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: Wrong Answer)

#include<stdio.h>

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

int count=0;

int main()
{
  int i;
  int S[500000], n;

  scanf("%d", &n);

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

  mergeSort(S, 0, n);

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

  return 0;
}

void merge(int *S, int left, int mid, int right)
{

  int i, j, k, l;
  int L[mid - left], R[right - mid];

  for(i = 0; i <= mid-left-1; i++) L[i] = S[left + i];
  for(i = 0; i <= right-mid-1; i++) R[i] = S[mid + i];

  L[mid - left] = 1000000;
  R[right - mid] = 1000000;
  i = j = 0;

  for(k = left; k <= right-1; k++){
    if(L[i] <= R[j]){
      S[k] = L[i];
      i++;
    }
    else{
      S[k] = R[j];
      j++;
    }
    count++;
  }
}

void mergeSort(int *S, int left, int right)
{

  int mid;

  if(left+1 < right){
    mid = (left + right)/2;
    mergeSort(S, left, mid);
    mergeSort(S, mid, right);
    merge(S, left, mid, right);
  }
}