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>
#include<stdlib.h>

#define INFTY 1000000000

int count=0;

void merge(int A[],int left,int mid,int right){
  int n1,n2,i,j,k;
  int *L,*R;

  n1 = mid - left;
  n2 = right - mid;
  /*L[0...n1], R[0...n2] を生成*/
  L=(int *)malloc(sizeof(int)*(n1+1));
  R=(int *)malloc(sizeof(int)*(n2+1));
  for( i = 0; i<=n1-1; i++){
    L[i] = A[left + i];
  }

  for (j = 0; j<=n2-1; j++){
    R[j] = A[mid + j];
  }
    L[n1] = INFTY;
    R[n2] = INFTY;
    i = 0;
    j = 0;

  for( k = left; k<=right-1; k++){
      if( L[i] <= R[j]){
        A[k] = L[i];
        i = i + 1;
        count++;
      }

      else{
        A[k] = R[j];
        j = j + 1;
        count++;
      }
    }

    free(L);
    free(R);
  }

void mergeSort(int A[],int left,int right){
        int i,mid;

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

 int main(){

   int A[5000000];
   int n,i;

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

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

   printf("\n");
   printf("%d\n",count);
   return 0;
 }