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 INFTY 2000000000

int L[250002],R[250002];

int cnt;

void merge(int *A, int n, int left, int mid, int right){

  int n1=mid-left;
  int n2=right-mid;
  int i,j=0,k;

  for(i=0;i<n1;i++) L[i]=A[left+i];
  for(i=0;i<n2;i++) R[i]=A[mid+i];

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

  i=0;

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

    cnt++;
    if(L[i]<=R[j]){
      A[k]=L[i++];
    }
    else{
      A[k]=R[j++];
    }
  }
}

void mergesort(int *A, int n, int left, int right){

  int mid;

  if(left+1<right){
    mid=(left+right)/2;

    mergesort(A,n,left,mid);
    mergesort(A,n,mid,right);
    merge(A,n,left,mid,right);
  }
}

int main(){

  int i,n;

  cnt=0;

  scanf("%d",&n);

  int A[n];

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

  mergesort(A,n,0,n);

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

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

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

  return 0;

}