Problem:
Score : 300 points

Problem Statement

You are given an undirected unweighted graph with N vertices and M edges that contains neither self-loops nor double edges.

Here, a self-loop is an edge where a_i = b_i (1≤i≤M), and double edges are two edges where (a_i,b_i)=(a_j,b_j) or (a_i,b_i)=(b_j,a_j) (1≤i<j≤M).

How many different paths start from vertex 1 and visit all the vertices exactly once?

Here, the endpoints of a path are considered visited.

For example, let us assume that the following undirected graph shown in Figure 1 is given.

Figure 1: an example of an undirected graph

The following path shown in Figure 2 satisfies the condition.

Figure 2: an example of a path that satisfies the condition

However, the following path shown in Figure 3 does not satisfy the condition, because it does not visit all the vertices.

Figure 3: an example of a path that does not satisfy the condition

Neither the following path shown in Figure 4, because it does not start from vertex 1.

Figure 4: another example of a path that does not satisfy the condition

Constraints

2≦N≦8

0≦M≦N(N-1)/2

1≦a_i<b_i≦N

The given graph contains neither self-loops nor double edges.

Input

The input is given from Standard Input in the following format:

N M
a_1 b_1
a_2 b_2
:
a_M b_M

Output

Print the number of the different paths that start from vertex 1 and visit all the vertices exactly once.

Sample Input 1

3 3
1 2
1 3
2 3

Sample Output 1

2

The given graph is shown in the following figure:

The following two paths satisfy the condition:

Sample Input 2

7 7
1 3
2 7
3 4
4 5
4 6
5 6
6 7

Sample Output 2

1

This test case is the same as the one described in the problem statement.

Solution in C++14 (GCC 5.4.1) (judge verdict: Runtime Error)


#include <bits/stdc++.h>

class kin{
public:
	inline void open(FILE *,int);
	inline void close(void);
	inline void scan(void);
	inline kin &operator>(char &);
	inline kin &operator>(int &);
	inline kin &operator>(long long &);
	inline kin &operator>(double &);
	inline kin &operator>(long double &);
	inline kin &operator>(char *);
	template<class T>
	inline void get(T *,int);
private:
	FILE *fp;
	char *buf;
	int siz;
	int idx;
}in;

class kout{
public:
	inline void open(FILE *,int);
	inline void close(void);
	inline void print(void);
	inline kout &operator<(char);
	inline kout &operator<(int);
	inline kout &operator<(long long);
	inline kout &operator<(double);
	inline kout &operator<(long double);
	inline kout &operator<(const char *);
	template<class T>
	inline void put(T *,int,char,char);
private:
	FILE *fp;
	char *buf;
	int siz;
	int idx;
}out;

class edgeidxset{
public:
	inline void open(int,int);
	inline void close(void);
	inline int first(int);
	inline int next(int);
	inline void add(int);
	inline int vertex(void);
	inline int edge(void);
	inline edgeidxset();
	inline edgeidxset(int,int);
private:
	int sizv;
	int size;
	int *idxf;
	int *idxn;
};

edgeidxset s;
int dest[28],k;
int cnt,v[8];
int ans;

inline void dfs(int num){
	v[num]=1;
	++cnt;
	for(int i=s.first(num);i!=-1;i=s.next(i)){
		if(!v[dest[i]]) dfs(dest[i]);
	}
	if(cnt==s.vertex()) ++ans;
	v[num]=0;
	--cnt;
	return;
}

int main(int argc,char **argv){
	in.open(stdin,512);
	out.open(stdout,512);
	in.scan();
	int n,m;
	in>n>m;
	s.open(n,m*2);
	for(int i=0;i<m;++i){
		int a,b;
		in>a>b;
		s.add(--a);
		s.add(--b);
		dest[k++]=b;
		dest[k++]=a;
	}
	dfs(0);
	out<ans<'\n';
	out.print();
	in.close();
	out.close();
	return 0;
}

inline void edgeidxset::open(int sizva,int sizea){
	sizv=sizva;
	size=0;
	idxf=new int[sizva];
	for(int i=0;i<sizva;++i) idxf[i]=-1;
	idxn=new int[sizea];
	for(int i=0;i<sizea;++i) idxn[i]=-1;
	return;
}
inline void edgeidxset::close(void){
	sizv=size=0;
	delete[] idxf;
	delete[] idxn;
	idxf=idxn=nullptr;
	return;
}
inline int edgeidxset::first(int num){
	return idxf[num];
}
inline int edgeidxset::next(int idx){
	return idxn[idx];
}
inline void edgeidxset::add(int num){
	idxn[size]=idxf[num];
	idxf[num]=size++;
	return;
}
inline int edgeidxset::vertex(void){
	return sizv;
}
inline int edgeidxset::edge(void){
	return size;
}
inline edgeidxset::edgeidxset(){
	sizv=size=0;
	idxf=idxn=nullptr;
}
inline edgeidxset::edgeidxset(int vertex,int siza){
	open(vertex,siza);
}

inline void kin::open(FILE *fpa,int siza){
	fp=fpa;
	buf=new char[siza];
	siz=siza;
	idx=0;
	return;
}
inline void kin::close(void){
	fp=nullptr;
	delete[] buf;
	buf=nullptr;
	siz=0;
	idx=0;
	return;
}
inline void kin::scan(void){
	int readsiz=(int)std::fread((void *)buf,(std::size_t)1,(std::size_t)siz,fp);
	if(readsiz!=siz) buf[readsiz]='\x00';
	idx=0;
	return;
}
inline kin &kin::operator>(char &var){
	if(!buf[idx]){
		var='\x00';
		return *this;
	}
	var=buf[idx];
	if(++idx==siz) scan();
	if(++idx==siz) scan();
	return *this;
}
inline kin &kin::operator>(int &var){
	if(!buf[idx]){
		var=0;
		return *this;
	}
	int sign=-1;
	if(buf[idx]=='-'){
		sign=1;
		if(++idx==siz) scan();
	}
	var=0;
	while(buf[idx]>='0'){
		var=var*10-(int)(buf[idx]-'0');
		if(++idx==siz) scan();
	}
	var*=sign;
	if(++idx==siz) scan();
	return *this;
}
inline kin &kin::operator>(long long &var){
	if(!buf[idx]){
		var=0LL;
		return *this;
	}
	long long sign=-1LL;
	if(buf[idx]=='-'){
		sign=1LL;
		if(++idx==siz) scan();
	}
	var=0LL;
	while(buf[idx]>='0'){
		var=var*10LL-(long long)(buf[idx]-'0');
		if(++idx==siz) scan();
	}
	var*=sign;
	if(++idx==siz) scan();
	return *this;
}
inline kin &kin::operator>(double &var){
	if(!buf[idx]){
		var=0.0;
		return *this;
	}
	double sign=-1.0;
	if(buf[idx]=='-'){
		sign=1.0;
		if(++idx==siz) scan();
	}
	var=0.0;
	while(buf[idx]>='0'){
		var=var*10.0-(double)(buf[idx]-'0');
		if(++idx==siz) scan();
	}
	if(buf[idx]=='.'){
		if(++idx==siz) scan();
		double dig=1.0;
		while(buf[idx]>='0'){
			var-=(double)(buf[idx]-'0')*(dig/=10.0);
			if(++idx==siz) scan();
		}
	}
	var*=sign;
	if(++idx==siz) scan();
	return *this;
}
inline kin &kin::operator>(long double &var){
	if(!buf[idx]){
		var=0.0L;
		return *this;
	}
	long double sign=-1.0L;
	if(buf[idx]=='-'){
		sign=1.0L;
		if(++idx==siz) scan();
	}
	var=0.0L;
	while(buf[idx]>='0'){
		var=var*10.0L-(long double)(buf[idx]-'0');
		if(++idx==siz) scan();
	}
	if(buf[idx]=='.'){
		if(++idx==siz) scan();
		long double dig=1.0L;
		while(buf[idx]>='0'){
			var-=(long double)(buf[idx]-'0')*(dig/=10.0L);
			if(++idx==siz) scan();
		}
	}
	var*=sign;
	if(++idx==siz) scan();
	return *this;
}
inline kin &kin::operator>(char *var){
	if(!buf[idx]){
		var[0]='\x00';
		return *this;
	}
	int ptr=0;
	while(buf[idx]>='!'){
		var[ptr++]=buf[idx];
		if(++idx==siz) scan();
	}
	var[ptr]='\x00';
	if(++idx==siz) scan();
	return *this;
}
template<class T>
inline void kin::get(T *var,int num){
	for(int i=0;i<num;++i) (*this)>var[i];
	return;
}

inline void kout::open(FILE *fpa,int siza){
	fp=fpa;
	buf=new char[siza];
	siz=siza;
	idx=0;
	return;
}
inline void kout::close(void){
	fp=nullptr;
	delete[] buf;
	buf=nullptr;
	siz=0;
	idx=0;
	return;
}
inline void kout::print(void){
	std::fwrite((void *)buf,(std::size_t)1,(std::size_t)idx,fp);
	idx=0;
	return;
}
inline kout &kout::operator<(char val){
	buf[idx]=val;
	if(++idx==siz) print();
	return *this;
}
inline kout &kout::operator<(int val){
	if(val<0){
		buf[idx]='-';
		if(++idx==siz) print();
	}
	else val*=-1;
	char dig[10];
	int ptr=0;
	do{
		int tmp=val/10;
		dig[ptr++]=(char)-(val-tmp*10)+'0';
		val=tmp;
	}while(val);
	while(ptr--){
		buf[idx]=dig[ptr];
		if(++idx==siz) print();
	}
	return *this;
}
inline kout &kout::operator<(long long val){
	if(val<0LL){
		buf[idx]='-';
		if(++idx==siz) print();
	}
	else val*=-1LL;
	char dig[19];
	int ptr=0;
	do{
		long long tmp=val/10LL;
		dig[ptr++]=(char)-(val-tmp*10LL)+'0';
		val=tmp;
	}while(val);
	while(ptr--){
		buf[idx]=dig[ptr];
		if(++idx==siz) print();
	}
	return *this;
}
inline kout &kout::operator<(double val){
	if(val<0.0){
		buf[idx]='-';
		if(++idx==siz) print();
	}
	else val*=-1.0;
	double dig=1.0;
	while(val/dig<=-10.0) dig*=10.0;
	int tmp;
	while(dig>=1.0){
		buf[idx]=(char)-(tmp=(int)(val/dig))+'0';
		if(++idx==siz) print();
		val-=(double)tmp*dig;
		dig/=10.0;
	}
	buf[idx]='.';
	if(++idx==siz) print();
	for(int i=0;i<12;++i){
		buf[idx]=(char)-(tmp=(int)(val/dig))+'0';
		if(++idx==siz) print();
		val-=(double)tmp*dig;
		dig/=10.0;
	}
	return *this;
}
inline kout &kout::operator<(long double val){
	if(val<0.0L){
		buf[idx]='-';
		if(++idx==siz) print();
	}
	else val*=-1.0L;
	long double dig=1.0L;
	while(val/dig<=-10.0L) dig*=10.0L;
	int tmp;
	while(dig>=1.0L){
		buf[idx]=(char)-(tmp=(int)(val/dig))+'0';
		if(++idx==siz) print();
		val-=(long double)tmp*dig;
		dig/=10.0L;
	}
	buf[idx]='.';
	if(++idx==siz) print();
	for(int i=0;i<16;++i){
		buf[idx]=(char)-(tmp=(int)(val/dig))+'0';
		if(++idx==siz) print();
		val-=(long double)tmp*dig;
		dig/=10.0L;
	}
	return *this;
}
inline kout &kout::operator<(const char *val){
	for(int i=0;val[i];++i){
		buf[idx]=val[i];
		if(++idx==siz) print();
	}
	return *this;
}
template<class T>
inline void kout::put(T *val,int num,char dlm,char end){
	--num;
	for(int i=0;i<num;++i) (*this)<val[i]<dlm;
	(*this)<val[num]<end;
	return;
}