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 10000000000

int n, cnt = 0;

void merge(int*, int, int, int);
void mergeSort(int*, int, int);

int main() {
  int i, S[500000];
  scanf("%d\n", &n);
  for (i = 0; i < n; i++) {
    scanf("%d", &S[i]);
  }

  mergeSort(S, 0, n);
  for (i = 0; i < n; i++) {
    if (i == n-1) {
      printf("%d", S[i]);
      break;
    }
    printf("%d ", S[i]);
  }
  printf("\n%d\n", cnt);

  return 0;
}

void merge(int* A,int left, int mid, int right) {
  int n1, n2, i, j, k;
  n1 = mid - left;
  n2 = right - mid;
  int l[n1];
  int r[n2];
  for (i = 0; i < n1; i++) {
    l[i] = A[left+i];
  }
  for (i = 0; i < n2; i++) {
    r[i] = A[mid+i];
  }
  l[n1] = MAX;
  r[n2] = MAX;
  i = j = 0;
  for (k = left; k < right; k++) {
    if (l[i] <= r[j]) {
      A[k] = l[i];
      i++;
      cnt++;
    } else {
      A[k] = r[j];
      j++;
      cnt++;
    }
  }
}

void mergeSort(int* A, int left, int right) {
  if (left+1 < right) {
    int mid = (left + right) / 2;
    mergeSort(A, left, mid);
    mergeSort(A, mid, right);
    merge(A, left, mid, right);
  }
}