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  • POJ 2104: K-th Number

    K-th Number

    Time Limit: 20000MS   Memory Limit: 65536K
    Total Submissions: 52878   Accepted: 18188
    Case Time Limit: 2000MS

    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 109 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

    Hint

    This problem has huge input,so please use c-style input(scanf,printf),or you may got time limit exceed.

    Source

    Northeastern Europe 2004, Northern Subregion

    题意:

    给出n个数,询问区间第k大...

    分析:

    这题解法有很多...

    之前写了整体二分...然后还可以用静态主席树水过...

    感觉时间空间复杂度还是差很多的...

    Run ID User Problem Result Memory Time Language Code Length Submit Time
    16573738 NEIGHTHORN 2104 Accepted 22644K 1735MS G++ 1196B 2017-02-12 11:25:34
    16456326 NEIGHTHORN 2104 Accepted 7672K 2829MS G++ 1492B 2017-01-07 11:10:22

    代码:

    #include<algorithm>
    #include<iostream>
    #include<cstring>
    #include<cstdio>
    //by NeighThorn
    using namespace std;
    
    const int maxn=100000+5,maxm=10000000+5;
    
    int n,m,len,tot,a[maxn],mp[maxn],ls[maxm],rs[maxm],sum[maxm],root[maxn];
    
    inline int find(int x){
    	int l=1,r=len,ans;
    	while(l<=r){
    		int mid=(l+r)>>1;
    		if(mp[mid]>=x)
    			ans=mid,r=mid-1;
    		else
    			l=mid+1;
    	}
    	return ans;
    }
    
    inline void change(int l,int r,int x,int &y,int val){
    	y=++tot,sum[y]=sum[x]+1;
    	if(l==r)
    		return;
    	int mid=(l+r)>>1;ls[y]=ls[x],rs[y]=rs[x];
    	if(val<=mid)
    		change(l,mid,ls[x],ls[y],val);
    	else
    		change(mid+1,r,rs[x],rs[y],val);
    }
    
    inline int query(int l,int r,int x,int y,int num){
    	if(l==r)
    		return l;
    	int mid=(l+r)>>1;
    	if(sum[ls[y]]-sum[ls[x]]>=num)
    		return query(l,mid,ls[x],ls[y],num);
    	else
    		return query(mid+1,r,rs[x],rs[y],num-(sum[ls[y]]-sum[ls[x]]));
    }
    
    signed main(void){
    	scanf("%d%d",&n,&m);
    	for(int i=1,x;i<=n;i++)
    		scanf("%d",&a[i]),mp[i]=a[i];
    	sort(mp+1,mp+n+1);
    	len=unique(mp+1,mp+n+1)-mp-1;
    	for(int i=1;i<=n;i++)
    		change(1,n,root[i-1],root[i],find(a[i]));
    	for(int i=1,s,x,y;i<=m;i++)
    		scanf("%d%d%d",&x,&y,&s),printf("%d
    ",mp[query(1,len,root[x-1],root[y],s)]);
    	return 0;
    }
    //1234
    

      


    By NeighThorn

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  • 原文地址:https://www.cnblogs.com/neighthorn/p/6390649.html
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