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 N 500000
#define M 2000000000

int cnt=0, L[N/2+2], R[N/2+2];

void merge(int A[], int left, int mid, int right){
    int n1, n2, i, j;
    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] = M;
    i=0; j=0;

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

void mergeSort(int A[], int left, int right){
    if(left+1<right){
        int mid = (left+right) / 2;
        mergeSort(A, left, mid);
        mergeSort(A, mid, right);
        merge(A, left, mid, right);
    }
}
int main(void){
    int n, S[500000];
    scanf("%d", &n);
    for(int i=0 ; i<n ; i++) scanf("%d", &S[i]);
    mergeSort(S, 0, n);
    for(int i=0 ; i<n ; i++)
        if(i==n-1)    printf("%d\n", S[i]);
        else            printf("%d ", S[i]);
    printf("%d\n",cnt);
    return 0;

}