【Loj #10100. 「一本通 3.6 练习 1」网络】题解

题目链接

题目就是给出一幅图，求其割点个数。

由于 \(n\leqslant 100\)，所以可以暴力删点。

当然也可以跑割点。

(感谢crx老师教我割点模板)

暴力Code

// Problem: #10100. 「一本通 3.6 练习 1」网络
// Contest: LibreOJ
// URL: https://loj.ac/p/10100
// Memory Limit: 10 MB
// Time Limit: 1000 ms
// 
// Powered by CP Editor (https://cpeditor.org)

#include<bits/stdc++.h>
using namespace std;
//#define int long long
inline int read(){int x=0,f=1;char ch=getchar();
while(ch<'0'||ch>'9'){if(ch=='-')f=-1;
ch=getchar();}while(ch>='0'&&ch<='9'){x=(x<<1)+
(x<<3)+(ch^48);ch=getchar();}return x*f;}
//#define mo
#define N 110
struct node
{
	int x, y, n; 
}d[N*N*2]; 
int n, m, i, j, k; 
int x, y, z, ans; 
int h[N], c[N]; 
char ch; 

void cun(int x, int y)
{
	d[++k].x=x; d[k].y=y; 
	d[k].n=h[x]; h[x]=k; 
}

void init()
{
	m=i=j=k=x=y=z=ans=ch=0; 
	memset(h, 0, sizeof(h)); 
	memset(c, 0, sizeof(c)); 
	memset(d, 0, sizeof(d)); 
}

void dfs(int x)
{
	for(int g=h[x]; g; g=d[g].n)
	{
		int y=d[g].y; 
		if(c[y]) continue; 
		c[y]=1; 
		dfs(y); 
	}
}

signed main()
{
//	freopen("tiaoshi.in","r",stdin);
//	freopen("tiaoshi.out","w",stdout);
	n=read(); 
	while(n)
	{
		init(); 
		scanf("%d", &i); 
		while(i) 
		{
			scanf("%d%c", &j, &ch); 
			// printf("%d %d\n", i, j); 
			cun(i, j); cun(j, i); 
			while(ch>=32)
			{
				scanf("%d%c", &j, &ch); 
				// printf("%d %d\n", i, j); 
				cun(i, j); cun(j, i); 
			}
			scanf("%d", &i); 
			// printf("%d\n", i); 
		}
		i=k=0; 
		for(j=1; j<=n; ++j) 
			if(!c[j]) c[j]=1, dfs(j), ++k; 
		// printf("k:%d\n", k); 
		for(i=1; i<=n; ++i)
		{
			memset(c, 0, sizeof(c)); 
			c[i]=1; m=0; 
			for(j=1; j<=n; ++j) 
				if(!c[j]) c[j]=1, dfs(j), ++m; 
			if(m!=k) ++ans; 
			// printf("m:%d\n", m); 
		}
		printf("%d\n", ans); 
		n=read(); 
	}
	return 0;
}

割点Code

// Problem: #10100. 「一本通 3.6 练习 1」网络
// Contest: LibreOJ
// URL: https://loj.ac/p/10100
// Memory Limit: 10 MB
// Time Limit: 1000 ms
// 
// Powered by CP Editor (https://cpeditor.org)

#include<bits/stdc++.h>
using namespace std;
//#define int long long
inline int read(){int x=0,f=1;char ch=getchar();
while(ch<'0'||ch>'9'){if(ch=='-')f=-1;
ch=getchar();}while(ch>='0'&&ch<='9'){x=(x<<1)+
(x<<3)+(ch^48);ch=getchar();}return x*f;}
//#define mo
#define N 110
struct node
{
	int x, y, n; 
}d[N*N*2]; 
int n, m, i, j, k; 
int x, y, z, ans; 
int h[N], c[N], f[N], zi[N]; 
char ch; 

void cun(int x, int y)
{
	d[++k].x=x; d[k].y=y; 
	d[k].n=h[x]; h[x]=k; 
}

void init()
{
	m=i=j=k=x=y=z=ans=ch=0; 
	memset(h, 0, sizeof(h)); 
	memset(c, 0, sizeof(c)); 
	memset(d, 0, sizeof(d)); 
	memset(f, 0, sizeof(f)); 
	memset(zi, 0, sizeof(zi)); 
}

void dfs(int x)
{
	for(int g=h[x]; g; g=d[g].n)
	{
		int y=d[g].y; 
		if(!c[y])
		{
			c[y]=c[x]+1;
			dfs(y); 
			if(c[f[y]]<c[f[x]]) f[x]=f[y]; 
			if(c[f[y]]>=c[x]) ++zi[x]; 
		}
		else if(c[y]<c[f[x]]) f[x]=y; 
	}
}



signed main()
{
//	freopen("tiaoshi.in","r",stdin);
//	freopen("tiaoshi.out","w",stdout);
	n=read(); 
	while(n)
	{
		init(); 
		scanf("%d", &i); 
		while(i) 
		{
			scanf("%d%c", &j, &ch); 
			// printf("%d %d\n", i, j); 
			cun(i, j); cun(j, i); 
			while(ch>=32)
			{
				scanf("%d%c", &j, &ch); 
				// printf("%d %d\n", i, j); 
				cun(i, j); cun(j, i); 
			}
			scanf("%d", &i); 
			// printf("%d\n", i); 
		}
		for(i=1; i<=n; ++i) f[i]=i; 
		for(i=1; i<=n; ++i)
			if(!c[i]) c[i]=1, dfs(i); 
		for(i=1; i<=n; ++i)
			if((zi[i]>1)||(f[i]!=i&&zi[i])) ++ans; 
		printf("%d\n", ans); 
		n=read(); 
	}
	return 0;
}