Quikselect -code_select kincode-优快云博客

本文介绍了一种线性时间复杂度的快速选择算法，该算法能在未排序数组中找到第k小的元素。通过递归地将数组部分排序，快速选择算法能够实现O(n)的时间复杂度，优于传统的排序方法。文章提供了详细的C++实现示例。

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What is Quick Select Algorithm? How to implement in C++?
The QuickSelect algorithm quickly finds the k-th smallest element of an unsorted array of n elements.
It is an  $O (n)$ , worst-case linear time, selection algorithm. A typical selection by sorting method would need atleast O(n log n) time.
This algorithm is identical to quick sort but it does only a partial sort, since we already know which partition our desired element lies as the pivot is in final sorted position.

#include <iostream>
using namespace std;

// A simple print function
void print(int *input)
{
    for ( int i = 0; i < 5; i++ )
        cout << input[i] << " ";
    cout << endl;
}

int partition(int* input, int p, int r)
{
    int pivot = input[r];
    
    while ( p < r )
    {
        while ( input[p] < pivot )
            p++;
        
        while ( input[r] > pivot )
            r--;
        
        if ( input[p] == input[r] )
            p++;
        else if ( p < r ) {
            int tmp = input[p];
            input[p] = input[r];
            input[r] = tmp;
        }
    }
    
    return r;
}

int quick_select(int* input, int p, int r, int k)
{
    if ( p == r ) return input[p];
    int j = partition(input, p, r);
    int length = j - p + 1;
    if ( length == k ) return input[j];
    else if ( k < length ) return quick_select(input, p, j - 1, k);
    else  return quick_select(input, j + 1, r, k - length);
}

int main()
{
    int A1[] = { 100, 400, 300, 500, 200 };
    cout << "1st order element " << quick_select(A1, 0, 4, 1) << endl;
    int A2[] = { 100, 400, 300, 500, 200 };
    cout << "2nd order element " << quick_select(A2, 0, 4, 2) << endl;
    int A3[] = { 100, 400, 300, 500, 200 };
    cout << "3rd order element " << quick_select(A3, 0, 4, 3) << endl;
    int A4[] = { 100, 400, 300, 500, 200 };
    cout << "4th order element " << quick_select(A4, 0, 4, 4) << endl;
    int A5[] = { 100, 400, 300, 500, 200 };
    cout << "5th order element " << quick_select(A5, 0, 4, 5) << endl;
}

OUTPUT:-

1st order element 100
2nd order element 200
3rd order element 300
4th order element 400
5th order element 500