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)

/* 学籍番号 17D8101029G 石塚 博之 ID: mcatpolo 言語:C */
#include <stdio.h>
#include <math.h>
#define N 500000

long c = 0;

long A[N];

void merge(int left, int mid, int right){
    long L[N/2+1], R[N/2+1];
    int n1, n2, i, j, k;

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

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

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

   L[n1] = (long)INFINITY;
   R[n2] = (long)INFINITY;

   i=0;
   j=0;

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

}

void mergeSort(int left, int right){
    int mid;
    if(left+1<right){
        mid = (left+right)/2;
        mergeSort(left, mid);
        mergeSort(mid, right);
        merge(left, mid, right);
    }
}

int main(void){
    int i, n;

    scanf("%d", &n);

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

   mergeSort(0, n);

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

   printf("%d\n", c);

   return 0;
}