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)

// Merge Sort
#include <stdio.h>
#include <stdlib.h>
#define SENTINEL 1000000000

void merge(int *a, int left, int mid, int right);
void mergeSort(int *a, int left, int right);

int cnt = 0;

int main() {
  int i, n;
  int *a;
  int left, right, mid;

  // input the length
  scanf("%d", &n);
  // memory allocation
  a = (int *)malloc(n * sizeof(int));
  // input the number
  for(i = 0; i < n; i++) {
    scanf("%d", &a[i]);
  }

  left = 0;
  right = n;
  mid = (left + right) / 2;

  //merge sort
  mergeSort(a, left, right);

  // output
  for(i = 0; i < n; i++) {
    printf("%d", a[i]);
    if(i == n - 1) printf("\n");
    else printf(" ");
  }
  printf("%d\n", cnt);
  
  return 0;
}

void merge(int *a, int left, int mid, int right) {
  int n1, n2;
  int i, j, k;
  int *l, *r;

  n1 = mid - left;
  n2 = right - mid;
  // create array L and R
  l = (int *)malloc((n1+1)*sizeof(int));
  r = (int *)malloc((n2+1)*sizeof(int));
  for(i = 0; i < n1; i++) {
    l[i] = a[left + i];
  }
  for(i = 0; i < n2; i++) {
    r[i] = a[mid + i];
  }
  l[n1] = SENTINEL;
  r[n2] = SENTINEL;
  i = 0;
  j = 0;
  for(k = left; k < right; k++) {
    if(l[i] <= r[j]) {
      a[k] = l[i];
      i = i + 1;
    }
    else {
      a[k] = r[j];
      j = j + 1;
    }
    cnt++;
  }
}

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