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K-th Number
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
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静态区间第k大查询，学习主席树第一题
1 /************************************************************************* 2 > File Name: cf.cpp 3 > Author: acvcla 4 > QQ: 5 > Mail: acvcla@gmail.com 6 > Created Time: 1949Äê10ÔÂ1ÈÕ ÐÇÆÚÒ» 0ʱ0·Ö0Ãë 7 ************************************************************************/ 8 #include<iostream> 9 #include<algorithm> 10 #include<cstdio> 11 #include<vector> 12 #include<cstring> 13 #include<map> 14 #include<queue> 15 #include<stack> 16 #include<string> 17 #include<cstdlib> 18 #include<ctime> 19 #include<set> 20 #include<math.h> 21 using namespace std; 22 typedef long long LL; 23 const int maxn = 1e5 + 10; 24 #define rep(i,a,b) for(int i=(a);i<=(b);i++) 25 #define pb push_back 26 int tot,n,m,date[maxn],sorted[maxn],root[maxn]; 27 struct chairTnode 28 { 29 int s,rc,lc; 30 chairTnode(int s=0,int lc=0,int rc=0):s(s),lc(lc),rc(rc){} 31 }; 32 chairTnode chairT[maxn*20]; 33 int newnode(int sum,int lson,int rson) 34 { 35 int rt=++tot; 36 chairT[rt]=chairTnode(sum,lson,rson); 37 return rt; 38 } 39 void Insert(int &rt,int pre_rt,int pos,int L,int R) 40 { 41 chairTnode &t=chairT[pre_rt]; 42 rt=newnode(t.s+1,t.lc,t.rc); 43 if(L==R)return; 44 int mid=(L+R)>>1; 45 if(pos<=mid)Insert(chairT[rt].lc,t.lc,pos,L,mid); 46 else Insert(chairT[rt].rc,t.rc,pos,mid+1,R); 47 } 48 int Query(int ql,int qr,int L,int R,int k) 49 { 50 if(L==R)return L; 51 int sum=chairT[chairT[qr].lc].s-chairT[chairT[ql].lc].s; 52 int mid=(L+R)>>1; 53 if(k<=sum)return Query(chairT[ql].lc,chairT[qr].lc,L,mid,k); 54 return Query(chairT[ql].rc,chairT[qr].rc,mid+1,R,k-sum); 55 } 56 int main() 57 { 58 while(~scanf("%d%d",&n,&m)) 59 { 60 rep(i,1,n){ 61 scanf("%d",date+i); 62 sorted[i]=date[i]; 63 } 64 tot=root[0]=0; 65 sort(sorted+1,sorted+1+n); 66 int cnt=unique(sorted+1,sorted+1+n)-sorted-1; 67 for(int i=1;i<=n;i++){ 68 int pos=lower_bound(sorted+1,sorted+1+n,date[i])-sorted; 69 Insert(root[i],root[i-1],pos,1,cnt); 70 } 71 int ql,qr,k; 72 while(m--) 73 { 74 scanf("%d%d%d",&ql,&qr,&k); 75 printf("%d ",sorted[Query(root[ql-1],root[qr],1,cnt,k)]); 76 } 77 } 78 return 0; 79 }