从N个元素中选择第i小的元素

时常在笔试,面试题中看到这个问题,《算法导论》中给出了很好的解答。

Selection of the ith smallest element of the array A can be done in θ(n) times.

The psuedocode is following:

Randomized_Select(A,p,r,i)
{
    if p==r
        then return A[p]
    q=Randomized_Partition(A,p,r)
    k=q-p+1
    if i==k
        then return A[q]
    else if i<k
        then return Randomized_select(A,p,q-1,i)
    else
        return Randomized_select(A,q+1,r,i-k)
}


=====================================
Randomized_Partition(A,p,r)
{
    i=RANDOW(p,r)
    exchange A[r] ↔ A[i]
    return Partition(A,p,r)
}
=====================================
Partition(A,p,r)
{
    x=A[r]
    i=p-1
    for j=p to r-1
        if A[j]<=x
              then i=i+1
                  exchange A[i]↔A[j]
    exchange A[i+1] ↔A[r]
    return i+1
}

 

Transfer to C# code:

 

namespace SelectMinimum
{
class Program
    {
static void Main(string[] args)
        {
int[] A = new int[] {0,25,12,14,57,45,18,75,85,74,45,63,35,28,39 };
            SelectSort ss = new SelectSort();
int result;
            result=ss.Randomized_Select(A,0,14,11);
            Console.WriteLine(result);
            Console.ReadLine();
        }


    }

public class SelectSort
    {
public int Randomized_Select(int[] A, int p, int r, int i)
        {
if (p == r)
return A[p];
int q = Randomize_Partition(A, p, r);
int k = q - p + 1;
if (i == k)
return A[q];
else if (i < k)
return Randomized_Select(A, p, q - 1, i);
else
return Randomized_Select(A, q + 1, r, i - k);

        }

public int Randomize_Partition(int[] A, int p, int r)
        {
            Random rd = new Random();
int i = rd.Next(p, r);
int temp;
            temp = A[r];
            A[r] = A[i];
            A[i] = temp;
return Partition(A, p, r);
        }

public int Partition(int[] A, int p, int r)
        {
int x = A[r];
int i = p - 1;
for (int j = p; j <= r - 1; j++)
            {
if (A[j] <= x)
                {
                    i += 1;
int temp;
                    temp = A[i];
                    A[i] = A[j];
                    A[j] = temp;
                }
            }
int temp2;
            temp2 = A[i + 1];
            A[i + 1] = A[r];
            A[r] = temp2;
return i + 1;
        }
    }
}