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)

/* MergeSort */
#include <stdio.h>

int Merge(int *, int, int, int);
int MergeSort(int *, int, int);
int sum=0;

int 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);
    }
    else { return 0; }
}

int Merge(int *A, int left, int mid, int right)
{
    int k, n1, n2, L[500000], R[500000], 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] = 999999999;
    R[n2] = 999999999;
    i = 0;
    j = 0;

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

int main()
{
    int i, n;
    int S[500000];

    scanf("%d", &n);
    for(i=0; i<n; i++){
        scanf("%d", &S[i]);
    }

    MergeSort(S, 0, n);

    for (i=0; i<n-1; i++){
        printf("%d ", S[i]);
    }
    printf("%d\n", S[i]);
    printf("%d\n", sum);
    return 0;
}