Query on a tree 树链剖分第一次写-优快云博客

本文介绍了一种利用树状结构进行高效路径查询的方法，并通过线段树实现节点属性的快速更新与查询优化。文章详细展示了如何构建树形结构、进行节点划分以及线段树的具体实现细节。

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#include <cstring>
#include <cstdio>
#include <iostream>
#include <algorithm>
#include <vector>
#include <map>
#include <cmath>
#include <queue>
#include <string>
#include <set>
#include <stack>

using namespace std;
#define ll long long
#define eps 1e-8
#define pi acos(-1.0)
#define inf 0x3f3f3f3f
#define mod 1000000007
#define sqr(x) ((x)*(x))
#define lson (u<<1)
#define rson (u<<1|1)
#define N 10100
#define M 100100

int n;
int h[N],vv[M],nxt[M],ww[M],e;
int sz[N],son[N],fa[N],top[N],dep[N];
int eid[N],E,cost[N];
int re[N];

int ma[N<<2];

void add(int u,int v,int w)
{
	vv[e] = v, ww[e] = w, nxt[e] = h[u], h[u] = e++;
	vv[e] = u, ww[e] = w, nxt[e] = h[v], h[v] = e++;

}
void dfs1(int u,int f,int d){
	sz[u] = 1, fa[u] = f, dep[u] = d;
	son[u] = -1;
	for(int i=h[u];i+1;i=nxt[i])
	{
		int v = vv[i];
		if(v==f) continue;
		dfs1(v,u,d+1);
		if(son[u]==-1||sz[vv[son[u]]]<sz[v]) {
			son[u] = i;
		}
		sz[u] += sz[v];

	}

}
void dfs2(int u,int f)
{
	top[u] = u;

	if(f+1) {
        int fv = vv[f^1];
		top[u] = ( son[fv]==f ? top[fv]:u );
		re[u] = ++E;
		eid[f/2+1] = E;
		cost[E] = ww[f];
	}

	if(son[u]+1){

		dfs2(vv[son[u]],son[u]);
	}
	for(int i=h[u];i+1;i=nxt[i]){
		int v = vv[i];
		if(v==fa[u]||i==son[u]) continue;
		dfs2(v,i);
	}

}

void pushUp(int u){
	ma[u] = max(ma[lson],ma[rson]);
}
void build(int u,int l,int r){
	if(l>=r){
		ma[u] = cost[l];
		return;
	}
	int mid = (l+r)>>1;
	build(lson,l,mid);
	build(rson,mid+1,r);
	pushUp(u);
}
void update(int u,int l,int r,int pos,int val){
	if(l>=r){
		ma[u] = val;
		return;
	}
	int mid = (l+r)>>1;
	if(pos<=mid) update(lson,l,mid,pos,val);
	else update(rson,mid+1,r,pos,val);
	pushUp(u);
}
int query(int u,int L,int R,int l,int r){
	if(l<=L&&R<=r){
		return ma[u];
	}
	if(l>R||r<L) return 0;
	int mid = (L+R)>>1;
	return max(query(lson,L,mid,l,r),query(rson,mid+1,R,l,r));

}
int cal(int u,int v)
{
	int ret = 0;
	int f1 = top[u],f2 = top[v];
	while(f1!=f2){
		if(dep[f1]<dep[f2]){
			swap(f1,f2);
			swap(u,v);
		}
		ret = max(ret,query(1,1,E,re[f1],re[u]));
		u = fa[f1],f1 = top[u];

	}
	if(u==v) return ret;
	if(dep[u]>dep[v]) swap(u,v);
	return max(ret,query(1,1,E,re[vv[son[u]]],re[v]));
}
int main()
{
	char op[20];
	int T,a,b,c;
	scanf("%d",&T);
	while(T--)
	{

		memset(h,-1,sizeof(h));
		E = e = 0;
		scanf("%d",&n);
		for(int i=1;i<n;i++)
			scanf("%d%d%d",&a,&b,&c),add(a,b,c);

		dfs1(1,-1,1);

		dfs2(1,-1);

		build(1,1,E);

		while(~scanf("%s",op))
		{
			if(strcmp(op,"DONE")==0) break;
			scanf("%d%d",&a,&b);
			if(strcmp(op,"CHANGE")==0){
				update(1,1,E,eid[a],b);
			}
			else
				printf("%d\n",cal(a,b));
		}

	}


}