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>

void merge(int,int,int);
void mergeSort(int,int);

int count=0,S[500000];
int main(){
  int i,n,left=0,mid,right;
  scanf("%d",&n);
  for(i=0;i<n;i++){
    scanf("%d",&S[i]);
  }
  right=n;
  mergeSort(left,right);
  for(i=0;i<n;i++){
    printf("%d",S[i]);
    if(i<n-1)printf(" ");
    if(i==n-1)printf("\n");
  }
  printf("%d\n",count);
}



void merge(int left,int mid,int right){
    int i,j,k,n1,n2,L[mid-left],R[right-mid];
    n1=mid-left;
    n2=right-mid;
    for(i=0;i<n1;i++){
      L[i]=S[left+i];
    }
    L[n1]=1000000001;
    for(j=0;j<n2;j++){
      R[j]=S[mid+j];
    }
    R[n2]=1000000001;
    i=0;
    j=0;
    for(k=left;k<right;k++){
      if(L[i]<=R[j]){
	S[k]=L[i];
	i=i+1;
	count++;
      } else {
	S[k]=R[j];
	j=j+1;
	count++;
      }
    }
  }

void mergeSort(int left,int right){
    int mid;
    if((left+1)<right){
      mid=(left+right)/2;
      mergeSort(left,mid);
      mergeSort(mid,right);
      merge(left,mid,right);
    }
  }