Select算法（最坏复杂度O(n)）

#include<iostream>
#include <stdio.h>
#include <stdlib.h>
#include <algorithm>
#include <string>
#include <string.h>
using namespace std;

const int nMax = 3000;
int A[nMax+1];
int B[nMax+1];//用来每次5分法后保存要比较的值在A中的下标
int AIndex[nMax+1]; //用来保存A的初始化下标

//通过插入排序获取中位数下标
int InsertSort(int A[], int B[], int start, int end)
{
    if (start == end)
    {
        return B[start];
    }

    for (int i = start+1; i <= end; ++i)
    {
        int num = A[B[i]];
        int j = i-1;
        for ( ; j >= start; --j)
        {
            if (num < A[B[j]])
            {
                A[B[j + 1]] = A[B[j]];
            }
            else
            {
                break;
            }
        }
        A[B[j + 1]] = num;
    }

    return B[(start + end)/2];
}

//获取中位数的中位数的下标
int GetMidMid(int A[], int AIndex[], int k, int n)
{
    if (k == n)
    {
        return AIndex[n];
    }

    int len_s = n - k + 1;
    //筛选出n/5份的中位数
    int mod = len_s % 5;
    int len = len_s / 5 + (mod != 0);
    for (int i = 1, j = k; i<= len && j <= n-mod; ++i, j+=5)
    {
        B[i] = InsertSort(A, AIndex,j, j+4);
    }
    if (mod != 0)
    {
        B[len] = InsertSort(A, AIndex, n - mod + 1, n);
    }
    return GetMidMid(A, B, 1, len);
}

//原址排序
int Partition(int A[], int p, int n)
{
    int pivot = A[n];
    int j = p - 1;
    for (int i = p; i <= n - 1; ++i)
    {
        if (A[i] <= pivot)
        {
            j++;
            swap(A[j], A[i]);
        }
    }

    swap(A[j + 1], A[n]);
    return j + 1;
}

int Select(int A[], int k, int n, int i)
{
    if (k == n)
    {
        return A[n];
    }

    int midValueIndex = GetMidMid(A, AIndex, k, n);

    //将该中位数作为主元(pivot element)
    //使用一次原址重排
    int pivot = A[midValueIndex];
    swap(A[midValueIndex], A[n]);
    int mid = Partition(A, k, n);

    int t = mid - k + 1;
    if (i == t)
    {
        return A[mid];
    }
    else if (i < t)
    {
        return Select(A, k, mid-1, i);
    }
    else
    {
        return Select(A, mid+1, n, i-t);
    }
}
int main(int argc, char** argv)
{
    int n = 1111;
    for (int i = 1; i <= n; ++i)
    {
        A[i] = i;
        AIndex[i] = i;
    }

    //for (int i = 1; i <= n; ++i)
    //{
    //    cout << A[i] << " ";
    //}
    //cout << endl;
    
    int equalNum = 0;
    for (int i = 1; i <= n; ++i)
    {
        //随机排列A数组
        for (int i = 1; i <= n; ++i)
        {
            int j = i + rand() % nMax;
            //swap(A[i], A[j]);
            A[i] = j;
        }

        int ans1 = Select(A, 1, n, i);
        sort(A + 1, A + n + 1);
        int ans2 = A[i];

        if (ans1 == ans2)
        {
            equalNum++;
        }
    }
    cout << n << " " << equalNum << endl;
    return 0;
}