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 S 1000000000
 
int merge(int *, int, int, int);
void mergeSort(int *, int, int);
 
int n, s[N], tmp[N], x[N];
int  count = 0;
 
int main(){
    int i, x;
 
    scanf("%d", &n);
    for(i = 0; i < n; i++){
        scanf("%d", &s[i]);
    }
    
    mergeSort(s, 0, n-1);

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

    return 0;

}
 
void mergeSort(int A[], int left, int right){
    int mid, i, j, k;
    
    if(left >= right) return;

    mid = (left + right) / 2;

    mergeSort(A, left, mid);
    mergeSort(A, mid + 1, right);
    
    for(i = left; i <= mid; i++){
        tmp[i] = A[i];
        }
 
    for(i = mid + 1, j = right; i <= right; i++, j--){
        tmp[i] = A[j];
        }
        
    i = left;
    j = right;
 
    for(k = left; k <= right; k++){
      if(tmp[i] <= tmp[j]) A[k] = tmp[i++];
      else A[k] = tmp[j--];
      count++;
    }
}