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 INFTY 2000000000

int S[1000000001];
int count=0;

void merge(int left, int mid, int right){
    int n1=mid-left;
    int n2=right-mid;
    int L[n1+1], R[n2+2];
    
    for(int i=0;i<n1;i++) L[i]=S[left+i];
    for(int i=0;i<n2;i++) R[i]=S[mid+i];
    L[n1]=INFTY;
    R[n2]=INFTY;
    int i=0;
    int j=0;
    for(int k=left;k<right;k++){
        count++;
        if(L[i]<=R[j]){
            S[k]=L[i];
            i++;
        }
        else{
            S[k]=R[j];
            j++;
        }
    }
}

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

int main(void){
    int n;
    
    scanf("%d",&n);
    for(int i=0;i<n;i++){
        scanf("%d",&S[i]);
    }
    
    mergeSort(0,n);
    
    for(int i=0;i<n;i++){
        printf("%d",S[i]);
        if(i!=n-1) printf(" ");
        else printf("\n%d\n",count);
    }
    
    return 0;
}