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 MAX 500001 /*500000*/
#define INF 10000000

void merge(int A[],int left,int mid,int right,int *cnt){
int i,j,n1,n2;
int L[MAX];
int R[MAX];
int k;
n1=mid-left;
n2=right-mid;

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

L[n1]=2147483647;
R[n2]=2147483647;

i=0;
j=0;

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


void mergesort(int A[],int left,int right,int *cnt){
int mid;
 if(left+1 < right){
   mid=(left+right)/2;
   mergesort(A,left,mid,cnt);
   mergesort(A,mid,right,cnt);
   merge(A,left,mid,right,cnt);
 }
}



int main(){
int n,i;
int A[MAX];
int cnt=0;

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

mergesort(A,0,n,&cnt);

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

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

return 0;
}