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 A[], int n, int left, int mid, int right) {
    int n1, n2;
    int 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 = 0, 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 n, int left, int right) {
    if (left+1 < right) {
        int mid = (left + right) / 2;
        mergeSort(A, n, left, mid);
        mergeSort(A, n, mid, right);
        merge(A, n, left, mid, right);
    }
}

int main () {
    int n, i, A[MAX];
    count = 0;

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

    mergeSort(A, n, 0, n);

    for (i = 0; i < n; i++) {
        if (i > 0) printf(" ");
        printf("%d",A[i]); 
    }
    printf("\n");
    printf("%d\n",count);

    return 0;
}