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 Rust (judge verdict: Accepted)

use std::io;

/// a[st..end]について、a[st..q] < a[q] < a[q+1..end]となるように操作してqを返す関数
/// なお、分割の基準にはa[end]を用いるものとする
/// こちらは自分が教科書で見ていたやつ
fn partition2(vec: &mut Vec<u32>, st: usize, end: usize) -> usize {
    let num = vec[end];
    let mut i = st;
    let mut j = end-1;

    while i < j {
        while vec[i] <= num {
            i+=1;
        }
        while vec[j] > num && j > 0 {
            j-=1;
        }
        if i < j{
            vec.swap(i, j);
        }
    }
    vec.swap(end, i);
    i
}

/// AOJの疑似コートで指定されていたもの
fn partition(vec: &mut Vec<u32>, st: usize, end: usize) -> usize {
    let num = vec[end];
    let mut i: i32 = st as i32 - 1;

    for j in st..end {
        if vec[j] <= num {
            i += 1;
            vec.swap(i as usize, j);
        }
    }
    vec.swap(end, i as usize +1);
    i as usize + 1
}

fn main() {
    let sin = io::stdin();
    let mut buf = String::new();
    sin.read_line(&mut buf).ok();
    let _n: usize = buf.trim().parse().unwrap();

    let mut buf = String::new();
    sin.read_line(&mut buf).ok();
    let mut a: Vec<u32> = buf.split_whitespace()
        .map(|v| v.parse::<u32>().unwrap())
        .collect::<Vec<u32>>();

    let l = a.len() - 1;
    // let idx = partition2(&mut a, 0, l);
    let idx = partition(&mut a, 0, l);

    for (i,v) in a.iter().enumerate() {
        if i == idx {
            print!("[{}]", v);
        } else {
            print!("{}", v);
        }
        if i != l {
            print!(" ");
        } else {
            println!("");
        }
    }
}