A. BZOj 4390: [Usaco2015 dec]Max Flow

題目

BZOJ 4390

題解

樹上差分的模板題。

程式碼

#include<bits/stdc++.h>
using namespace std;
const int maxn=5e4+10;
template<typename T>inline void read(T &x)
{
	x=0;
	T f=1,ch=getchar();
	while (!isdigit(ch)) ch=getchar();
	if (ch=='-') f=-1, ch=getchar();
	while (isdigit(ch)) x=(x<<1)+(x<<3)+(ch^48), ch=getchar();
	x*=f;
}
int ver[maxn<<1],Next[maxn<<1],head[maxn],len;
inline void add(int x,int y)
{
	ver[++len]=y,Next[len]=head[x],head[x]=len;
}
int fa[maxn],d[maxn],f[maxn][21];
inline void dfs1(int x,int father,int deep)
{
	fa[x]=father,d[x]=deep;
	for (int i=1;i<16;++i)
		f[x][i]=f[f[x][i-1]][i-1];
	for (int i=head[x];i;i=Next[i])
	{
		int y=ver[i];
		if (y==father) continue;
		f[y][0]=x;
		dfs1(y,x,deep+1);
	}
}
inline int lca(int x,int y)
{
	if (d[x]>d[y]) swap(x,y);
	for (int i=15;i>=0;--i)
		if (d[f[y][i]]>=d[x])
			y=f[y][i];
	if (x==y) return x;
	for (int i=15;i>=0;--i)
		if (f[x][i]!=f[y][i])
			x=f[x][i],y=f[y][i];
	return f[x][0];
}
int siz[maxn],sum[maxn],ans;
inline void dfs2(int x,int father)
{
	siz[x]=sum[x];
	for (int i=head[x];i;i=Next[i])
	{
		int y=ver[i];
		if (y==father) continue;
		dfs2(y,x);
		siz[x]+=siz[y];
	}
	ans=max(ans,siz[x]);
}
int main()
{
	int n,k;read(n);read(k);
	for (int i=1;i<n;++i)
	{
		int x,y;
		read(x);read(y);
		add(x,y);add(y,x);
	}
	dfs1(1,0,1);
	for (int i=1;i<=k;++i)
	{
		int a,b;
		read(a);read(b);
		int c=lca(a,b);
		++sum[a],++sum[b],--sum[c];
		if (c!=1) --sum[fa[c]];
	}
	dfs2(1,0);
	printf("%d\n",ans);
	return 0;
}

B. POJ 3417 Network

題目

POJ 3417

題解

這道題借鑑了演算法進階的思路。

程式碼

#include<algorithm>
#include<bitset>
#include<cctype>
#include<cerrno>
#include<clocale>
#include<cmath>
#include<complex>
#include<cstdio>
#include<cstdlib>
#include<cstring>
#include<ctime>
#include<deque>
#include<exception>
#include<fstream>
#include<functional>
#include<limits>
#include<list>
#include<map>
#include<iomanip>
#include<ios>
#include<iosfwd>
#include<iostream>
#include<istream>
#include<ostream>
#include<queue>
#include<set>
#include<sstream>
#include<stack>
#include<stdexcept>
#include<streambuf>
#include<string>
#include<utility>
#include<vector>
#include<cwchar>
#include<cwctype>
using namespace std;
const int maxn=1e5+10;
template<typename T>inline void read(T &x)
{
	x=0;
	T f=1,ch=getchar();
	while (!isdigit(ch)) ch=getchar();
	if (ch=='-') f=-1, ch=getchar();
	while (isdigit(ch)) x=(x<<1)+(x<<3)+(ch^48), ch=getchar();
	x*=f;
}
int ver[maxn<<1],Next[maxn<<1],head[maxn],len;
inline void add(int x,int y)
{
	ver[++len]=y,Next[len]=head[x],head[x]=len;
}
int fa[maxn],d[maxn],f[maxn][21];
inline void dfs1(int x,int father,int deep)
{
	fa[x]=father,d[x]=deep;
	for (int i=1;i<=20;++i)
		f[x][i]=f[f[x][i-1]][i-1];
	for (int i=head[x];i;i=Next[i])
	{
		int y=ver[i];
		if (y==father) continue;
		f[y][0]=x;
		dfs1(y,x,deep+1);
	}
}
inline int lca(int x,int y)
{
	if (d[x]>d[y]) swap(x,y);
	for (int i=20;i>=0;--i)
		if (d[f[y][i]]>=d[x])
			y=f[y][i];
	if (x==y) return x;
	for (int i=20;i>=0;--i)
		if (f[x][i]!=f[y][i])
			x=f[x][i],y=f[y][i];
	return f[x][0];
}
int siz[maxn],sum[maxn],ans;
inline void dfs2(int x,int father)
{
	siz[x]=sum[x];
	for (int i=head[x];i;i=Next[i])
	{
		int y=ver[i];
		if (y==father) continue;
		dfs2(y,x);
		siz[x]+=siz[y];
	}
}
int main()
{
	int n,m;
	read(n);read(m);
	for (int i=1;i<n;++i)
	{
		int x,y;
		read(x);read(y);
		add(x,y);add(y,x);
	}
	dfs1(1,0,1);
	for (int i=1;i<=m;++i)
	{
		int a,b;
		read(a);read(b);
		int c=lca(a,b);
		++sum[a],++sum[b],sum[c]-=2;
	}
	dfs2(1,0);
	for (int i=1;i<=n;++i)
		if (!siz[i] && i!=1) ans+=m;
		else if (siz[i]==1) ++ans;
	printf("%d\n",ans);
	return 0;
}

C. CF 739B Alyona and a tree

題目

LUOGU CF 739B
CF 739B

程式碼

#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
const int maxn=2e5+10;
template<typename T>inline void read(T &x)
{
	x=0;
	register int f=1;
	register char ch=getchar();
	while (!isdigit(ch)) { if (ch=='-') f=-1; ch=getchar();}
	while (isdigit(ch)) x=(x<<1)+(x<<3)+(ch^48), ch=getchar();
	x*=f;
}
template<typename T>inline void print(T x)
{
	if (x<0) putchar('-'),x=-x;
	if (x>9) print(x/10);
	putchar(x%10+48);
}
int ver[maxn<<1],edge[maxn<<1],Next[maxn<<1],head[maxn],len;
inline void add(int x,int y,int z)
{
	ver[++len]=y,edge[len]=z,Next[len]=head[x],head[x]=len;
}
ll d[maxn];//必須用long long，否則過不了，如果你想一直莫名WA的話，可以不管
int f[maxn][19];
int a[maxn];
int ans[maxn];
inline void dfs(int x,int fa,int dist)
{
	d[x]=d[fa]+dist,f[x][0]=fa;
	for (int i=1;i<=18;++i)
		f[x][i]=f[f[x][i-1]][i-1];
	for (int i=head[x];i;i=Next[i])
	{
		int y=ver[i],z=edge[i];
		if (y==fa) continue;
		dfs(y,x,z);
		register int val=a[y],k=1,now=y;
		while (k&&now)
		{
			if (d[now]-d[f[now][k]]<=val)
			{
				val-=d[now]-d[f[now][k]];
				now=f[now][k];
				k<<=1;
			}
			else k>>=1;
		}
		if (d[now]-d[f[now][0]]<=val)
			now=f[now][0];
		--ans[f[now][0]],++ans[f[y][0]];
	}
	ans[fa]+=ans[x];
}
int main()
{
	int n,y,z;read(n);
	for (int i=1;i<=n;++i)
		read(a[i]);
	for (int i=2;i<=n;++i)
	{
		read(y);read(z);
		add(i,y,z);add(y,i,z);
	}
	dfs(1,0,0);
	for (int i=1;i<=n;++i)
		print(ans[i]),putchar(' ');
	return 0;
}