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 C (judge verdict: Accepted)

#include <stdio.h>
#define MAX 500000

void Merge(int [],int,int,int);
void Merge_Sort(int [],int,int);


int total;

int main(void){
    int A[MAX];
    int i,n;

    //要素の個数を指定
    scanf("%d",&n);

    //読み込む
    for(i=0;i<n;i++)
        scanf("%d",&A[i]);


    Merge_Sort(A,0,n);

    //ソートされた数列を表示させる
    for(i=0;i<n-1;i++)
        printf("%d ",A[i]);
    printf("%d\n%d\n",A[i],total);

    return 0;
}


//Merge_Sortから送られてきたデータを結合する。
void Merge(int A[],int left,int mid,int right){
    int n1 = mid - left;
    int n2 = right - mid;
    int L[n1 + 1];
    int R[n2 + 1];
    int i,j,k;

    for(i = 0;i < n1;i++)
        L[i] = A[left + i];

    for(i = 0;i < n2;i++)
        R[i] = A[mid + i];

    L[n1] = 1000000000;
    R[n2] = 1000000000;

    i = 0;
    j = 0;

    for(k = left;k < right;k++){
        if(L[i] < R[j])
            A[k] = L[i++];
        else
            A[k] = R[j++];

        total++;
    }
}


//ここで分割できるだけ分割する
void Merge_Sort(int A[],int left,int right){
    int mid;

    // 2つになるまで分割して行く
    if(left + 1 < right){
        mid = (left + right)/2;
        Merge_Sort(A,left,mid);
        Merge_Sort(A,mid,right);
        Merge(A,left,mid,right);
    }
}