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
#define INFTY 2000000000

void Merge(int[MAX], int, int, int);
void MergeSort(int[MAX], int, int);

int count = 0;

int main(){

  int i, n;
  int A[MAX];

  scanf("%d", &n);

  for(i =0; i < n; i++){

    scanf("%d", &A[i]);

  }

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

  }

  printf("%d\n", A[i]);

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

}

void Merge(int A[MAX], int left, int mid, int right){

  int i, j, k;

  int n1, n2;

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

  int L[MAX], R[MAX];

  for(i = 0; i < n1; i++){

    L[i] = A[left + i];

  }

  for(i = 0; i < n2; i++){

    R[i] = A[mid + i];

  }

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

  i = 0;
  j = 0;

  for(k = left; k < right; k++){

    if(L[i] <= R[j]){

      A[k] = L[i];

      i++;

    }
    else{

      A[k] = R[j];
      
      j++;

    }

    count++;

  }

}

void MergeSort(int A[MAX], int left, int right){

  int mid;

  if((left + 1) < right){

    mid = (left + right) / 2;

    MergeSort(A, left, mid);

    MergeSort(A, mid, right);

    Merge(A, left, mid, right);

  }

}