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>

int partition(int, int);

int A[100000];

int main(){
  int n,key;
  int i,j;
  
  scanf("%d",&n);
  for(i=1; i<=n; i++){
    scanf("%d",&A[i]);
  }
  
  i = 1;
  key = partition(i,n);
  
  for(i=1; i <= n; i++){
    
    if(i == key){
      printf("[%d]",A[i]);
    }
    else printf("%d",A[i]);

    if((i >= 1) && (i < n))
      printf(" ");
  }
  printf("\n");
  
  return 0;
}

int partition(int p, int r){
  int x,i,j;
  int temp;
  
  x = A[r];
  i = p-1;

  for(j=p; j <= r-1; j++){
    if(A[j] <= x){
      i = i+1;

      temp = A[i];
      A[i] = A[j];
      A[j] = temp;
    } 
  }
    temp = A[i+1];
    A[i+1] = A[r];
    A[r] = temp; 
  
  return i+1;
}