一个小技巧总结

当题目是区间求和或者其他区间询问时，如果询问是离线的，而且询问涉及 l-r内有多少个不同的xxx。这个xxx可以是不同的数 不同的gcd 不同的异或和 等等

这时候我们可以把询问按右端点排序，然后把a[i]的出现永远存在靠右的一边 当i==q.r的时候 求答案

有三道例题

hdu3333

Problem : 3333 ( Turing Tree )     Judge Status : Accepted
RunId : 18401449    Language : C++    Author : GeniusYang
Code Render Status : Rendered By HDOJ C++ Code Render Version 0.01 Beta

#include <iostream>

#include <cstdio>

#include <string.h>

#include <vector>

#include <map>

#include <algorithm>

using namespace std;

const int maxn=30000;

typedef long long LL;

int t;

int len;

int n,q;

LL a[maxn+10];

LL c[maxn+10];

LL res[maxn*10+10];

map<int,int> m;

struct qy{
  int l,r;
  int id;
}Q[maxn*10+10];

int cmp(qy a,qy b){
   return a.r<b.r;
}

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

void modify(int x,int add){
    while(x<=n){
        c[x]+=add;
        x+=lowbit(x);
    }
}

LL get_sum(int x){
    LL ret=0;
    while(x!=0){
        ret+=c[x];
        x-=lowbit(x);
    }
    return ret;
}

void init(){
   m.clear();
   memset(c,0,sizeof(c));
   memset(Q,0,sizeof(Q));
   memset(res,0,sizeof(res));
}

int main()
{
    scanf("%d",&t);
    while(t--){
       init();
       scanf("%d",&n);
       for(int i=1;i<=n;i++){
           scanf("%I64d",&a[i]);
       }
       scanf("%d",&q);
       for(int i=1;i<=q;i++){
          scanf("%d%d",&Q[i].l,&Q[i].r);
          Q[i].id=i;
       }
       len=1;
       sort(Q+1,Q+q+1,cmp);
       for(int i=1;i<=n;i++){
            int temp=m[a[i]];
            if(temp){
               modify(temp,-a[i]);
               modify(i,a[i]);
               m[a[i]]=i;
            } else {
               m[a[i]]=i;
               modify(i,a[i]);
            }
            while(Q[len].r==i&&len<=q){
                res[Q[len].id]=get_sum(Q[len].r)-get_sum(Q[len].l-1);
                len++;
            }
       }
       for(int i=1;i<=q;i++){
            printf("%I64d
",res[i]);
       }
    }
    return 0;
}

hdu5869

Problem : 5869 ( Different GCD Subarray Query )     Judge Status : Accepted
RunId : 18402625    Language : G++    Author : GeniusYang
Code Render Status : Rendered By HDOJ G++ Code Render Version 0.01 Beta

#include <iostream>

#include <vector>

#include <algorithm>

#include <map>

#include <string.h>

using namespace std;

const int maxn=100000;

typedef pair<int,int> P;

int len;

int n,q;

vector<P> G[maxn+10];

map<int,int> m;

int a[maxn+10];

int c[maxn+10];

int res[maxn*10+10];

int gcd(int a,int b){
  return b==0?a:gcd(b,a%b);
}

struct qy{
 int l,r;
 int id;
}Q[maxn*10+10];

int cmp(qy a,qy b){
   return a.r<b.r;
}

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

void add(int x,int y){
   while(x<=n){
       c[x]+=y;
       x+=lowbit(x);
   }
}

int sum(int x){
   int res=0;
   while(x!=0){
       res+=c[x];
       x-=lowbit(x);
   }
   return res;
}

void init(){
    len=1;
    m.clear();
    G[0].clear();
    memset(c,0,sizeof(c));
    memset(Q,0,sizeof(Q));
    memset(res,0,sizeof(res));
}

int main()
{
    while(scanf("%d%d",&n,&q)!=EOF){
        init();
        for(int i=1;i<=n;i++){
            G[i].clear();
            scanf("%d",&a[i]);
        }
        for(int i=1;i<=n;i++){
            int x=a[i],y=i;
            for(size_t j=0;j<G[i-1].size();j++){
                int temp=gcd(x,G[i-1][j].first);
                if(temp!=x){
                    G[i].push_back(make_pair(x,y));
                    x=temp,y=G[i-1][j].second;
                }
            }
            G[i].push_back(make_pair(x,y));
        }
        for(int i=1;i<=q;i++){
            Q[i].id=i;
            scanf("%d%d",&Q[i].l,&Q[i].r);
        }
        sort(Q+1,Q+1+q,cmp);
        for(int i=1;i<=n;i++){
            for(size_t j=0;j<G[i].size();j++){
                  int t1=m[G[i][j].first];
                  int t2=G[i][j].second;
                  if(t1){
                    add(t1,-1);
                  }
                  add(t2,1);
                  m[G[i][j].first]=t2;
            }
            while(Q[len].r==i&&len<=q){
                res[Q[len].id]=sum(Q[len].r)-sum(Q[len].l-1);
                len++;
            }
        }
        for(int i=1;i<=q;i++){
             printf("%d
",res[i]);
        }
    }
    return 0;
}

codeforces 703D

#include<bits/stdc++.h>

#define inf 0x3f3f3f3f

const int maxn=1000000;

using namespace std;

typedef long long ll;

int n;

int m;

int a[maxn+10];

int c[maxn+10];

ll sum[maxn+10];

ll ans[maxn+10];

map<int,int> flag;

struct node{
  int l,r;
  int id;
  bool operator<(const node &t)const{
        return r<t.r;
  }
}q[maxn+10];

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

void add(int x,int y){
      while(x<=n){
        c[x]^=y;
        x+=lowbit(x);
      }
}

ll get_sum(int x){
   ll res=0;
   while(x){
        res^=c[x];
        x-=lowbit(x);
   }
   return res;
}

int cmp(node a,node b){
   return a.id<b.id;
}

int main()
{
    scanf("%d",&n);
    for(int i=1;i<=n;i++){
        scanf("%d",&a[i]);
        sum[i]=sum[i-1]^a[i];
    }
    scanf("%d",&m);
    for(int i=1;i<=m;i++){
        scanf("%d%d",&q[i].l,&q[i].r);
        q[i].id=i;
    }
    sort(q+1,q+1+m);
    int len=1;
    for(int i=1;i<=n;i++){
        int temp=flag[a[i]];
        if(temp){
           add(temp,a[i]);
           flag[a[i]]=i;
           add(i,a[i]);
        } else {
           flag[a[i]]=i;
           add(i,a[i]);
        }
        while(q[len].r==i){
                ans[q[len].id]=get_sum(q[len].r)^get_sum(q[len].l-1)^sum[q[len].r]^sum[q[len].l-1];
                len++;
        }
    }
    sort(q+1,q+1+m,cmp);
    for(int i=1;i<=m;i++){
        printf("%I64d
",ans[i]);
    }
    return 0;
}