Problem:
Merge Sort

Write a program of a Merge Sort algorithm implemented by the following pseudocode. You should also report the number of comparisons in the Merge function.

Merge(A, left, mid, right)
n1 = mid - left;
n2 = right - mid;
create array L[0...n1], R[0...n2]
for i = 0 to n1-1
do L[i] = A[left + i]
for i = 0 to n2-1
do R[i] = A[mid + i]
L[n1] = SENTINEL
R[n2] = SENTINEL
i = 0;
j = 0;
for k = left to right-1
if L[i] <= R[j]
then A[k] = L[i]
i = i + 1
else A[k] = R[j]
j = j + 1

Merge-Sort(A, left, right){
if left+1 < right
then mid = (left + right)/2;
call Merge-Sort(A, left, mid)
call Merge-Sort(A, mid, right)
call Merge(A, left, mid, right)

Input

In the first line n is given. In the second line, n integers are given.

Output

In the first line, print the sequence S. Two consequtive elements should be separated by a space character.

In the second line, print the number of comparisons.

Constraints

n ≤ 500000

0 ≤ an element in S ≤ 109

Sample Input 1

10
8 5 9 2 6 3 7 1 10 4

Sample Output 1

1 2 3 4 5 6 7 8 9 10
34

Notes

Solution in Rust (judge verdict: Accepted)

use std::collections::VecDeque;
use std::env;
//use std::fmt::Debug;
use std::io;
use std::io::prelude::*;
//use std::time::{Duration, Instant};

//===================================================
// MACROs need to be defined above the use place ... ?
macro_rules! dprintln {
    ($($x:expr),*) => {{
        if $crate::is_debug_mode() {
            let f = || {println!( $($x),*)};
            f()
        }
    }}
}

/// Backward For-Loop Helper
///  from -> to (exclude `to`)
///
/// # Examples
/// see tests::macro_backward()
///
#[macro_export]
macro_rules! backward_ho {
    ($from:expr, $to:expr) => {{
        (($to + 1)..($from + 1)).rev()
    }};
}
//===================================================

fn main() {
    // Initialize
    set_debug_mode(false);
    for arg in env::args() {
        if arg == "--debug" {
            set_debug_mode(true);
        }
    }
    dprintln!("[DebugMode] {}", "On");

    // Execute
    dprintln!("=================");
    dprintln!("= READ INPUT     ");
    let stdin = io::stdin();
    let input = BufReadInput::new(stdin.lock());
    dprintln!("[Input] \n{:?}", input);
    dprintln!("=================");
    dprintln!("= INTERPRET INPUT");
    let q = input.into_quiz();
    dprintln!("[Quiz] \n{:?}", q);
    dprintln!("=================");
    dprintln!("= SOLVE QUIZE    ");
    let a = q.solve();
    dprintln!("[Answer] \n{:?}", a);
    dprintln!("=================");
    dprintln!("= PRINT ANSWER   ");
    a.print();
    dprintln!("=================");
}

#[derive(Debug)]
struct Quiz {
    n: usize,    // n <= 500,000
    s: Vec<u32>, // 0 <= s[i] <= 100,000,000, length=n
}

#[derive(Debug)]
struct Answer {
    v: Vec<u32>,
    count: u32,
}

trait IntoQuiz {
    fn into_quiz(self) -> Quiz;
}

impl<I: Input> IntoQuiz for I {
    fn into_quiz(mut self) -> Quiz {
        let n: usize = self.parse_next().unwrap();
        let s: Vec<u32> = self.parse_next_vec(n).unwrap();
        Quiz { n, s }
    }
}

impl Quiz {
    fn solve(mut self) -> Answer {
        let mut solver = Solver::new();
        solver.merge_sort(&mut self.s, 0usize, self.n);
        Answer{
            v: self.s,
            count: solver.count,
        }
    }
}

struct Solver {
    count: u32,
}

impl Solver {
    fn new() -> Self {
        Solver{ count: 0 }
    }

    fn merge_sort(&mut self, a: &mut [u32], left: usize, right: usize) {
        dprintln!("merge_sort l:{}, r:{}", left, right);
        if right - left > 1 {
            let mid = (left + right) / 2;
            self.merge_sort(a, left, mid);
            self.merge_sort(a, mid, right);
            self.merge(a, left, mid, right);
        } else {
        }
    }

    fn merge(&mut self, a: &mut [u32], left: usize, mid: usize, right: usize) {
        dprintln!("merge: l:{}, m:{}, r:{}, count:{}", left, mid, right, self.count);
        let n1 = mid - left;
        let n2 = right - mid;
        let mut lv = Vec::with_capacity(n1+1);
        let mut rv = Vec::with_capacity(n2+1);
        for i in 0..n1 {
            lv.push(a[left + i]);
        }
        lv.push(std::u32::MAX);
        for i in 0..n2 {
            rv.push(a[mid + i]);
        }
        rv.push(std::u32::MAX);
        let mut li = 0;
        let mut ri = 0;
        for i in left..right {
            self.count += 1;
            dprintln!(" a[{}] <- lv[{}]:{} or rv[{}]:{}", i, li, lv[li], ri, rv[ri]);
            if lv[li] <= rv[ri] {
                a[i] = lv[li];
                li += 1;
            } else {
                a[i] = rv[ri];
                ri += 1;
            }
        }
    }
}

impl Answer {
    fn print(self) {
        println!("{}", concat_vec_to_string(&self.v));
        println!("{}", self.count);
    }
}

// =====================================================
// =
// =====================================================

//==================================================
// Stdin Reader
#[derive(Debug)]
pub enum Token {
    Word(String),
    LineBreak,
}

impl Token {
    pub fn is_word(&self) -> bool {
        match *self {
            Token::Word(ref _x) => true,
            _ => false,
        }
    }
}

#[derive(Debug)]
pub struct BufReadInput<R: BufRead> {
    input: R,
    tokens: VecDeque<Token>,
}

pub trait Input {
    fn read_next_word(&mut self) -> Option<Token>;

    fn parse_next<T>(&mut self) -> Option<T>
    where
        T: std::str::FromStr,
    {
        if let Some(Token::Word(str)) = self.read_next_word() {
            match str.parse() {
                Ok(x) => Some(x),
                _ => None,
            }
        } else {
            None
        }
    }

    fn parse_next_vec<T>(&mut self, size: usize) -> Option<Vec<T>>
    where
        T: std::str::FromStr,
    {
        let mut v = Vec::new();

        for _i in 0..size {
            if let Some(t) = self.parse_next() {
                v.push(t);
            } else {
                return None;
            }
        }

        Some(v)
    }

    fn parse_next_vec2<T>(&mut self, size2: usize, size1: usize) -> Option<Vec<Vec<T>>>
    where
        T: std::str::FromStr,
    {
        let mut v = Vec::new();

        for _i in 0..size2 {
            if let Some(t) = self.parse_next_vec(size1) {
                v.push(t);
            } else {
                return None;
            }
        }

        Some(v)
    }

    fn parse_all_remaining_into_vec<T>(&mut self) -> Vec<T>
    where
        T: std::str::FromStr,
    {
        let mut v = Vec::new();

        loop {
            match self.parse_next() {
                Some(x) => v.push(x),
                None => return v,
            }
        }
    }
}
impl<R: BufRead> BufReadInput<R> {
    pub fn new(input: R) -> Self {
        let tokens = VecDeque::new();

        BufReadInput { input, tokens }
    }
}

impl<R: BufRead> Input for BufReadInput<R> {
    fn read_next_word(&mut self) -> Option<Token> {
        loop {
            match self.tokens.pop_front() {
                None => {
                    // Read Input
                    let mut line = String::new();
                    let n = self.input.read_line(&mut line).expect("Read Error.");
                    if n == 0 {
                        return None;
                    }
                    let mut line_tokens = tokenaize(line);
                    self.tokens.append(&mut line_tokens);
                }
                Some(Token::LineBreak) => (),
                x => return x,
            }
        }
    }

}

//TODO: Make CaseIterator
// ex) 
//  let mut input: Input ...
//  let mut iter: CaseIterator<Case=Command> = input.rest_into_cases(|i|   
//    let cmd:String = i.parse_next().expect("Parse error cmd");
//    let num:u32    = i.parse_next().expect("Parse error num");
//
//    Command::new(cmd, num)
//  );
//  let case1 = iter.next();
//  let case2 = iter.next();
//  ...


fn tokenaize(str: String) -> VecDeque<Token> {
    let mut v = VecDeque::new();

    for w in str.split_whitespace() {
        v.push_back(Token::Word(w.to_string()));
    }
    v.push_back(Token::LineBreak);
    v
}

//==================================================
// Utility Functions
pub fn concat_vec_to_string<T>(v: &Vec<T>) -> String
where
    T: std::fmt::Display,
{
    let mut string = String::with_capacity(v.len() * 2);

    if let Some((h, t)) = v.split_first() {
        string = h.to_string();

        for obj in t {
            string.push(' ');
            string.push_str(&obj.to_string());
        }
    }

    return string;
}

//==================================================
// Debug Switch
static mut S_DEBUG_MODE: bool = false;
fn is_debug_mode() -> bool {
    unsafe { S_DEBUG_MODE }
}

fn set_debug_mode(mode: bool) {
    unsafe {
        S_DEBUG_MODE = mode;
    }
}

//==================================================
// Usage
#[cfg(test)]
mod tests {
    use super::*;

    #[test]
    fn macro_backward() {
        let mut v = Vec::new();
        for i in backward_ho!(5, 1) {
            v.push(i);
        }
        assert_eq!(vec![5, 4, 3, 2], v);
    }
}