zoukankan      html  css  js  c++  java
  • POJ2104 K-th Number(主席树)

    题目

    Source

    http://poj.org/problem?id=2104

    Description

    You are working for Macrohard company in data structures department. After failing your previous task about key insertion you were asked to write a new data structure that would be able to return quickly k-th order statistics in the array segment.
    That is, given an array a[1...n] of different integer numbers, your program must answer a series of questions Q(i, j, k) in the form: "What would be the k-th number in a[i...j] segment, if this segment was sorted?"
    For example, consider the array a = (1, 5, 2, 6, 3, 7, 4). Let the question be Q(2, 5, 3). The segment a[2...5] is (5, 2, 6, 3). If we sort this segment, we get (2, 3, 5, 6), the third number is 5, and therefore the answer to the question is 5.

    Input

    The first line of the input file contains n --- the size of the array, and m --- the number of questions to answer (1 <= n <= 100 000, 1 <= m <= 5 000).
    The second line contains n different integer numbers not exceeding 10 9 by their absolute values --- the array for which the answers should be given.
    The following m lines contain question descriptions, each description consists of three numbers: i, j, and k (1 <= i <= j <= n, 1 <= k <= j - i + 1) and represents the question Q(i, j, k).

    Output

    For each question output the answer to it --- the k-th number in sorted a[i...j] segment.

    Sample Input

    7 3
    1 5 2 6 3 7 4
    2 5 3
    4 4 1
    1 7 3

    Sample Output

    5
    6
    3

    分析

    题目是给一个序列,多次询问序列区间中第k小的元素。

    经典主席树入门题。。相当于序列各个前缀建一棵权值线段树,区间上的信息就是两个前缀和的差分了。。复习复习,已经忘了。

    代码

    #include<cstdio>
    #include<cstring>
    #include<algorithm>
    using namespace std;
    #define MAXN 111111
    
    int root[MAXN],tree[MAXN*20],lch[MAXN*20],rch[MAXN*20],x,y,N;
    void update(int i,int j,int a,int &b){
        b=++N;
        if(i==j){
            tree[b]=tree[a]+1;
            return;
        }
        lch[b]=lch[a];
        rch[b]=rch[a];
        int mid=i+j>>1;
        if(x<=mid) update(i,mid,lch[a],lch[b]);
        else update(mid+1,j,rch[a],rch[b]);
        tree[b]=tree[lch[b]]+tree[rch[b]];
    }
    int query(int i,int j,int l,int r,int k){
        if(i==j) return i;
        int mid=i+j>>1;
        int lcnt=tree[lch[r]]-tree[lch[l]];
        if(k<=lcnt) return query(i,mid,lch[l],lch[r],k);
        return query(mid+1,j,rch[l],rch[r],k-lcnt);
    }
    
    int a[MAXN],b[MAXN];
    int main(){
        int n,m;
        scanf("%d%d",&n,&m);
        for(int i=1; i<=n; ++i){
            scanf("%d",&a[i]);
        }
    
        memcpy(b,a,sizeof(b));
        sort(b+1,b+1+n);
        int bn=unique(b+1,b+1+n)-b-1;
    
        for(int i=1; i<=n; ++i){
            x=lower_bound(b+1,b+1+n,a[i])-b;
            update(1,bn,root[i-1],root[i]);
        }
    
        int l,r,k;
        while(m--){
            scanf("%d%d%d",&l,&r,&k);
            printf("%d
    ",b[query(1,bn,root[l-1],root[r],k)]);
        }
        return 0;
    }
    
  • 相关阅读:
    域名、主机名、网站名以及 URL 基础概念
    c# oracle 数据库连接以及参数化查询
    c# 委托(Func、Action)
    xcode pod install 安装失败,提示缺少文件
    一个服务器的IIS只能绑定一个HTTPS也就是443端口
    APP UI设计及切图规范
    Day7 字符串和常用数据结构
    Day6 函数和模块的使用
    Day5 练习
    python 疑难杂症
  • 原文地址:https://www.cnblogs.com/WABoss/p/5936129.html
Copyright © 2011-2022 走看看