Find the k-th smallest element

本文介绍了一种算法用于在给定数组中找到第k+1小的元素,包括函数实现和具体示例。

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1001. Find the k-th smallest element   

Given a sequence A=(a1,...,an), your job is to find the (k+1)-th smallest element of A.


For example, A=(3, 2, 3, 4, 5) and k=1, then 3 is returned, since 3 is the second smallest element of A.


Please implement and submit the following function:


int select(int a[], int n, int k) {


  // Your code will be here. You may invoke other functions.


}


Note: 0<=k<n<=1000000


int select(int a[], int n, int k , int l = 0 ) {
    int pivot = a[l] ;
    int left = l + 1 , right = n - 1 ;
    while(left <= right){
        while(a[left] <= pivot){
            if(left > right) break ;
            left ++ ;
        }
        while(a[right] > pivot){
            if(left > right) break ;
            right -- ;
        }
        if(left > right) break ;
        swap(a[right] , a[left]) ;
    }
    swap(a[right] , a[l]) ;
    if(k == right) return a[right] ;
    if(k < right){
        return select(a , right , k , l) ;
    }else{
        return select(a , n, k , right + 1) ;
    }
}                                 




 
B. Serval and Final MEX time limit per test1 second memory limit per test256 megabytes You are given an array a consisting of n≥4 non-negative integers. You need to perform the following operation on a until its length becomes 1 : Select two indices l and r (1≤l<r≤|a| ), and replace the subarray [al,al+1,…,ar] with a single integer mex([al,al+1,…,ar]) , where mex(b) denotes the minimum excluded (MEX)∗ of the integers in b . In other words, let x=mex([al,al+1,…,ar]) , the array a will become [a1,a2,…,al−1,x,ar+1,ar+2,…,a|a|] . Note that the length of a decreases by (r−l) after this operation. Serval wants the final element in a to be 0 . Help him! More formally, you have to find a sequence of operations, such that after performing these operations in order, the length of a becomes 1 , and the final element in a is 0 . It can be shown that at least one valid operation sequence exists under the constraints of the problem, and the length of any valid operation sequence does not exceed n . Note that you do not need to minimize the number of operations. ∗ The minimum excluded (MEX) of a collection of integers b1,b2,…,bk is defined as the smallest non-negative integer x which does not occur in the collection b . Input Each test contains multiple test cases. The first line contains the number of test cases t (1≤t≤1000 ). The description of the test cases follows. The first line of each test case contains a single integer n (4≤n≤5000 ) — the length of the array a . The second line contains n integers a1,a2,…,an (0≤ai≤n ) — the elements of the array a . It is guaranteed that the sum of n over all test cases does not exceed 5000 . Output For each test case, output a single integer k (0≤k≤n ) in the first line of output — the length of the operation sequence. Then, output k lines, the i -th line containing two integers li and ri (1≤li<ri≤|a| ) — the two indices you choose in the i -th operation, where |a| denotes the length of the array be
03-23
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