[AHOI2013]作业莫队树状数组

最新推荐文章于 2019-07-27 17:09:00 发布

原创最新推荐文章于 2019-07-27 17:09:00 发布 · 167 阅读

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CC 4.0 BY-SA版权

本文深入探讨了一种基于块划分和树状数组的区间查询优化算法，通过预处理和动态更新，实现了对大规模数据集上复杂查询的高效处理。文章详细介绍了算法的设计思路、实现细节及代码示例。

Code:

#include<cmath>
#include<cstdio>
#include<algorithm>
#include<string>
#include<cstring>
#include<iostream>
#define REP(i,a,n)for(int i=a;i<=n;++i)
#define CLR(d,a)memset(d,a,sizeof(d));

using namespace std;

void SetIO(string a){
	string in=a+".in", out=a+".out";
	freopen(in.c_str(),"r",stdin);
	freopen(out.c_str(),"w",stdout);
}

void End(){
	fclose(stdin);
	fclose(stdout);
}

const int maxn=300000+4;

int val[maxn];

int n,m;

struct Queries{
	int l,r,a,b;
	Queries(int l=0,int r=0,int a=0,int b=0):l(l),r(r),a(a),b(b){}
}ask[maxn];

void Read(){
	scanf("%d%d",&n,&m);
	REP(i,1,n)scanf("%d",&val[i]);
	REP(i,1,m){
		int a,b,c,d;
		scanf("%d%d%d%d",&a,&b,&c,&d);
		ask[i]=Queries(a,b,c,d);
	}
}

int block, belong[maxn], A[maxn];

int get_belong(int i){ return (i-1)/block+1; }

bool cmp(int i,int j){
	if(belong[ask[i].l]==belong[ask[j].l]) return ask[i].r<ask[j].r;
	return belong[ask[i].l]<belong[ask[j].l];
}

void Build(){
	block=sqrt(n);
	REP(i,1,n) belong[i]=get_belong(i);
	REP(i,1,m) A[i]=i;
	sort(A+1,A+1+m,cmp);
}

int count1[maxn];

struct BIT{
	int C[2][maxn];

	int lowbit(int t){return t&(-t);}

	void update(int pos,int o,int delta){
		while(pos<=n){
			C[o][pos]+=delta;
			pos+=lowbit(pos);
		}
	}

	int query(int pos,int o){
		int sum=0;
		while(pos>0){
			sum+=C[o][pos];
			pos-=lowbit(pos);
		}
		return sum;
	}
	void Modify(int i,int delta){
		if(i==0) return ;
		update(i,0,delta);
		count1[i]+=delta;
		if(delta<0 && count1[i]==0) update(i,1,delta);
		if(delta>0 && count1[i]==1) update(i,1,delta); 
	}

}Tree;

int ans1[maxn], ans2[maxn];

void Work(){
    int l=1,r=1;
    Tree.Modify(val[1],1);
    REP(i,1,m){
    	int cur=A[i];
    	int l2=ask[cur].l;
    	int r2=ask[cur].r;

  
    	if(r<r2) { 
    		++r; 
    		while(r<=r2){ Tree.Modify(val[r],1), ++r; }
    		--r; 
    	} 
    	else 
    		while(r>r2) { Tree.Modify(val[r],-1), --r; }

    	if(l<l2) { 
    		while(l<l2){ Tree.Modify(val[l],-1);  ++l;  }
    	}
    	else {
    		--l;
    		while(l>=l2) { Tree.Modify(val[l],1), --l; }
    		++l;
    	}


    	ans1[cur]=Tree.query(ask[cur].b,0)-Tree.query(ask[cur].a-1,0);
    	ans2[cur]=Tree.query(ask[cur].b,1)-Tree.query(ask[cur].a-1,1);
    }
}

void Print(){
	REP(i,1,m)
		printf("%d %d\n",ans1[i],ans2[i]);
}

int main(){
	SetIO("input");
	Read();
	Build();
	Work();
	Print();
	End();
	return 0;
}