COT2 - Count on a tree II（树上莫队）

COT2 - Count on a tree II

You are given a tree with N nodes. The tree nodes are numbered from 1 to N. Each node has an integer weight.

We will ask you to perform the following operation:

u v : ask for how many different integers that represent the weight of nodes there are on the path from u to v.

---

Input

In the first line there are two integers N and M. (N <= 40000, M <= 100000)

In the second line there are N integers. The i-th integer denotes the weight of the i-th node.

In the next N-1 lines, each line contains two integers u v, which describes an edge (u, v).

In the next M lines, each line contains two integers u v, which means an operation asking for how many different integers that represent the weight of nodes there are on the path from u to v.

---

Output

For each operation, print its result.

---

Example

Input:

8 2
105 2 9 3 8 5 7 7
1 2
1 3
1 4
3 5
3 6
3 7
4 8
2 5
7 8

Output:

4
4

思路：树上莫队的模板题

LCA用tarjan算法来找，可以变成DFS以后的序列，然后再用莫队算法的思路。

#include <bits/stdc++.h>

using namespace std;
int const SIZE=40100;
int const BLOCK_SIZE=300;

//利用hash记录LCA
struct Hash{
    typedef struct __t{int a;int b;__t(int aa=0,int bb=0):a(aa),b(bb){}}key_t;
    typedef int value_t;
    enum{MOD=0x1fffff};
    key_t keys[MOD+1];
    value_t values[MOD+1];

    int head[MOD+1];
    int next[MOD+1];
    int toUsed;

    Hash():toUsed(0){fill(head,head+MOD+1,-1);}

    void clear(){fill(head,head+MOD+1,-1);toUsed=0;}

    int getKey(key_t const&key)const {
        int ret=17;
        ret=ret*37+key.a;
        ret=ret*37+key.b;
        return ret;
    }

    void insert(key_t const&key,value_t const&value){
        int k = getKey(key) & MOD;
        keys[toUsed] = key;
        values[toUsed] = value;
        next[toUsed] = head[k];
        head[k] = toUsed++;
    }

    value_t find(key_t const&key)const{
        int k = getKey(key) & MOD;
        for(int i=head[k];i!=-1;i=next[i]){
            if ( keys[i].a == key.a && keys[i].b == key.b ) return values[i];
        }
        return 0;
    }

    void disp(FILE*fp)const{
        for(int i=1;i<toUsed;++i){
            fprintf(fp,"(%d %d): %d\n",keys[i].a,keys[i].b,values[i]);
        }
    }
}Lca;

struct dege_t{
    int to;
    int next;
}Edge[SIZE<<1];

int ECnt=1;
int Vertex[SIZE]={0};

inline void makeEdge(int a,int b)
{
    Edge[ECnt].to=b;
    Edge[ECnt].next=Vertex[a];
    Vertex[a]=ECnt++;

    Edge[ECnt].to=a;
    Edge[ECnt].next=Vertex[b];
    Vertex[b]=ECnt++;
}

//生成DFS序
int InIdx[SIZE],OutIdx[SIZE];
int NewIdx[SIZE<<1];
int NCnt = 1;
void dfs(int node,int parent){
    NewIdx[NCnt] = node;
    InIdx[node] = NCnt++;
    for(int next=Vertex[node];next;next=Edge[next].next){
        int to = Edge[next].to;
        if ( to != parent ) dfs(to,node);
    }
    NewIdx[NCnt] = node;
    OutIdx[node] = NCnt++;
}

//Tarjan算法中用到的并查集
int Father[SIZE];
int find(int x){return x==Father[x]?x:Father[x]=find(Father[x]);}

bool Flag[SIZE] = {false};
vector<vector<int> > Questions(SIZE,vector<int>());

//Tarjan算法一次性求出所有的LCA
void Tarjan(int u,int parent){
    Father[u] = u;
    Flag[u] = true;

    for(int next=Vertex[u];next;next=Edge[next].next){
        int to = Edge[next].to;
        if ( to == parent ) continue;
        Tarjan(to,u);
        Father[to] = u;
    }

    vector<int>&vec=Questions[u];
    for(vector<int>::iterator it=vec.begin();it!=vec.end();++it){
        int v = *it;
        if ( Flag[v] ){
            int r = find(v);
            Lca.insert(Hash::key_t(u,v),r);
            Lca.insert(Hash::key_t(v,u),r);
        }
    }
}

struct _t{
    int s,e;
    int idx;
    int lca;
};

bool operator  < (_t const&lhs,_t const&rhs){
    int ln = lhs.s / BLOCK_SIZE;
    int rn = rhs.s / BLOCK_SIZE;
    return ln < rn || ( ln == rn && lhs.e < rhs.e );
}
int N,M;
int A[SIZE];
_t B[100000];

//将原树上的路径问题转化为DFS序中的区间问题
inline void mkQuestion(int a,int b,int idx){
    int lca = Lca.find(Hash::key_t(a,b));
    if ( lca == a || lca == b ){
        int t = lca == a ? b : a;
        B[idx].s = OutIdx[t];
        B[idx].e = OutIdx[lca];
        B[idx].lca = 0;
    }else{
        B[idx].lca = lca;
        if ( OutIdx[a] < InIdx[b] ) B[idx].s = OutIdx[a], B[idx].e = InIdx[b];
        else B[idx].s = OutIdx[b], B[idx].e = InIdx[a];
    }
}

int MoAns;
int Ans[100000],Cnt[SIZE];
inline void insert(int n){
    if ( 1 == ++Cnt[n] ) ++MoAns;
}

inline void remove(int n){
    if ( 0 == --Cnt[n] ) --MoAns;
}

void MoOp(int idx){
    int k = NewIdx[idx];
    if ( Flag[k] ) remove(A[k]);
    else insert(A[k]);
    Flag[k] ^= 1;
}
void Mo(){
    sort(B,B+M);

    fill(Flag,Flag+N+1,false);
    int curLeft = 1;
    int curRight = 0;
    MoAns = 0;

    for(int i=0;i<M;++i){
        while( curRight < B[i].e  ) MoOp(++curRight);
        while( curLeft > B[i].s ) MoOp(--curLeft);
        while( curRight > B[i].e ) MoOp(curRight--);
        while( curLeft < B[i].s ) MoOp(curLeft++);
        if ( B[i].lca ){
            Ans[B[i].idx] = MoAns + ( 0 == Cnt[A[B[i].lca]] ? 1 : 0 );
        }else{
            Ans[B[i].idx] = MoAns;
        }

    }
}
void init(int n){
    ECnt = NCnt = 1;
    fill(Vertex,Vertex+n+1,0);
    fill(Flag,Flag+n+1,false);
}
int getUnsigned(){
    char ch = getchar();
    while( ch > '9' || ch < '0' ) ch = getchar();

    int ret = 0;
    do ret = ret * 10 + (int)(ch-'0');while( '0' <= (ch=getchar()) && ch <= '9' );
    return ret;
}

int W[SIZE];
bool read(){
    if ( EOF == scanf("%d",&N) ) return false;
    M = getUnsigned();

    init(N);

    //权值输入并离散化
    for(int i=1;i<=N;++i) W[i] = A[i] = getUnsigned();
    sort(W+1,W+N+1);
    int* pn = unique(W+1,W+N+1);
    for(int i=1;i<=N;++i) A[i] = lower_bound(W+1,pn,A[i]) - W;

    int a,b;
    for(int i=1;i<N;++i){
        a = getUnsigned();
        b = getUnsigned();
        makeEdge(a,b);
    }
    dfs(1,0);

    for(int i=0;i<M;++i){
        B[i].s = getUnsigned();
        B[i].e = getUnsigned();
        B[i].idx = i;
        Questions[B[i].s].push_back(B[i].e);
        Questions[B[i].e].push_back(B[i].s);
    }

    Tarjan(1,0);
    for(int i=0;i<M;++i) mkQuestion(B[i].s,B[i].e,i);

    return true;
}
int main(){
    //freopen("1.txt","r",stdin);
    while ( read() ){
        Mo();
        for(int i=0;i<M;++i)printf("%d\n",Ans[i]);
    }
    return 0;
}