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 500000
#define SENTINEL 2000000000

int L[MAX/2+2],R[MAX/2+2];
int count;

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


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


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


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