CCPC 2022桂林 J.Permutation Puzzle

模拟赛的时候这道题细节写挂了，硬是调不出来。。。

首先想到拓补排序。然后可以发现，正反各跑一次可以获得每个点的取值范围，即上界和下界。（特殊地，对于已知点，其上下界相等且等于自己）

然后，将这些上下界看成一条条线段，问题转化：\(n\) 个线段区间，每次取 \([1,n]\) 中一个值，且包含在线段内。

经典问题。按照 \(r\) 排序，将排列存在 \(set\) 中， 最后对左端点 \(lowerbound\) 一下即可。

点击查看代码

#include <bits/stdc++.h>
using namespace std;
#define N 1000010

int n; 
int a[N]; 
set <int> s; 

struct node{
	int u, v, next;
} ;

namespace zheng{

node t[N << 1]; 

int head[N]; 

int bian = 0;
inline void addedge(int u, int v){
	t[++bian] = (node){u, v, head[u]}, head[u] = bian;
	return ; 
}

int in[N]; 

}

namespace fan{
	node t[N << 1]; 
	int head[N]; 

int bian = 0;
inline void addedge(int u, int v){
	t[++bian] = (node){u, v, head[u]}, head[u] = bian;
	return ; 
}

int in[N]; 
	
}

int lim[N], lmax[N];

struct point{
int l, r, id; 

bool operator < (const point& a) const{
	return r < a.r || (r == a.r && l < a.l);
}

} h[N] ; 

bool isfixed(int i){
	return a[i] >= 1 && a[i] <= n; 
}

void topo_fan(){
	queue <int> q; 
	for(int i = 1; i <= n; i++){
		if(isfixed(i)) lim[i] = a[i]; 
		else lim[i] = 1; 
	}
	
	for(int i = 1; i <= n; i++){
		if(!fan::in[i]) q.push(i); 
	}
	
	while(!q.empty()){
		int u = q.front(); q.pop(); 
		for(int i = fan::head[u]; i; i = fan::t[i].next){
			int v = fan::t[i].v; 
			lim[v] = max(lim[v], lim[u] + 1); 
			fan::in[v]--; 
			if(!fan::in[v]){
				q.push(v); 
			}
		}
	}
	return ; 
}


int ans[N]; 

void topo_zheng(){
	queue <int> q; 
	for(int i = 1; i <= n; i++){
		lmax[i] = n; 
		if(isfixed(i)) lmax[i] = a[i]; 
	}

  for(int i = 1; i <= n; i++)
    if(!zheng::in[i]) q.push(i); 

	while(!q.empty()){
		int u = q.front(); 
		q.pop();
		for(int i = zheng::head[u]; i; i = zheng::t[i].next){
			int v = zheng::t[i].v; 
			lmax[v] = min(lmax[v], lmax[u] - 1); 
			zheng::in[v]--; 
			if(zheng::in[v] == 0) q.push(v); 
		}
	}
	
	return ; 
}

int m; 

void clean(){
	for(int i = 0; i <= n; i++) zheng::head[i] = fan::head[i] = 0; 
	zheng::bian = fan::bian = 0;
	for(int i = 0; i <= n; i++)
		zheng::in[i] = fan::in[i] = 0; 
  for(int i = 0; i <= n; i++)
    h[i].l = h[i].r = 0; 
	s.clear(); 
	return ; 
}

int main(){
	// freopen("hh.txt", "r", stdin); 
	int T; cin >> T;
	while(T--){
		clean(); 
		cin >> n >> m;
		for(int i = 1; i <= n; i++)
			scanf("%d", &a[i]); 

		for(int i = 1; i <= n; i++){
			s.insert(i); 
			ans[i] = 0; 
		}
		for(int i = 1; i <= m; i++){
			int x, y;
			scanf("%d %d", &x, &y); 
			zheng::addedge(y, x); 
			zheng::in[x]++; 
			fan::addedge(x, y); 
			fan::in[y]++; 
		}
		topo_fan();   // 
		topo_zheng(); 

    for(int i = 1; i <= n; i++){
		  h[i].l = lim[i]; 
		  h[i].r = lmax[i];
		  h[i].id = i;  
	  }

		sort(h + 1, h + n + 1); 
		bool flag = 1; 
		for(int i = 1; i <= n; i++){
			set<int>::iterator it = s.lower_bound(h[i].l); 
			if(*it > h[i].r || it == s.end()){
				flag = 0; 
				break; 
			} 
			ans[h[i].id] = *it; 
			s.erase(it); 
		}
		if(!flag){
			puts("-1"); 
			continue; 
		}
		for(int i = 1; i <= n; i++)
			printf("%d ", ans[i]); 
		cout << endl; 
		//
	}
	return 0; 
}