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>
#include <stdlib.h>

#define SENTINEL (1<<30)

int Merge(int *A, int left, int mid, int right) {
  int cnt = 0;
  int i,j,k;
  int n1, n2;
  int *L, *R;
  n1 = mid - left;
  n2 = right - mid;
  L = malloc(sizeof(int)*(n1+1));
  R = malloc(sizeof(int)*(n2+1));
  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) {
    ++cnt;
    if(L[i] <= R[j]) {
      A[k] = L[i];
      i = i + 1;
    } else {
      A[k] = R[j];
      j = j + 1;
    }
  }
  free(L);
  free(R);
  return cnt;
}

int Merge_Sort(int *A, int left, int right) {
  int cnt = 0;
  int mid;
  if(left+1 < right) {
    mid = (left + right)/2;
    cnt += Merge_Sort(A, left, mid);
    cnt += Merge_Sort(A, mid, right);
    cnt += Merge(A, left, mid, right);
  }
  return cnt;
}

int main() {
  int i;
  int n, A[500000], cnt;
  scanf("%d", &n);
  for(i = 0; i < n; ++i) {
    scanf("%d", A+i);
  }
  cnt = Merge_Sort(A,0,n);
  for(i = 0; i < n; ++i) {
    printf(i ? " %d" : "%d", A[i]);
  }
  printf("\n%d\n", cnt);
  return 0;
}