POJ 2104 K-th Number （主席樹 || 劃分樹）

靜態區間查詢第K大   主席樹入門  也可以用劃分樹

//#include <bits/stdc++.h>
#include <iostream>
#include <cstring>
#include <cstdio>
#include <algorithm>
using namespace std;

const int MAXN = 100010;
const int M = MAXN * 30;
int n,q,m,tot;
int a[MAXN], t[MAXN];
int T[M], 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;  //去重
}

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; //找中位數
}

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()
{
    while(scanf("%d%d",&n,&q) == 2)
    {
        tot = 0;
        for(int i = 1; i <= n; i++)
            scanf("%d",&a[i]);
        Init_Hash();                    //離散建樹
        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);
        }
        while(q--)
        {
            int l,r,k;
            scanf("%d%d%d",&l,&r,&k);
            printf("%d\n",t[query(T[l],T[r+1],k)]);
        }
    }
    return 0;
}

劃分樹

//#include <bits/stdc++.h>
#include <iostream>
#include <cstring>
#include <cstdio>
#include <algorithm>
using namespace std;

const int MAXN = 100010;
int tree[20][MAXN];//表示每層每個位置的值 
int sorted[MAXN];//已經排序好的數 
int toleft[20][MAXN];//toleft[p][i]表示第i層從1到i有數分入左邊

void build(int l,int r,int dep)
{
    if(l == r)
        return;
    int mid = (l+r)>>1;
    int same = mid - l + 1;//表示等於中間值而且被分入左邊的個數
    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);
}

//查詢區間第k大的數,[L,R]是大區間，[l,r]是要查詢的小區間
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];
        int newl = newr - (r-l-cnt);
        return 
        query(mid+1,R,newl,newr,dep+1,k-cnt);
    }
}

int main()
{
    int n,m;
    while(scanf("%d%d",&n,&m)==2)
    {
        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);

        int s,t,k;
        while(m--)
        {
            scanf("%d%d%d",&s,&t,&k);
            printf("%d\n",query(1,n,s,t,0,k));
        }
    }
    return 0;
}