• CF375 D. Tree and Queries


    题目传送门:https://codeforces.com/problemset/problem/375/D

    题目大意:
    给定一个(n)个节点的树,每个节点有颜色(C_x),给定(m)组询问,每次询问(v_i)及其子树内,出现次数(geqslant k_i)的颜色种数


    首先给树上节点打上Dfs序,这样树上询问便可以转化为区间询问

    由于没有牵涉到修改,因此我们考虑莫队

    每次需要统计次数(geqslant k_i)的颜色种数,故我们用树状数组维护

    理论时间复杂度(O(nsqrt n log_2n)),但常数很小,因为莫队跑不满

    /*program from Wolfycz*/
    #include<map>
    #include<cmath>
    #include<cstdio>
    #include<vector>
    #include<cstring>
    #include<iostream>
    #include<algorithm>
    #define Fi first
    #define Se second
    #define ll_inf 1e18
    #define MK make_pair
    #define sqr(x) ((x)*(x))
    #define pii pair<int,int>
    #define int_inf 0x7f7f7f7f
    using namespace std;
    typedef long long ll;
    typedef unsigned int ui;
    typedef unsigned long long ull;
    inline char gc(){
    	static char buf[1000000],*p1=buf,*p2=buf;
    	return p1==p2&&(p2=(p1=buf)+fread(buf,1,1000000,stdin),p1==p2)?EOF:*p1++;
    }
    template<typename T>inline T frd(T x){
    	int f=1; char ch=gc();
    	for (;ch<'0'||ch>'9';ch=gc())	if (ch=='-')    f=-1;
    	for (;ch>='0'&&ch<='9';ch=gc())	x=(x<<1)+(x<<3)+ch-'0';
    	return x*f;
    }
    template<typename T>inline T read(T x){
    	int f=1; char ch=getchar();
    	for (;ch<'0'||ch>'9';ch=getchar())	if (ch=='-')	f=-1;
    	for (;ch>='0'&&ch<='9';ch=getchar())	x=(x<<1)+(x<<3)+ch-'0';
    	return x*f;
    }
    inline void print(int x){
    	if (x<0)	putchar('-'),x=-x;
    	if (x>9)	print(x/10);
    	putchar(x%10+'0');
    }
    const int N=1e5;
    int pre[(N<<1)+10],now[N+10],child[(N<<1)+10],DFN[N+10],FND[N+10],Sz[N+10];
    int Time,tot;
    void join(int x,int y){pre[++tot]=now[x],now[x]=tot,child[tot]=y;}
    void insert(int x,int y){join(x,y),join(y,x);}
    void Dfs(int x,int fa){
    	FND[DFN[x]=++Time]=x,Sz[x]++;
    	for (int p=now[x];p;p=pre[p]){
    		int son=child[p];
    		if (son==fa)	continue;
    		Dfs(son,x),Sz[x]+=Sz[son];
    	}
    }
    int pos[N+10],C[N+10],Cnt[N+10],Ans[N+10];
    struct node{
    	int l,r,K,ID;
    	node(int _l=0,int _r=0,int _K=0,int _ID=0){l=_l,r=_r,K=_K,ID=_ID;}
    	bool operator <(const node &tis)const{return pos[l]!=pos[tis.l]?l<tis.l:r<tis.r;}
    }Ask[N+10];
    struct S1{
    	#define lowbit(x) ((x)&(-x))
    	int V[N+10],n;
    	void Add(int x,int v){for (;x<=n;x+=lowbit(x))	V[x]+=v;}
    	int Query(int x){
    		int res=0;
    		for (;x;x-=lowbit(x))	res+=V[x];
    		return res;
    	}
    	#undef lowbit
    }TA;//Tree like Array
    int n,m,len;
    #define T(x) (n-(x)+1)
    void Add(int x,int v){
    	TA.Add(T(Cnt[C[FND[x]]]),-1);
    	Cnt[C[FND[x]]]+=v;
    	TA.Add(T(Cnt[C[FND[x]]]), 1);
    }
    int Query(int K){return K>n?0:TA.Query(T(K));}
    #undef T
    int main(){
    //	freopen(".in","r",stdin);
    //	freopen(".out","w",stdout);
    	n=read(0),m=read(0),len=sqrt(n);
    	for (int i=1;i<=n;i++)	C[i]=read(0),pos[i]=(i-1)/len+1;
    	for (int i=1;i<n;i++){
    		int x=read(0),y=read(0);
    		insert(x,y);
    	}
    	Dfs(1,0);
    	for (int i=1;i<=m;i++){
    		int x=read(0),k=read(0);
    		Ask[i]=node(DFN[x],DFN[x]+Sz[x]-1,k,i);
    	}
    	sort(Ask+1,Ask+1+m); TA.n=n;
    	for (int i=1,l=1,r=0;i<=m;i++){
    		while (r<Ask[i].r)	Add(++r, 1);
    		while (r>Ask[i].r)	Add(r--,-1);
    		while (l<Ask[i].l)	Add(l++,-1);
    		while (l>Ask[i].l)	Add(--l, 1);
    		Ans[Ask[i].ID]=Query(Ask[i].K);
    	}
    	for (int i=1;i<=m;i++)	printf("%d
    ",Ans[i]);
    	return 0;
    }
    
    作者:Wolfycz
    本文版权归作者和博客园共有,欢迎转载,但必须在文章开头注明原文出处,否则保留追究法律责任的权利
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  • 原文地址:https://www.cnblogs.com/Wolfycz/p/14963281.html
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