首页 > 代码库 > 算法总结——主席树(poj2104)
算法总结——主席树(poj2104)
题目:
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.
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).
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
题解:
主席树模板题,关于主席树的知识见下:
代码:
#include<iostream> #include<cstdio> #include<cstdlib> #include<algorithm> #include<cstring> #include<string> #include<cmath> #include<ctime> #include<cctype> using namespace std; const int N=100010; int rank[N],root[N]; int n,m,tot; struct node { int x,id; }a[N]; inline bool operator<(node a,node b) { return a.x<b.x; } struct tree { int l; int r; int sum; }tr[N*20]; void build(int num,int &x,int l,int r) { tr[tot++]=tr[x],x=tot-1; tr[x].sum++; if(l==r) return; int mid=(l+r)/2; if(num<=mid) build(num,tr[x].l,l,mid); else build(num,tr[x].r,mid+1,r); } int query(int i,int j,int k,int l,int r) { if(l==r) return l; int mid=(l+r)/2; int T=tr[tr[j].l].sum-tr[tr[i].l].sum; if(k<=T) return query(tr[i].l,tr[j].l,k,l,mid); else return query(tr[i].r,tr[j].r,k-T,mid+1,r); } int main() { //freopen("a.in","r",stdin); int d,b,c; while(scanf("%d%d",&n,&m)!=EOF) { for(int i=1;i<=n;i++) { scanf("%d",&a[i].x); a[i].id=i; } sort(a+1,a+n+1); for(int i=1;i<=n;i++) rank[a[i].id]=i; tot=1; for(int i=1;i<=n;i++) { root[i]=root[i-1]; build(rank[i],root[i],1,n); } while(m--) { scanf("%d%d%d",&d,&b,&c); cout<<a[query(root[d-1],root[b],c,1,n)].x<<endl; } } return 0; }
算法总结——主席树(poj2104)
声明:以上内容来自用户投稿及互联网公开渠道收集整理发布,本网站不拥有所有权,未作人工编辑处理,也不承担相关法律责任,若内容有误或涉及侵权可进行投诉: 投诉/举报 工作人员会在5个工作日内联系你,一经查实,本站将立刻删除涉嫌侵权内容。