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: Time Limit Exceeded)

#include<stdio.h>
#define MAX 500001
#define SENTINEL 2000000

 int count=0;

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

 int mergesort(int S[MAX],int left,int right){
        while(right-left>1){
             int mid=(left+right)/2;
             mergesort(S,left,mid);
             mergesort(S,mid,right);
             merge(S,left,right,mid);
             }
        }

 int main(){
        int i,n,left,right;
        int S[MAX];
        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%c",S[i],(i==n-1)?"\n":" ");
                   }
        printf("%d",count);
        return 0;
        }