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 cnt;

void merge(int A[], int n, int left, int mid, int right){
  int i, j, k;

  int n1 = mid - left;
  int 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 = j = 0;
  for ( 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 ){
  int mid;
  if ( left+1 < right ){
    mid = (left + right)/2;
    mergeSort(A, n, left, mid);
    mergeSort(A, n, mid, right);
    merge(A, n, left, mid, right);
  }
}

main(){
  int A[MAX], n, i;
  scanf("%d", &n);
  cnt = 0;
  for ( i = 0; i < n; i++ ) {
    scanf("%d", &A[i]);
    if (A[i] >= SENTINEL ){
      return 1;
    }
  }
  mergeSort(A, n, 0, n);

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

  printf("%d\n", cnt);

  return 0;
}