hdu 4217 Data Structure? 树状数组求第K小

Data Structure?

Time Limit: 10000/5000 MS (Java/Others)    Memory Limit: 65536/65536 K (Java/Others)

Problem Description

Data structure is one of the basic skills for Computer Science students, which is a particular way of storing and organizing data in a computer so that it can be used efficiently. Today let me introduce a data-structure-like problem for you.
Original, there are N numbers, namely 1, 2, 3...N. Each round, iSea find out the Ki-th smallest number and take it away, your task is reporting him the total sum of the numbers he has taken away.

 

Input

The first line contains a single integer T, indicating the number of test cases.
Each test case includes two integers N, K, K indicates the round numbers. Then a line with K numbers following, indicating in i (1-based) round, iSea take away the Ki-th smallest away.

Technical Specification
1. 1 <= T <= 128
2. 1 <= K <= N <= 262 144
3. 1 <= Ki <= N - i + 1

 

Output

For each test case, output the case number first, then the sum.

 

Sample Input

2 3 2 1 1 10 3 3 9 1

 

Sample Output

Case 1: 3 Case 2: 14

 

Author

iSea@WHU

 

Source

首届华中区程序设计邀请赛暨第十届武汉大学程序设计大赛

 思路：taobanzi；

#include<bits/stdc++.h>
using namespace std;
#define ll long long
#define pi (4*atan(1.0))
#define eps 1e-14
const int N=3e5+10,M=4e6+10,inf=1e9+10,mod=1e9+7;
const ll INF=1e18+10;
int tree[N],n,k;
int lowbit(int x)
{
    return x&-x;
}
void update(int x,int change)
{
    while(x<=n)
    {
        tree[x]+=change;
        x+=lowbit(x);
    }
}
int k_thfind(int K)//树状数组求第K小
{
    int sum=0;
    for(int i=18;i>=0;i--)
    {
        if(sum+(1<<i)<=n&&tree[sum+(1<<i)]<K)
        {
            K-=tree[sum+(1<<i)];
            sum+=1<<i;
        }
    }
    return sum+1;
}
int main(){
    int T,cas=1;
    scanf("%d",&T);
    while(T--)
    {
        memset(tree,0,sizeof(tree));
        scanf("%d%d",&n,&k);
        for(int i=1;i<=n;i++)
            update(i,1);
        ll ans=0;
        for(int i=0;i<k;i++)
        {
            int z;
            scanf("%d",&z);
            int v=k_thfind(z);
            ans+=v;
            update(v,-1);
        }
        printf("Case %d: %lld
",cas++,ans);
    }
    return 0;
}