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 100000

int n, k;
int A[MAX];

void exchange(int *a, int *b) {
  int tmp = *a;
  *a = *b;
  *b = tmp;
}

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

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

  return i+1;
}

int main() {
  int i, q;

  scanf("%d", &n);
  for (i = 0; i < n; i++) {
    scanf("%d", &A[i]);
  }

  q = partition(A, 0, n-1);
  for (i = 0; i < n; i++) {
    if (i == n-1) {
      printf("%d\n", A[i]);
      break;
    } if (i == q) {
      printf("[%d] ", A[i]);
      continue;
    }
    printf("%d ", A[i]);
  }

  return 0;
}