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 1000000000
int cnt=0;
void merge(int *,int,int,int);
void mergeSort(int *,int,int);
int main(){
  int n;
  int S[500001];
  int i;
  scanf("%d",&n);
  for(i=0;i<n;i++) scanf("%d",&S[i]);
  mergeSort(S,0,n);
  for(i=0;i<n;i++){
    printf("%d",S[i]);
    if(i!=n-1) printf(" ");
  }
  printf("\n");
  printf("%d\n",cnt);
  return 0;
}
 
void merge(int S[],int left,int mid,int right){
  int n1 = mid - left;
  int n2 = right - mid;
  int L[n1+1],R[n2+1];
  int i,j,k;
  for(i=0;i<n1;i++) L[i] = S[left + i];
  for(i=0;i<n2;i++) R[i] = S[mid + i];
  L[n1] = INF;
  R[n2] = INF;
  i = 0;
  j = 0;
  for(k = left; k< right;k++){
    if(L[i] <= R[j]){
      S[k] = L[i];
      i++;
    }
    else {
      S[k] = R[j];
      j++;
    }
    cnt++;
  }
}
 
void mergeSort(int S[],int left,int right){
  int mid;
  if(left + 1 < right){
    mid = (left + right) / 2;
    mergeSort(S,left,mid);
    mergeSort(S,mid,right);
    merge(S,left,mid,right);
  }
}