Problem:
Partition

Quick sort is based on the Divide-and-conquer approach. In QuickSort(A, p, r), first, a procedure Partition(A, p, r) divides an array A[p..r] into two subarrays A[p..q-1] and A[q+1..r] such that each element of A[p..q-1] is less than or equal to A[q], which is, inturn, less than or equal to each element of A[q+1..r]. It also computes the index q.

In the conquer processes, the two subarrays A[p..q-1] and A[q+1..r] are sorted by recursive calls of QuickSort(A, p, q-1) and QuickSort(A, q+1, r).

Your task is to read a sequence A and perform the Partition based on the following pseudocode:

Partition(A, p, r)
1 x = A[r]
2 i = p-1
3 for j = p to r-1
4 do if A[j] <= x
5 then i = i+1
6 exchange A[i] and A[j]
7 exchange A[i+1] and A[r]
8 return i+1

Note that, in this algorithm, Partition always selects an element A[r] as a pivot element around which to partition the array A[p..r].

Input

The first line of the input includes an integer n, the number of elements in the sequence A.

In the second line, Ai (i = 1,2,...,n), elements of the sequence are given separated by space characters.

Output

Print the sorted sequence. Two contiguous elements of the sequence should be separated by a space character. The element which is selected as the pivot of the partition should be indicated by [  ].

Constraints

1 ≤ n ≤ 100,000

0 ≤ Ai ≤ 100,000

Sample Input 1

12
13 19 9 5 12 8 7 4 21 2 6 11

Sample Output 1

9 5 8 7 4 2 6 [11] 21 13 19 12

Solution in C (judge verdict: Accepted)


#include  <stdio.h>
#define MAX 100001

int Partition(int *A, int left, int right);
void Swap(int *x, int i, int j);

int main()
{     
  int A[MAX], n, i, j, pivot;
  scanf("%d",&n);
  for(i=0;i<n;i++){
    scanf("%d",&A[i]);
  }
  pivot=A[n-1];
  j=Partition(A, 0, n-1);
 
  for(i=0;i<j;i++){
    printf("%d ",A[i]);
  }
  printf("[%d]",pivot);
  for(i=j+1;i<n-1;i++){
  printf(" %d",A[i]);
  }
  printf(" %d\n",A[i]);  
  return 0;
}

int Partition(int *A, int left, int right)
{
  int i, j, x;
    x = A[right];
    i = left-1;
    for(j=left; j<right; j++){
      if(A[j]<=x){
	i++;
	Swap(A, i, j);
      } 
    }
    Swap(A, i+1, right);
    return i+1;
}

void Swap(int *x, int i, int j)
{
    int temp;
    temp = x[i];
    x[i] = x[j];
    x[j] = temp;
}