Problem Description: Given the set S consisting of n different numbers and the positive integer k < n, we try to design an O(n) time algorithm to find the number of K that is closest to the median of S.

Algorithmic description:

1. Finding the Median with the Algorithms Realized by Linear Time Selection
2. S'= S excluding median
3. Value in S"=|S'- Value of Median|
4. Finding the k-th Minimum Number by the Algorithms Implemented by Linear Time Selection
5. Value in S corresponding to the number of output S less than the smallest number in k

Algorithmic implementation:

selectorder Function, partition Function, sord The function is implemented with the algorithm of linear time selection program.
int main()
{
    void sord(int a[],int h,int t);
    int selectorder(int x,int a[],int h,int t);
    int partition(int a[],int h,int t,int k);
    int n;
    scanf("%d",&n);
    int *a;
    a=(int *)malloc(sizeof(int)*n);
    for(int i=0;i<n;i++)
         a[i]=rand();
    for(int i=0;i<n;i++)
         printf("%d ",a[i]);
    //Dynamic allocation array a
    //Random generated array a Elements, outputs
    /*
    int n=7;
    int a[7]={0,-1,20,-4,-100,2000,2001};
    for(int i=0;i<n;i++)
         printf("%d ",a[i]);
     */   
    printf("\n");       
    int middle;
    middle=selectorder((n-1)/2,a,0,n-1);
    printf("%d\n",middle);
    //Find array a Median and assign to middle    
    int *b;
    b=(int *)malloc(sizeof(int)*n);   
    for(int i=0;i<n;i++)
      if(a[i]>=middle)b[i]=a[i]-middle;
      else b[i]=middle-a[i];
    //Dynamic allocation array b
    //array b Medium element=|array a Medium element-middle|  
    int *c;
    c=(int *)malloc(sizeof(int)*n);
    for(int i=0;i<n;i++)c[i]=b[i];
    //array c Medium element=array b Medium element 
    int k;
    scanf("%d",&k);
    //input k
    int last;
    last=selectorder(k-1,b,0,n-1);
    //Find array b pass the civil examinations k Small elements are assigned to last        
    for(int i=0;i<n;i++)
     if(c[i]<=last)printf("%d ",a[i]);
    //foreach c，If array c Medium element less than last，
    //Then output the array at the corresponding position a Elements
    printf("\n");
    sord(a,0,n-1);
    for(int i=0;i<n;i++)printf("%d ",a[i]);
      return 0;    
}