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 500010
#define INF 2000000000
 
int count = 0;
int A[MAX];
int L[MAX/2+2], R[MAX/2+2];
 
int merge(int A[], int l, int m, int r)
{
    int i;    
    for (i=0; i<m-l; i++) L[i] = A[l+i];
    for (i=0; i<r-m; i++) R[i] = A[m+i];
     
    L[m-l] = R[r-m] = INF;
     
    int p=0, q=0;
    for (i=l; i<r; i++) {
        if (L[p] <= R[q]) {
            A[i] = L[p++];
        }
        else {
            A[i] = R[q++];
        }
        count++;
    }
     
}
 
void mergeSort(int A[], int l, int r)
{
    if (l+1 < r) {
        int m = (l + r) / 2;
        mergeSort(A, l, m);
        mergeSort(A, m, r);
        merge(A, l, m, r);
    }
}
 
int main()
{
    int i;    
    int N;
     
    scanf("%d", &N);
    for (i = 0; i < N; i++) {
        scanf("%d", &A[i]);
    }
     
    mergeSort(A, 0, N); // N?????§???
     
    for (i = 0; i < N-1; i++) {
        printf("%d ", A[i]);
    }
    printf("%d\n", A[i]);
    printf("%d\n", count);
     
    return 0;
}