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 N 500001
#define SENTINEL 1000000005

int n, S[N];
int cnt = 0;

void merge(int left, int mid, int right){

    int n1 = mid - left;
    int n2 = right - mid;

    // 番兵用に一つ余分に確保
    int L[n1+1], R[n2+1];

    int i, j, k;

    // 配列を2つに分ける
    for(i = 0; i < n1; i++) L[i] = S[left + i];
    for(i = 0; i < n2; i++) R[i] = S[mid + i];

    // 配列の最後に番兵を設置
    L[n1] = R[n2] = SENTINEL;

    i = j =0;

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

    // int iw = 0, il = left, ir = mid;
    //
    // while(il < mid && mid < right){
    //     if(S[il] <= S[ir]) work[iw++] = S[il++];
    //     else  work[iw++] = S[ir++];
    // }
    //
    // while(il < mid) work[iw++] = S[il++];
    // while(ir < right) work[iw++] = S[ir++];
}

void mergeSort(int left, int right){
    int mid;

    // 配列の長さが1以下ならソート済
    if(right - left <= 1) return;

    // 配列をleft~mid, mid~rightの2つに分けてソート
    mid = (left + right) / 2;
    mergeSort(left, mid);
    mergeSort(mid, right);

    // 配列をマージ
    merge(left, mid, right);
}



int main() {

    int i;
    int left, right;

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

    left = 0;
    right = n;

    mergeSort(left, right);

    for(i = 0; i < n-1; i++) printf("%d ", S[i]);
    printf("%d\n", S[n-1]);
    printf("%d\n", cnt);

    return 0;

}