主席树

#include <iostream>
#include <algorithm>
#include <cstdio>
#include <cstring>
#include <cmath>
#include <string>
#include <cstdlib>
#define maxn 100005
using namespace std;
int b[maxn],t[maxn],n,m,size,v[maxn],tot=0;
struct chairtree
{
    int l,r,size;
}a[maxn*30];
int Build(int l,int r)
{
    int root=++tot;
    a[root].size=0;
    if (l==r) return root;
    int m=(l+r)>>1;
    a[root].l=Build(l,m);
    a[root].r=Build(m+1,r);
    return root;
}
int Update(int root,int x)
{
    int now=++tot;
    int tmp=now;
    a[tot].size=a[root].size+1;
    int l=1,r=size;
    while (l<r)
    {
        int m=(l+r)>>1;
        if (x<=m)
        {
            a[now].l=++tot;
            a[now].r=a[root].r;   //充分利用原来相同的结点
            root=a[root].l;
            now=tot;
            r=m;
        }
        else
        {
            a[now].l=a[root].l;
            a[now].r=++tot;
            root=a[root].r;
            now=tot;
            l=m+1;
        }
        a[now].size=a[root].size+1;
    }
    return tmp;
}
int Ask(int lx,int rx,int k)
{
    int l=1,r=size;
    while (l<r)
    {
        int m=(l+r)>>1;
        if (a[a[rx].l].size-a[a[lx].l].size>=k)
        {
            r=m;
            lx=a[lx].l;
            rx=a[rx].l;
        }
        else
        {
            l=m+1;
            k-=a[a[rx].l].size-a[a[lx].l].size;
            lx=a[lx].r;
            rx=a[rx].r;
        }
    }
    return l;
}
void Hash1()
{
    sort(b+1,b+1+n);
    size=unique(b+1,b+1+n)-b-1;  //求不相同的数有几个
}
int Hash(int x)
{
    return lower_bound(b+1,b+1+size,x)-b;   //找到x在排好序的序列中出现的位置,即离散化后的值
}
int main()
{
    while (scanf("%d%d",&n,&m)==2)
    {
        for (int i=1;i<=n;i++)
            scanf("%d",&v[i]),b[i]=v[i];
        Hash1();
        t[0]=Build(1,size);
        for (int i=1;i<=n;i++)   //建n棵线段树
            t[i]=Update(t[i-1],Hash(v[i]));
        while (m--)
        {
            int l,r,k;
            scanf("%d%d%d",&l,&r,&k);
            printf("%d
",b[Ask(t[l-1],t[r],k)]);
        }
    }
    return 0;
}
主席树求区间第K大
#include <iostream>
#include <algorithm>
#include <cstdio>
#include <cstring>
#include <cstdlib>
#include <cmath>
#define maxn 10005
using namespace std;
int use[maxn*10],n,m,size,tot=0,all=0,h[maxn*10],v[maxn*10],t[maxn*10];
struct chairtree
{
    int l,r,size;
}a[maxn*300];
struct question
{
    int l,r,k;
}q[maxn];
int lowbit(int x)
{
    return x&(-x);
}
void Hash1()
{
    sort(h+1,h+1+all);
    size=unique(h+1,h+1+all)-h-1;
}
int Hash(int x)
{
    return lower_bound(h+1,h+1+size,x)-h;
}
int Build(int l,int r)
{
    int now=++tot;
    a[now].size=0;
    if (l==r) return now;
    int m=(l+r)>>1;
    a[now].l=Build(l,m);
    a[now].r=Build(m+1,r);
    return now;
}
int Update(int root,int p,int val)
{
    int now=++tot,tmp=now;
    int l=1,r=size;
    a[now].size=a[root].size+val;
    while (l<r)
    {
        int m=(l+r)>>1;
        if (p<=m)
        {
            a[now].l=++tot;
            a[now].r=a[root].r;
            root=a[root].l;
            now=a[now].l;
            r=m;
        }
        else
        {
            a[now].l=a[root].l;
            a[now].r=++tot;
            root=a[root].r;
            now=a[now].r;
            l=m+1;
        }
        a[now].size=a[root].size+val;
    }
    return tmp;
}
void Add(int x,int p,int val)
{
    for (int i=x;i<=n;i+=lowbit(i))    //树状数组只需修改logn个
        t[i]=Update(t[i],p,val);
}
int Getsum(int x)
{
    int ans=0;
    for (int i=x;i;i-=lowbit(i))
        ans+=a[a[use[i]].l].size;
    return ans;
}
int Query(int lx,int rx,int k)
{
    int l=1,r=size;
    for (int i=lx-1;i;i-=lowbit(i)) use[i]=t[i];
    for (int i=rx;i;i-=lowbit(i)) use[i]=t[i];
    while (l<r)
    {
        int m=(l+r)>>1;
        int tmp=Getsum(rx)-Getsum(lx-1);
        if (tmp>=k)
        {
            for (int i=lx-1;i;i-=lowbit(i)) 
                use[i]=a[use[i]].l;
            for (int i=rx;i;i-=lowbit(i)) 
                use[i]=a[use[i]].l;
            r=m;
        }
        else
        {
            for (int i=lx-1;i;i-=lowbit(i))
                use[i]=a[use[i]].r;
            for (int i=rx;i;i-=lowbit(i))
                use[i]=a[use[i]].r;
            k-=tmp;
            l=m+1;
        }
    }
    return l;
}
int main()
{
        scanf("%d%d",&n,&m);
    for (int i=1;i<=n;i++)
        scanf("%d",&v[i]),h[i]=v[i];
    all=n;
    for (int i=1;i<=m;i++)
    {
        char str[10];
        int l,r,k;
        scanf("%s",str);
        if (str[0]=='Q')
        {
            scanf("%d%d%d",&l,&r,&k);
            q[i].l=l,q[i].r=r,q[i].k=k;
        }
        else
        {
            scanf("%d%d",&r,&k);
            q[i].l=0,q[i].r=r,q[i].k=k;
                        h[++all]=k;
        }
    }
    Hash1();
    t[0]=Build(1,size);
    for (int i=1;i<=n;i++)
        t[i]=t[0];
    for (int i=1;i<=n;i++)
        Add(i,Hash(v[i]),1);
    for (int i=1;i<=m;i++)
    {
        if (q[i].l)
        {
            printf("%d
",h[Query(q[i].l,q[i].r,q[i].k)]);
        }
        else
        {
            Add(q[i].r,Hash(v[q[i].r]),-1);
            Add(q[i].r,Hash(q[i].k),1);
            v[q[i].r]=q[i].k;
        }
    }
    return 0;
}
同上 但是带修改操作
#include <cstdio>
#include <iostream>
#include <map>
using namespace std;
const int MX = 1e5+5;
const int N = MX*20;
int n,q,tot;
int A[MX];
int T[N],lson[N],rson[N],sum[N];

int build(int l,int r)
{
    int rt = tot++;
    sum[rt] = 0;
    int mid = (l+r)>>1;
    if(l!=r) {
        lson[rt] = build(l,mid);
        rson[rt] = build(mid+1,r);
    }
    return rt;
}
int update(int rt,int pos,int val)
{
    int nrt = tot++;
    int tmp = nrt;
    int l=1,r=n;
    sum[nrt] = sum[rt] + val;
    while(l<r) {
        int mid = (l+r)>>1;
        if(pos<=mid) {
            lson[nrt] = tot++;
            rson[nrt] = rson[rt];
            nrt = lson[nrt];
            rt =  lson[rt];
            r  = mid;
        } else {
            rson[nrt] = tot++;
            lson[nrt] = lson[rt];
            nrt = rson[nrt];
            rt = rson[rt];
            l = mid+1;
        }
        sum[nrt] = sum[rt]+val;
    }
    return tmp;
}
int query(int rt,int pos)
{
    int  l= 1,r = n,ret = 0;
    while(pos>l) {
        int mid = (l+r)>>1;
        if(pos>mid)  {
            l = mid+1;
            rt= rson[rt];
        } else{
            r  = mid;
            ret += sum[rson[rt]];
            rt  =  lson[rt];
        }
    }
    return ret+sum[rt];
}

int main()
{freopen("in.txt","r",stdin);
    scanf("%d",&n);
    for(int i=1;i<=n;i++) scanf("%d",&A[i]);
    T[0] = build(1,n);
    map<int,int>mp;
    for(int i=1;i<=n;i++) {
        if(mp.find(A[i])==mp.end()) T[i] =  update(T[i-1],i,1);
        else {
            int tmp  = update(T[i-1],mp[A[i]],-1);
            T[i]  = update(tmp,i,1);
        }
        mp[A[i]] = i;
    }
    scanf("%d",&q);
    while(q--)  {
        int l,r;
        scanf("%d%d",&l,&r);
        printf("%d
",query(T[r],l));
    }
    return 0;
}
求区间内不同数的个数(离散化)
原文地址:https://www.cnblogs.com/Aragaki/p/7282538.html