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 INF 1000000005

int cnt;

int merge(int A[],int l,int m,int r){
  int R[250010],L[250010];
  int i,j,k;
  int n1,n2;
  n1 = m - l;
  n2 = r - m;

  for(i=0;i<n1;i++){
    L[i] = A[l+i];
  }
  for(i=0;i<n2;i++){
    R[i] = A[m+i];
  }
  L[n1] = INF;
  R[n2] = INF;
  i = 0;
  j = 0;

  for(k=l;k<r;k++){
    cnt++;
    if(L[i] <= R[j]){
       A[k] = L[i];
       i += 1;
    }else{
      A[k] = R[j];
      j += 1;
    }
  }
}

void  mergesort(int A[],int l,int r){
  int m;
  if(l + 1 < r){
    m = (l+r)/2;
    mergesort(A,l,m);
    mergesort(A,m,r);
    merge(A,l,m,r);
  }
}


int main(){
  int n;
  int S[500005];
  int i;
  cnt = 0;
  scanf("%d",&n);
  for(i=0;i<n;i++){
    scanf("%d",&S[i]);
  }
    mergesort(S,0,i);

    for(i=0;i<n;i++){
      printf("%d",S[i]);
      if(i<n-1){
        printf(" ");
      }
    }
    puts("");
    printf("%d\n",cnt);
    return 0;
}