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>
#include <stdlib.h>

int partition(int *,int);
void swapping(int *,int *,int *);

int main(){
  int *A,n,i,box;

  scanf("%d",&n);
  A = (int *)malloc(1 + n * sizeof(int));
  for(i = 1;i < n + 1;i++) scanf("%d",&A[i]);

  box = partition(A,n);


  for(i = 1;i < box;i++) printf("%d ",A[i]);
  printf("[%d] ",A[box]);
  for(i = box + 1;i < n + 1;i++){
    printf("%d",A[i]);
    if(i != n) printf(" ");
  }
  printf("\n");
  
  free(A);
  return 0;
}

int partition(int *A,int n){
  int x,i,j,hako = 0;
  x = A[n];
  i = -1;
  for(j = 0;j < n;j++){
    if(A[j] <= x){
      i += 1;
      swapping(&A[i],&A[j],&hako);
    }
  }
  swapping(&A[i + 1],&A[n],&hako);
  
  return i + 1;
}

void swapping(int *A,int *AA,int *dust){
  *dust = *A;
  *A = *AA;
  *AA = *dust;
}