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<iostream>
using namespace std;
#define MAX 500000
#define SENTINEL 2000000000

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

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

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

int main() {
    int A[MAX], n, i;
    cnt = 0;
    
    cin >> n;
    for(i=0;i<n;i++) cin >> A[i];
    mergeSort(A, n, 0, n);
    
    for( i = 0; i < n; i++) {
        if(i) cout << " ";
        cout << A[i];
    }
    cout << endl;
    
    cout << cnt << endl;
    
    return 0;
}