https://www.51nod.com/Challenge/Problem.html#!#problemId=1766
在点集S1 S2中各找出两个最远的点 将S1 S2合并后最远的两个点一定在这四个点之间 满足区间可加性 线段树优化
还有就是求LCA 发现之前一直写的是假算法 每次查询都是log的复杂度。。完全可以利用倍增数组结合位运算做到O1查询 就和普通rmq一样
#include <bits/stdc++.h>
using namespace std;
const int maxn=1e5+10;
struct node1
{
int v,w,next;
};
struct node2
{
int u,v,val;
};
node1 edge[2*maxn];
node2 tree[4*maxn];
int dp[2*maxn][20];
int first[maxn],deep[maxn],dis[maxn],mp1[maxn],mp2[2*maxn],logval[2*maxn];
int n,q,num;
template <class T>
inline void _cin(T &ret)
{
char c;
ret = 0;
while((c = getchar()) < '0' || c > '9');
while(c >= '0' && c <= '9')
{
ret = ret * 10 + (c - '0');
c = getchar();
}
}
void addedge(int u,int v,int w)
{
edge[num].v=v;
edge[num].w=w;
edge[num].next=first[u];
first[u]=num++;
}
void dfs(int cur,int fa)
{
int i,v,w;
num++;
mp1[cur]=num,mp2[num]=cur;
for(i=first[cur];i!=-1;i=edge[i].next){
v=edge[i].v,w=edge[i].w;
if(v!=fa){
dp[v][0]=cur;
deep[v]=deep[cur]+1,dis[v]=dis[cur]+w;
dfs(v,cur);
num++;
mp2[num]=cur;
}
}
}
void solve()
{
int i,j;
dp[1][0]=0;
deep[1]=1,dis[1]=0;
num=0;
dfs(1,0);
logval[0]=-1;
for(i=1;i<=num;i++) logval[i]=logval[i/2]+1;
for(i=1;i<=num;i++) dp[i][0]=mp2[i];
for(j=1;j<=20;j++){
for(i=1;i+(1<<j)<=num;i++){
if(deep[dp[i][j-1]]<deep[dp[i+(1<<(j-1))][j-1]]) dp[i][j]=dp[i][j-1];
else dp[i][j]=dp[i+(1<<(j-1))][j-1];
}
}
}
int getlca(int x,int y)
{
int res,k;
if(mp1[x]>mp1[y]) swap(x,y);
k=logval[mp1[y]-mp1[x]+1];
if(deep[dp[mp1[x]][k]]<deep[dp[mp1[y]-(1<<k)+1][k]]) res=dp[mp1[x]][k];
else res=dp[mp1[y]-(1<<k)+1][k];
return res;
}
void pushup(int cur)
{
int u,v,val,tu,tv,lca;
val=-1;
if(val<tree[2*cur].val){
u=tree[2*cur].u,v=tree[2*cur].v,val=tree[2*cur].val;
}
if(val<tree[2*cur+1].val){
u=tree[2*cur+1].u,v=tree[2*cur+1].v,val=tree[2*cur+1].val;
}
tu=tree[2*cur].u,tv=tree[2*cur+1].u,lca=getlca(tu,tv);
if(val<dis[tu]+dis[tv]-2*dis[lca]){
u=tu,v=tv,val=dis[tu]+dis[tv]-2*dis[lca];
}
tu=tree[2*cur].u,tv=tree[2*cur+1].v,lca=getlca(tu,tv);
if(val<dis[tu]+dis[tv]-2*dis[lca]){
u=tu,v=tv,val=dis[tu]+dis[tv]-2*dis[lca];
}
tu=tree[2*cur].v,tv=tree[2*cur+1].u,lca=getlca(tu,tv);
if(val<dis[tu]+dis[tv]-2*dis[lca]){
u=tu,v=tv,val=dis[tu]+dis[tv]-2*dis[lca];
}
tu=tree[2*cur].v,tv=tree[2*cur+1].v,lca=getlca(tu,tv);
if(val<dis[tu]+dis[tv]-2*dis[lca]){
u=tu,v=tv,val=dis[tu]+dis[tv]-2*dis[lca];
}
tree[cur].u=u,tree[cur].v=v,tree[cur].val=val;
}
void build(int l,int r,int cur)
{
int m;
if(l==r){
tree[cur].u=l,tree[cur].v=l,tree[cur].val=0;
return;
}
m=(l+r)/2;
build(l,m,2*cur);
build(m+1,r,2*cur+1);
pushup(cur);
}
void query(int &uu,int &vv,int &vall,int pl,int pr,int l,int r,int cur)
{
int m;
int u1,v1,val1,u2,v2,val2;
int u,v,val,tu,tv,lca;
if(pl<=l&&r<=pr){
uu=tree[cur].u,vv=tree[cur].v,vall=tree[cur].val;
return;
}
m=(l+r)/2,u1=-1,u2=-1;
if(pl<=m) query(u1,v1,val1,pl,pr,l,m,2*cur);
if(pr>m) query(u2,v2,val2,pl,pr,m+1,r,2*cur+1);
if(u1==-1) uu=u2,vv=v2,vall=val2;
else if(u2==-1) uu=u1,vv=v1,vall=val1;
else{
val=-1;
if(val<val1){
u=u1,v=v1,val=val1;
}
if(val<val2){
u=u2,v=v2,val=val2;
}
tu=u1,tv=u2,lca=getlca(tu,tv);
if(val<dis[tu]+dis[tv]-2*dis[lca]){
u=tu,v=tv,val=dis[tu]+dis[tv]-2*dis[lca];
}
tu=u1,tv=v2,lca=getlca(tu,tv);
if(val<dis[tu]+dis[tv]-2*dis[lca]){
u=tu,v=tv,val=dis[tu]+dis[tv]-2*dis[lca];
}
tu=v1,tv=u2,lca=getlca(tu,tv);
if(val<dis[tu]+dis[tv]-2*dis[lca]){
u=tu,v=tv,val=dis[tu]+dis[tv]-2*dis[lca];
}
tu=v1,tv=v2,lca=getlca(tu,tv);
if(val<dis[tu]+dis[tv]-2*dis[lca]){
u=tu,v=tv,val=dis[tu]+dis[tv]-2*dis[lca];
}
uu=u,vv=v,vall=val;
}
}
int main()
{
int i,u,v,w;
int val,tu,tv,lca;
int a,b,c,d,u1,v1,val1,u2,v2,val2;
//scanf("%d",&n);
_cin(n);
memset(first,-1,sizeof(first));
num=0;
for(i=1;i<=n-1;i++){
//scanf("%d%d%d",&u,&v,&w);
_cin(u),_cin(v),_cin(w);
addedge(u,v,w);
addedge(v,u,w);
}
solve();
build(1,n,1);
//scanf("%d",&q);
_cin(q);
while(q--){
//scanf("%d%d%d%d",&a,&b,&c,&d);
_cin(a),_cin(b),_cin(c),_cin(d);
query(u1,v1,val1,a,b,1,n,1);
query(u2,v2,val2,c,d,1,n,1);
val=-1;
tu=u1,tv=u2,lca=getlca(tu,tv);
val=max(val,dis[tu]+dis[tv]-2*dis[lca]);
tu=u1,tv=v2,lca=getlca(tu,tv);
val=max(val,dis[tu]+dis[tv]-2*dis[lca]);
tu=v1,tv=u2,lca=getlca(tu,tv);
val=max(val,dis[tu]+dis[tv]-2*dis[lca]);
tu=v1,tv=v2,lca=getlca(tu,tv);
val=max(val,dis[tu]+dis[tv]-2*dis[lca]);
printf("%d\n",val);
}
return 0;
}
/*
20
9 10 1
9 4 1
10 11 1
10 12 1
10 6 1
10 1 1
12 7 1
12 2 1
1 13 1
1 14 1
1 5 1
7 3 1
7 8 1
14 15 1
14 16 1
14 17 1
3 18 1
17 19 1
17 20 1
1
8 20 4 4
*/