear();
	queue<ll> q;
	ll ret=3;	// 3成功 2不能确定 1冲突
	FOR(i,'A','Z'){
		if(vis[i] && op[i]==0) q.push(i),Ans.pb(i);
	}
	if(SZ(q)>1) ret=2;
	while(!q.empty()){
		if(SZ(q)>1) ret=2;
		ll node=q.front();q.pop();
		ll cnt=0;
		FOR(i,0,SZ(g[node])-1){
			ll lnode=g[node][i];
			op[lnode]-=1;
			if(op[lnode]==0){
				q.push(lnode);
				Ans.pb(lnode);
			}
		}
	}
	if(SZ(Ans)==siz){
		if(SZ(Ans)<N){	// 还没完全确定
			return 2;
		}else{
			return ret;
		}
	}else{	// 说明有环
		return 1;
	}
}
```

## AC代码

[https://www.luogu.com.cn/record/220236107](https://www.luogu.com.cn/record/220236107)



::: 源代码

```cpp
// Problem: P1347 排序
// Contest: Luogu
// URL: https://www.luogu.com.cn/problem/P1347
// Memory Limit: 125 MB
// Time Limit: 1000 ms
// 
// Powered by CP Editor (https://cpeditor.org)

#include <bits/stdc++.h>
#define all(vec) vec.begin(),vec.end()
#define CLR(i,a) memset(i,a,sizeof(i))
#define fi first
#define se second
#define pb push_back
#define SZ(a) ((int) a.size())
#define FOR(i, a, b) for (int i = (a); i <= (b); ++i)
#define ROF(i, a, b) for (int i = (a); i >= (b); --i)
#define debug(var) cerr << #var <<":"<<var<<"\n";
#define lson(var) (var<<1)
#define rson(var) ((var<<1)+1)

using namespace std;

typedef long long ll;typedef unsigned long long ull;
typedef double DB;typedef long double LD;
typedef __int128 i128;typedef pair<DB,DB> pdd;typedef pair<ll,bool> plb;
typedef pair<ll,ll> pll;
typedef array<ll,3> arr3;typedef array<ll,2> arr2;
constexpr ll MAXN=static_cast<ll>(3e2)+10,INF=static_cast<ll>(1e9)+9; // 1e18+9也是素数
constexpr ll mod=static_cast<ll>(1e9)+7;
constexpr double eps=1e-8;

ll N,M,Q,X,K,lT,A[MAXN];
vector<ll> g[MAXN];		// 记得要清空
bitset<MAXN> vis;
/*

*/
vector<ll> Ans;
inline void init(){
	
}

ll trop(const vector<ll> &a,ll siz){
	vector<ll> op=a;
	Ans.clear();
	queue<ll> q;
	ll ret=3;	// 3成功 2不能确定 1冲突
	FOR(i,'A','Z'){
		if(vis[i] && op[i]==0) q.push(i),Ans.pb(i);
	}
	if(SZ(q)>1) ret=2;
	while(!q.empty()){
		if(SZ(q)>1) ret=2;
		ll node=q.front();q.pop();
		ll cnt=0;
		FOR(i,0,SZ(g[node])-1){
			ll lnode=g[node][i];
			op[lnode]-=1;
			if(op[lnode]==0){
				q.push(lnode);
				Ans.pb(lnode);
			}
		}
	}
	if(SZ(Ans)==siz){
		if(SZ(Ans)<N){	// 还没完全确定
			return 2;
		}else{
			return ret;
		}
	}else{	// 说明有环
		return 1;
	}
}
inline void solve(){
	cin>>N>>M;
	init();
	// Inconsistency found after 2 relations.
	// Sorted sequence determined after 4 relations: ABCD.
	vector<ll> inde(300,0);
	set<char> occ;
	FOR(_,1,M){
		string s;
		cin>>s;
		g[s[0]].pb(s[2]);
		vis[s[0]]=true,vis[s[2]]=true;
		occ.insert(s[0]),occ.insert(s[2]);
		inde[s[2]]+=1;
		ll ret=trop(inde,SZ(occ));
		if(ret==1){
			cout<<"Inconsistency found after "<<_<<" relations.\n";
			return;
		}else if(ret==3){
			cout<<"Sorted sequence determined after "<<_<<" relations: ";
			FOR(i,0,SZ(Ans)-1){
				cout<<char(Ans[i]);
			}
			cout<<".\n";
			return;
		}
	}
	cout<<"Sorted sequence cannot be determined.\n";
}

int main()
{
	ios::sync_with_stdio(false);
	cin.tie(0);cout.tie(0);
	
	// cin>>lT;
	// while(lT--){
		// solve();
	// }
	solve();
	return 0;
}
/*
AC
https://www.luogu.com.cn/record/220236107
*/
```


:::


## 心路历程（WA，TLE，MLE……）