HDU 4251 --- 主席树（划分树是正解）

题意：查询区间中位数

思路：模板题，相当于区间第K大的数，主席树可以水过，但划分树是正解。但还没搞明白划分树，先上模板

#include <iostream>
#include <cstdio>
#include <cmath>
#include <cstring>
#include <cstdlib>
#include <string>
#include <vector>
#include <algorithm>
#include <set>
#define repu(i,a,b) for(int i=a;i<b;i++)
using namespace std;
#define N 1000010
#define ll long long
#define _cle(m, a) memset(m, a, sizeof(m))
const int MAXN = 100010;
const int M = MAXN * 30;
int n,q,m,tot;
int a[MAXN], t[MAXN];
int T[MAXN], lson[M], rson[M], c[M];
void Init_Hash()
{
    for(int i = 1; i <= n; i++)
        t[i] = a[i];
    sort(t+1,t+1+n);
    m = unique(t+1,t+1+n) -t-1;
}
int build(int l, int r)
{
    int root = tot++;
    c[root] = 0;
    if(l != r)
    {
        int mid = (l+r)>>1;
        lson[root] = build(l,mid);
        rson[root] = build(mid+1,r);
    }
    return root;
}
int Hash(int x)
{
    return lower_bound(t+1,t+1+m,x) - t;
}
int update(int root, int pos, int val)
{
    int newroot = tot++, tmp = newroot;
    c[newroot] = c[root] + val;
    int l = 1, r = m;
    while(l < r)
    {
        int mid = (l+r)>>1;
        if(pos <= mid)
        {
            lson[newroot] = tot++;
            rson[newroot] = rson[root];
            newroot = lson[newroot];
            root = lson[root];
            r = mid;
        }
        else
        {
            rson[newroot] = tot++;
            lson[newroot] = lson[root];
            newroot = rson[newroot];
            root = rson[root];
            l = mid+1;
        }
        c[newroot] = c[root] + val;
    }
    return tmp;
}
int query(int left_root, int right_root, int k)
{
    int l = 1, r = m;
    while( l < r)
    {
        int mid = (l+r)>>1;
        if(c[lson[left_root]] -c[lson[right_root]] >= k )
        {
            r = mid;
            left_root = lson[left_root];
            right_root = lson[right_root];
        }
        else
        {
            l = mid + 1;
            k -= c[lson[left_root]] - c[lson[right_root]];
            left_root = rson[left_root];
            right_root = rson[right_root];
        }
    }
    return l;
}
int main()
{
//freopen("in.txt","r", stdin);
//freopen("out.txt","w", stdout);
    int kase = 1;
    while(scanf("%d",&n) == 1)
    {
        tot = 0;
        for(int i = 1; i <= n; i++)
            scanf("%d",&a[i]);
        Init_Hash();
        T[n+1] = build(1,m);
        for(int i = n; i ; i--)
        {
            int pos = Hash(a[i]);
            T[i] = update(T[i+1],pos,1);
        }
        printf("Case %d:
",kase++);
        scanf("%d",&q);
        while(q--)
        {
            int l,r,k;
            scanf("%d%d",&l,&r);
            k = (r-l)/2+1;
            printf("%d
",t[query(T[l],T[r+1],k)]);
        }
    }
    return 0;
}

先上KB模板

//划分树
#include<cstdio>
#include<cstring>
#include<algorithm>
using namespace std;
const int MAXN=100010;
int tree[20][MAXN];//表示每层每个位置的值
int sorted[MAXN];//已经排序好的数
int toleft[20][MAXN];//toleft[p][i]表示第i层从1到i有数分入左边
void build(int l,int r,int dep){
    if(l==r)return;
    int mid=(l+r)>>1;
    int same=mid-l+1;//表示等于中间值而且被分入左边的个数
    for(int i=l;i<=r;i++)//注意是l,不是one
        if(tree[dep][i]<sorted[mid]) same--;
    int lpos=l;
    int rpos=mid+1;
    for(int i=l;i<=r;i++){
        if(tree[dep][i]<sorted[mid]) tree[dep+1][lpos++]=tree[dep][i];
        else if(tree[dep][i]==sorted[mid]&&same>0){
            tree[dep+1][lpos++]=tree[dep][i];
            same--;
        }
        else tree[dep+1][rpos++]=tree[dep][i];
        toleft[dep][i]=toleft[dep][l-1]+lpos-l;
    }
    build(l,mid,dep+1);
    build(mid+1,r,dep+1);
}
//查询区间第k大的数,[L,R]是大区间,[l,r]是要查询的小区间
int query(int L,int R,int l,int r,int dep,int k){
    if(l==r)return tree[dep][l];
    int mid=(L+R)>>1;
    int cnt=toleft[dep][r]-toleft[dep][l-1];
    if(cnt>=k){
        int newl=L+toleft[dep][l-1]-toleft[dep][L-1];int newr=newl+cnt-1;
        return query(L,mid,newl,newr,dep+1,k);
    }
    else{
        int newr=r+toleft[dep][R]-toleft[dep][r],newl=newr-(r-l-cnt);
        return query(mid+1,R,newl,newr,dep+1,k-cnt);
    }
}
int main(){
    int n,m,t=0;
    while(~scanf("%d",&n)){
        memset(tree,0,sizeof(tree));
        for(int i=1;i<=n;i++){
            scanf("%d",&tree[0][i]);
            sorted[i]=tree[0][i];
        }
        sort(sorted+1,sorted+n+1);
        build(1,n,0);
        scanf("%d",&m);
        printf("Case %d:
",++t);
        int s,t,k;
        while(m--){
            scanf("%d%d",&s,&t);
            k=(t-s+2)/2;
            printf("%d
",query(1,n,s,t,0,k));
        }
    }
    return 0;
}