「POJ3237」Tree

2014年12月21日5,8260

Description

You are given a tree with N nodes. The tree’s nodes are numbered 1 through N and its edges are numbered 1 through N − 1. Each edge is associated with a weight. Then you are to execute a series of instructions on the tree. The instructions can be one of the following forms:

`CHANGE` i v	Change the weight of the ith edge to v
`NEGATE` a b	Negate the weight of every edge on the path from a to b
`QUERY` a b	Find the maximum weight of edges on the path from a to b

Input

The input contains multiple test cases. The first line of input contains an integer t (t ≤ 20), the number of test cases. Then follow the test cases.

Each test case is preceded by an empty line. The first nonempty line of its contains N (N ≤ 10,000). The next N − 1 lines each contains three integers a, band c, describing an edge connecting nodes a and b with weight c. The edges are numbered in the order they appear in the input. Below them are the instructions, each sticking to the specification above. A lines with the word “DONE” ends the test case.

Output

For each “QUERY” instruction, output the result on a separate line.

Sample Input

1

3
1 2 1
2 3 2
QUERY 1 2
CHANGE 1 3
QUERY 1 2
DONE

1 2 1

2 3 2

QUERY 1 2

CHANGE 1 3

QUERY 1 2

DONE

Sample Output

1
3

题解

边权放到点权上，树链剖分裸题

negate是mx=-mn mn=-mx

#include<cstdio>
#include<cmath>
#include<cstring>
#include<iostream>
#include<algorithm>
#include<queue>
#define pa pair<int,int>
#define ll long long
#define inf 1000000000
using namespace std;
inline int read()
{
	int x=0,f=1;char ch=getchar();
	while(ch>'9'||ch<'0'){if(ch=='-')f=-1;ch=getchar();}
	while(ch>='0'&&ch<='9'){x=x*10+ch-'0';ch=getchar();}
	return x*f;
}
int bin[15];
int T,n,cnt,P;
int last[10005];
int bl[10005],pos[10005],to[10005];
int fa[10005][14],size[10005],deep[10005];
struct edge{
	int to,next,v;
}e[20005];
struct seg{
	int l,r,mn,mx,tag;
}t[40005];
void solve(int &x,int &y)
{
	int t=x;x=-y;y=-t;
}
void insert(int u,int v,int w)
{
	e[++cnt].to=v;e[cnt].next=last[u];last[u]=cnt;e[cnt].v=w;
	e[++cnt].to=u;e[cnt].next=last[v];last[v]=cnt;e[cnt].v=w;
}
void update(int k)
{
	t[k].mn=min(t[k<<1].mn,t[k<<1|1].mn);
	t[k].mx=max(t[k<<1].mx,t[k<<1|1].mx);
}
void pushdown(int k)
{
	int l=t[k].l,r=t[k].r;
	if(l==r||!t[k].tag)return;t[k].tag=0;
	t[k<<1].tag^=1;t[k<<1|1].tag^=1;
    solve(t[k<<1].mn,t[k<<1].mx);
	solve(t[k<<1|1].mn,t[k<<1|1].mx);
}
void build(int k,int l,int r)
{
	t[k].l=l;t[k].r=r;t[k].tag=0;
	t[k].mn=inf;t[k].mx=-inf;
	if(l==r)return;
	int mid=(l+r)>>1;
	build(k<<1,l,mid);build(k<<1|1,mid+1,r);
}
void change(int k,int x,int val)
{
	pushdown(k);
	int l=t[k].l,r=t[k].r,mid=(l+r)>>1;
	if(l==r)
	{
		t[k].mn=t[k].mx=val;return;
	}
	if(x<=mid)change(k<<1,x,val);
	else change(k<<1|1,x,val);
	update(k);
}
void rever(int k,int x,int y)
{
	pushdown(k);
	int l=t[k].l,r=t[k].r,mid=(l+r)>>1;
	if(l==x&&r==y)
	{
	    solve(t[k].mn,t[k].mx);
		t[k].tag=1;return;
	}
	if(y<=mid)rever(k<<1,x,y);
	else if(x>mid)rever(k<<1|1,x,y);
	else rever(k<<1,x,mid), rever(k<<1|1,mid+1,y);
	update(k);
}
int query(int k,int x,int y)
{
	pushdown(k);
	int l=t[k].l,r=t[k].r,mid=(l+r)>>1;
	if(x==l&&y==r)return t[k].mx;
	if(y<=mid)return query(k<<1,x,y);
	else if(x>mid)return query(k<<1|1,x,y);
	else return max(query(k<<1,x,mid),query(k<<1|1,mid+1,y));
}
void dfs1(int x)
{
	size[x]=1;
	for(int i=1;i<=13;i++)
		if(bin[i]<=deep[x])
			fa[x][i]=fa[fa[x][i-1]][i-1];
		else break;
	for(int i=last[x];i;i=e[i].next)
		if(e[i].to!=fa[x][0])
		{
			deep[e[i].to]=deep[x]+1;
			fa[e[i].to][0]=x;
			dfs1(e[i].to);
			size[x]+=size[e[i].to];
		}
}
void dfs2(int x,int chain)
{
	bl[x]=chain;pos[x]=++P;
	int k=0;
	for(int i=last[x];i;i=e[i].next)
		if(e[i].to!=fa[x][0])
		{
			if(size[e[i].to]>size[k])k=e[i].to;
		}
		else 
		{
			to[i>>1]=pos[x];change(1,pos[x],e[i].v);
		}
	if(!k)return;
	dfs2(k,chain);
	for(int i=last[x];i;i=e[i].next)
		if(e[i].to!=fa[x][0]&&e[i].to!=k)
			dfs2(e[i].to,e[i].to);
}
int lca(int x,int y)
{
	if(deep[x]<deep[y])swap(x,y);
	int t=deep[x]-deep[y];
	for(int i=0;i<=13;i++)
		if(t&bin[i])x=fa[x][i];
	for(int i=13;i>=0;i--)
		if(fa[x][i]!=fa[y][i])
			x=fa[x][i],y=fa[y][i];
	if(x==y)return x;
	return fa[x][0];
}
int solvequery(int x,int f)
{
	int mx=-inf;
	while(bl[x]!=bl[f])
	{
		mx=max(mx,query(1,pos[bl[x]],pos[x]));
		x=fa[bl[x]][0];
	}
	if(pos[f]+1<=pos[x])
		mx=max(mx,query(1,pos[f]+1,pos[x]));
	return mx;
}
void solverever(int x,int f)
{
	while(bl[x]!=bl[f])
	{
		rever(1,pos[bl[x]],pos[x]);
		x=fa[bl[x]][0];
	}
	if(pos[f]+1<=pos[x])
		rever(1,pos[f]+1,pos[x]);
}
int main()
{
	bin[0]=1;for(int i=1;i<15;i++)bin[i]=bin[i-1]<<1;
	T=read();
	while(T--)
	{
		P=0;cnt=1;
		memset(last,0,sizeof(last));
		memset(deep,0,sizeof(deep));
		memset(fa,0,sizeof(fa));
		n=read();
		for(int i=1;i<n;i++)
		{
			int u=read(),v=read(),w=read();
			insert(u,v,w);
		}
		build(1,1,n);
		dfs1(1);
		dfs2(1,1);
		char ch[10];
		while(scanf("%s",ch+1))
		{
			if(ch[1]=='D')break;
			int x=read(),y=read();
			if(ch[1]=='Q')
			{
				int f=lca(x,y);
				printf("%d\n",max(solvequery(x,f),solvequery(y,f)));
			}
			if(ch[1]=='C')
				change(1,to[x],y);
			if(ch[1]=='N')
			{
				int f=lca(x,y);
				solverever(x,f);solverever(y,f);
			}
		}
	}
	return 0;
}

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#include<cstdio>

#include<cmath>

#include<cstring>

#include<iostream>

#include<algorithm>

#include<queue>

#define pa pair<int,int>

#define ll long long

#define inf 1000000000

using namespace std;

inline int read()

{

int x=0,f=1;char ch=getchar();

while(ch>'9'||ch<'0'){if(ch=='-')f=-1;ch=getchar();}

while(ch>='0'&&ch<='9'){x=x*10+ch-'0';ch=getchar();}

return x*f;

}

int bin[15];

int T,n,cnt,P;

int last[10005];

int bl[10005],pos[10005],to[10005];

int fa[10005][14],size[10005],deep[10005];

struct edge{

int to,next,v;

}e[20005];

struct seg{

int l,r,mn,mx,tag;

}t[40005];

void solve(int &x,int &y)

{

int t=x;x=-y;y=-t;

}

void insert(int u,int v,int w)

{

e[++cnt].to=v;e[cnt].next=last[u];last[u]=cnt;e[cnt].v=w;

e[++cnt].to=u;e[cnt].next=last[v];last[v]=cnt;e[cnt].v=w;

}

void update(int k)

{

t[k].mn=min(t[k<<1].mn,t[k<<1|1].mn);

t[k].mx=max(t[k<<1].mx,t[k<<1|1].mx);

}

void pushdown(int k)

{

int l=t[k].l,r=t[k].r;

if(l==r||!t[k].tag)return;t[k].tag=0;

t[k<<1].tag^=1;t[k<<1|1].tag^=1;

solve(t[k<<1].mn,t[k<<1].mx);

solve(t[k<<1|1].mn,t[k<<1|1].mx);

}

void build(int k,int l,int r)

{

t[k].l=l;t[k].r=r;t[k].tag=0;

t[k].mn=inf;t[k].mx=-inf;

if(l==r)return;

int mid=(l+r)>>1;

build(k<<1,l,mid);build(k<<1|1,mid+1,r);

}

void change(int k,int x,int val)

{

pushdown(k);

int l=t[k].l,r=t[k].r,mid=(l+r)>>1;

if(l==r)

{

t[k].mn=t[k].mx=val;return;

}

if(x<=mid)change(k<<1,x,val);

else change(k<<1|1,x,val);

update(k);

}

void rever(int k,int x,int y)

{

pushdown(k);

int l=t[k].l,r=t[k].r,mid=(l+r)>>1;

if(l==x&&r==y)

{

solve(t[k].mn,t[k].mx);

t[k].tag=1;return;

}

if(y<=mid)rever(k<<1,x,y);

else if(x>mid)rever(k<<1|1,x,y);

else rever(k<<1,x,mid), rever(k<<1|1,mid+1,y);

update(k);

}

int query(int k,int x,int y)

{

pushdown(k);

int l=t[k].l,r=t[k].r,mid=(l+r)>>1;

if(x==l&&y==r)return t[k].mx;

if(y<=mid)return query(k<<1,x,y);

else if(x>mid)return query(k<<1|1,x,y);

else return max(query(k<<1,x,mid),query(k<<1|1,mid+1,y));

}

void dfs1(int x)

{

size[x]=1;

for(int i=1;i<=13;i++)

if(bin[i]<=deep[x])

fa[x][i]=fa[fa[x][i-1]][i-1];

else break;

for(int i=last[x];i;i=e[i].next)

if(e[i].to!=fa[x][0])

{

deep[e[i].to]=deep[x]+1;

fa[e[i].to][0]=x;

dfs1(e[i].to);

size[x]+=size[e[i].to];

}

void dfs2(int x,int chain)

{

bl[x]=chain;pos[x]=++P;

int k=0;

for(int i=last[x];i;i=e[i].next)

if(e[i].to!=fa[x][0])

{

if(size[e[i].to]>size[k])k=e[i].to;

}

else

{

to[i>>1]=pos[x];change(1,pos[x],e[i].v);

}

if(!k)return;

dfs2(k,chain);

for(int i=last[x];i;i=e[i].next)

if(e[i].to!=fa[x][0]&&e[i].to!=k)

dfs2(e[i].to,e[i].to);

}

int lca(int x,int y)

{

if(deep[x]<deep[y])swap(x,y);

int t=deep[x]-deep[y];

for(int i=0;i<=13;i++)

if(t&bin[i])x=fa[x][i];

for(int i=13;i>=0;i--)

if(fa[x][i]!=fa[y][i])

x=fa[x][i],y=fa[y][i];

if(x==y)return x;

return fa[x][0];

}

int solvequery(int x,int f)

{

int mx=-inf;

while(bl[x]!=bl[f])

{

mx=max(mx,query(1,pos[bl[x]],pos[x]));

x=fa[bl[x]][0];

}

if(pos[f]+1<=pos[x])

mx=max(mx,query(1,pos[f]+1,pos[x]));

return mx;

}

void solverever(int x,int f)

{

while(bl[x]!=bl[f])

{

rever(1,pos[bl[x]],pos[x]);

x=fa[bl[x]][0];

}

if(pos[f]+1<=pos[x])

rever(1,pos[f]+1,pos[x]);

}

int main()

{

bin[0]=1;for(int i=1;i<15;i++)bin[i]=bin[i-1]<<1;

T=read();

while(T--)

{

P=0;cnt=1;

memset(last,0,sizeof(last));

memset(deep,0,sizeof(deep));

memset(fa,0,sizeof(fa));

n=read();

for(int i=1;i<n;i++)

{

int u=read(),v=read(),w=read();

insert(u,v,w);

}

build(1,1,n);

dfs1(1);

dfs2(1,1);

char ch[10];

while(scanf("%s",ch+1))

{

if(ch[1]=='D')break;

int x=read(),y=read();

if(ch[1]=='Q')

{

int f=lca(x,y);

printf("%d\n",max(solvequery(x,f),solvequery(y,f)));

}

if(ch[1]=='C')

change(1,to[x],y);

if(ch[1]=='N')

{

int f=lca(x,y);

solverever(x,f);solverever(y,f);

}

return 0;

}

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