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 MAX 500000
#define INF 1000000000

void k_tmerge(int *,int,int,int);
void tmergesort(int *,int,int);

int count;


void tmergesort(int A[],int left,int right)
{
  int mid;
  if(left + 1 < right){
    mid = (left + right) / 2;
    tmergesort(A,left,mid);
    tmergesort(A,mid,right);
    k_tmerge(A,left,mid,right);
  }
}

void k_tmerge(int *A,int left,int mid,int right)
{
  int i,k,j,n1=0,n2=0;
  int *L,*R;

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

  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] = INF;
  R[n2] = INF;
  i = 0;
  j = 0;

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

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

  scanf("%d",&n);

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

  for(i = 0;i < n;i++){
    if( i > 0 ) printf(" ");
    printf("%d",A[i]);
  }
  printf("\n");
  printf("%d\n",count);
  return 0;
}