19暑假主席树D(区间不重复数字个数模板

本文探讨了如何使用主席树解决区间查询问题,具体为在一个整数序列中查询指定子区间内不同整数首次出现位置的中位数。通过构建主席树,可以高效地处理多个查询,每个查询涉及确定子区间内不同整数的数量,然后找到这些位置的中位数。

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Mr. Frog has an integer sequence of length n, which can be denoted as a1,a2,⋯,an There are m queries.

In the i-th query, you are given two integers li and ri. Consider the subsequence ali,ali+1,ali+2,⋯,ari.

We can denote the positions(the positions according to the original sequence) where an integer appears first in this subsequence as p(i)1,p(i)2,⋯,p(i)ki (in ascending order, i.e.,p(i)1<p(i)2<⋯<p(i)ki).

Note that ki is the number of different integers in this subsequence. You should output p(i)⌈ki2⌉for the i-th query.
Input
In the first line of input, there is an integer T (T≤2) denoting the number of test cases.

Each test case starts with two integers n (n≤2×105) and m (m≤2×105). There are n integers in the next line, which indicate the integers in the sequence(i.e., a1,a2,⋯,an,0≤ai≤2×105).

There are two integers li and ri in the following m lines.

However, Mr. Frog thought that this problem was too young too simple so he became angry. He modified each query to l‘i,r‘i(1≤l‘i≤n,1≤r‘i≤n). As a result, the problem became more exciting.

We can denote the answers as ans1,ans2,⋯,ansm. Note that for each test case ans0=0.

You can get the correct input li,ri from what you read (we denote them as l‘i,r‘i)by the following formula:
li=min{(l‘i+ansi−1) mod n+1,(r‘i+ansi−1) mod n+1}

ri=max{(l‘i+ansi−1) mod n+1,(r‘i+ansi−1) mod n+1}
Output
You should output one single line for each test case.

For each test case, output one line “Case #x: p1,p2,⋯,pm”, where x is the case number (starting from 1) and p1,p2,⋯,pm is the answer.
Sample Input
2
5 2
3 3 1 5 4
2 2
4 4
5 2
2 5 2 1 2
2 3
2 4
Sample Output
Case #1: 3 3
Case #2: 3 1
询问一个区间中数字第一次出现位置的中位数
主席树可以求出来一个区间中出现数字个数,所以先把数字个数求出来,再求由左边界一直到n范围中的第(k+1)/2小即可

#include<bits/stdc++.h>
#define N 200005
using namespace std;
typedef long long ll;
int T,n,m,cnt,pos,a[N],b[N],rt[N],f[N],ans[N];
struct Tree
{
    int ls,rs,sum;
}tr[N*40];
void Insert(int pre,int &node,int x,int l,int r)
{
    node = ++cnt;
    tr[node] = tr[pre];
    tr[node].sum += x;
    if(l == r) return;
    int mid = (l + r) >> 1;
    if(pos <= mid) Insert(tr[pre].ls,tr[node].ls,x,l,mid);
    else Insert(tr[pre].rs,tr[node].rs,x,mid+1,r);
}
int Ask(int node,int x,int l,int r)
{
    if(l == r) return tr[node].sum;
    int mid = (l+r)>>1;
    if(x <= mid) return Ask(tr[node].ls,x,l,mid);
    else return tr[tr[node].ls].sum + Ask(tr[node].rs,x,mid+1,r);
}
int Query(int node,int k,int l,int r)
{
	if(l == r) return l;
	int mid = (l+r)>>1;
	if(tr[tr[node].ls].sum >= k) return Query(tr[node].ls,k,l,mid);
	else return Query(tr[node].rs,k-tr[tr[node].ls].sum,mid+1,r);
}
int main()
{
    scanf("%d",&T);
    for(int t = 1;t <= T;t++)
    {
        cnt = 0;
        memset(f,0,sizeof(f));
        scanf("%d%d",&n,&m);
        for(int i = 1;i <= n;i++) scanf("%d",&a[i]);
        tr[n+1].ls=tr[n+1].rs=tr[n+1].sum=0;
	    rt[n+1]=0;
        for(int i = n;i;i--)
        {
            pos = f[a[i]];
            if(pos)
            {
                Insert(rt[i+1],rt[i],-1,1,n);
                pos = i;
                Insert(rt[i],rt[i],1,1,n);
            }
            else
            {
                pos = i;
                Insert(rt[i+1],rt[i],1,1,n);
            }
            f[a[i]] = i;
        }
        int pre = 0;
        for(int i = 1;i <= m;i++)
        {
            int l,r;
            scanf("%d%d",&l,&r);
            l = (l + pre) % n + 1,r = (r + pre) % n + 1;
            if(l > r) swap(l,r);
            int k = Ask(rt[l],r,1,n);
            pre = Query(rt[l],(k+1)/2,1,n);
            ans[i]=pre;
        }
        printf("Case #%d:",t);
			for(int i=1;i<=m;i++)
			printf(" %d",ans[i]);
		    printf("\n");
    }
}
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