題目連結

題目大意:  就是求在樹上 (u,v)的路上的第K小的權值

解題思路:  首先對於求第K小的問題 我們可以用主席樹搞 ,沒有問題,  但是對於一個樹形結構,我們需要將其轉化為線性,然後需要樹剖才能做.

然後考慮鏈上的第k值怎麼維護 ,  發現如果樹剖計算的話 維護不了啊  因為(u,v)的路 可能在很多個鏈上,那麼不能對每個求第K值,這樣明顯是錯誤的啊,

然後我們知道主席樹其實就是維護了一個字首和

那麼我們可以對每一個節點到根節點建立字首和,就能找任意一個節點到根節點的第K值,  那麼根據主席樹的性質,我們就能夠計算(u,v)的路上的第K值了  只要在查詢的時候稍改變一下就行了

cnt = sum[ls[u]]+sum[ls[v]]-sum[ls[lca(u,v)]]-sum[ls[fa[lca(u,v)]]];  

///                 .-~~~~~~~~~-._       _.-~~~~~~~~~-.
///             __.'              ~.   .~              `.__
///           .'//                  \./                  \\`.
///        .'//                     |                     \\`.
///       .'// .-~"""""""~~~~-._     |     _,-~~~~"""""""~-. \\`.
///     .'//.-"                 `-.  |  .-'                 "-.\\`.
///   .'//______.============-..   \ | /   ..-============.______\\`.
/// .'______________________________\|/______________________________`.
#pragma GCC optimize("Ofast")
#pragma comment(linker, "/STACK:102400000,102400000")
#pragma GCC target(sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx) 
#include<bits/stdc++.h>
using namespace std;

#define pi acos(-1)
#define s_1(x) scanf("%d",&x)
#define s_2(x,y) scanf("%d%d",&x,&y)
#define s_3(x,y,z) scanf("%d%d%d",&x,&y,&z)
#define s_4(x,y,z,X) scanf("%d%d%d%d",&x,&y,&z,&X)
#define S_1(x) scan_d(x)
#define S_2(x,y) scan_d(x),scan_d(y)
#define S_3(x,y,z) scan_d(x),scan_d(y),scan_d(z)
#define PI acos(-1)
#define endl '\n'
#define srand() srand(time(0));
#define me(x,y) memset(x,y,sizeof(x));
#define foreach(it,a) for(__typeof((a).begin()) it=(a).begin();it!=(a).end();it++)
#define close() ios::sync_with_stdio(0); cin.tie(0);
#define FOR(x,n,i) for(int i=x;i<=n;i++)
#define FOr(x,n,i) for(int i=x;i<n;i++)
#define fOR(n,x,i) for(int i=n;i>=x;i--)
#define fOr(n,x,i) for(int i=n;i>x;i--)
#define W while
#define sgn(x) ((x) < 0 ? -1 : (x) > 0)
#define bug printf("***********\n");
#define db double
#define ll long long
#define mp make_pair
#define pb push_back
#define sz size
#define fi first
#define se second
#define pf printf
typedef long long LL;
typedef pair <int, int> ii;
const int INF=0x3f3f3f3f;
const LL LINF=0x3f3f3f3f3f3f3f3fLL;
const int dx[]={-1,0,1,0,1,-1,-1,1};
const int dy[]={0,1,0,-1,-1,1,-1,1};
const int maxn=1e2+7;
const int _=1e5+10;
const double EPS=1e-8;
const double eps=1e-8;
const LL mod=1e9+7;
template<class T>inline T min(T a,T b,T c) { return min(min(a,b),c);}
template<class T>inline T max(T a,T b,T c) { return max(max(a,b),c);}
template<class T>inline T min(T a,T b,T c,T d) { return min(min(a,b),min(c,d));}
template<class T>inline T max(T a,T b,T c,T d) { return max(max(a,b),max(c,d));}
template <class T>
inline bool scan_d(T &ret){char c;int sgn;if (c = getchar(), c == EOF){return 0;}
while (c != '-' && (c < '0' || c > '9')){c = getchar();}sgn = (c == '-') ? -1 : 1;ret = (c == '-') ? 0 : (c - '0');
while (c = getchar(), c >= '0' && c <= '9'){ret = ret * 10 + (c - '0');}ret *= sgn;return 1;}

inline bool scan_lf(double &num){char in;double Dec=0.1;bool IsN=false,IsD=false;in=getchar();if(in==EOF) return false;
while(in!='-'&&in!='.'&&(in<'0'||in>'9'))in=getchar();if(in=='-'){IsN=true;num=0;}else if(in=='.'){IsD=true;num=0;}
else num=in-'0';if(!IsD){while(in=getchar(),in>='0'&&in<='9'){num*=10;num+=in-'0';}}
if(in!='.'){if(IsN) num=-num;return true;}else{while(in=getchar(),in>='0'&&in<='9'){num+=Dec*(in-'0');Dec*=0.1;}}
if(IsN) num=-num;return true;}

void Out(LL a){if(a < 0) { putchar('-'); a = -a; }if(a >= 10) Out(a / 10);putchar(a % 10 + '0');}
void print(LL a){ Out(a),puts("");}
//cerr << "run time is " << clock() << endl;

int n,m;
int w[_],b[_];

struct node{
    int to,next;
}G[_<<1];
int head[_],tot;
int rt[_],ls[_*20],rs[_*20],sum[_*20],chairtree,siz;

void build(int &rt,int l,int r){
    rt=++chairtree;
    sum[rt]=0;
    if(l>=r)return ;
    int m =((r-l)>>1)+l;
    build(ls[rt],l,m);
    build(rs[rt],m+1,r);
}

void update(int& rt,int l,int r,int last,int pos){
    rt=++chairtree;
    ls[rt]=ls[last];
    rs[rt]=rs[last];
    sum[rt]=sum[last]+1;

    if(l>=r) return ;
    int m=((r-l)>>1)+l;
    if(pos<=m) update(ls[rt],l  ,m,ls[last],pos);
    else       update(rs[rt],m+1,r,rs[last],pos);
}

int query(int rt,int l,int r,int last,int lca,int flca,int k){
    if(l>=r) return l;
    int m=((r-l)>>1)+l;
    int cnt=sum[ls[rt]]+sum[ls[last]]-sum[ls[lca]]-sum[ls[flca]];
    if(k<=cnt) query(ls[rt],l  ,m,ls[last],ls[lca],ls[flca],k);
    else       query(rs[rt],m+1,r,rs[last],rs[lca],rs[flca],k-cnt);
}

void dfs(int rt,int l,int r){

    int m = ((r-l)>>1)+l;
    printf("%d",sum[rt]);
    if(l>=r) return ;printf("( ");
    dfs(ls[rt],l,m);printf("_%*d,",2,ls[rt]);
    dfs(rs[rt],m+1,r);printf("_%*d )",2,rs[rt]);
}
/**
ChairTree end
*/

void add(int u,int v){
    G[++tot].to=v,G[tot].next=head[u],head[u]=tot;
    G[++tot].to=u,G[tot].next=head[v],head[v]=tot;
}

int dep[_],fa[_],sz[_],son[_];
void dfs1(int u,int f,int d){
    dep[u]=d,fa[u]=f,sz[u]=1,son[u]=0;
    for(int i=head[u],to;i;i=G[i].next){
        to=G[i].to;
        if(to==f)continue;
        dfs1(to,u,d+1);
        sz[u]+=sz[to];
        if(sz[son[u]]<sz[to])son[u]=to;
    }
}

int tree[_],top[_],pre[_],cnt;
void dfs2(int u,int tp){
    top[u]=tp,tree[u]=++cnt,pre[tree[u]]=u;
    update(rt[u],1,siz,rt[fa[u]],w[u]);
    if(!son[u])return;
    dfs2(son[u],tp);
    for(int i=head[u],to;i;i=G[i].next){
        to=G[i].to;
        if(to==fa[u]||to==son[u])continue;
        dfs2(to,to);
    }
}

int Lca(int x,int y){
    int fx=top[x],fy=top[y];
    while(fx!=fy){
        if(dep[fx]<dep[fy])swap(x,y),swap(fx,fy);
        x=fa[fx],fx=top[x];
    }
    if(dep[x]>dep[y])swap(x,y);
    return x;
}

 
void solve() {
	s_2(n,m);
	FOR(1,n,i) s_1(w[i]),b[i]=w[i];
	FOr(1,n,i) {
		int u,v;
		s_2(u,v);
		add(u,v);
	}
	fa[1]=0;
	sort(b+1,b+n+1);
	siz=unique(b+1,b+n+1)-(b+1);
	FOR(1,n,i)
		w[i]=lower_bound(b+1,b+siz+1,w[i])-b;
	build(rt[0],1,siz);
	dfs1(1,0,1);
	dfs2(1,1);
	while(m--) {
		int u,v,k;
		s_3(u,v,k);
		int lca=Lca(u,v);
		//cout<<lca<<endl; 
		print(b[query(rt[u],1,siz,rt[v],rt[lca]
			,rt[fa[lca]],k)]);
	}
}
int main() {
	//freopen( "1.in" , "r" , stdin );
    //freopen( "1.out" , "w" , stdout );
    int t=1;
    //init();
    //s_1(t);
    for(int cas=1;cas<=t;cas++) {
        //printf("Case #%d: ",cas);
        solve();
    }
}