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 N 500000
#define SENTINEL 1000000000
int count=0;
void Merge( int*, int, int, int );
void MergeSort( int*, int, int);

 int main(){
	 int i;
	 int n;
	 int S[N];
	 scanf("%d", &n);
	 for( i=0; i<n; i++ ){
		 scanf("%d", &S[i]);
	 }
	 MergeSort(S, 0, n);
	 for( i=0; i<n; i++ ){
		 printf("%d",S[i]);
		 if( i+1 != n) printf(" ");
	 }
	 printf("\n%d\n",count);
	 return 0;
 }
 void Merge( int *A, int left, int mid, int right ){
	 int n1 = mid-left;
	 int n2 = right-mid;
	 int L[n1];
	 int R[n2];
	 int i, j, k;
	 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++ ){
		 count++;
		 if( L[i] <= R[j] ){
			 A[k] = L[i];
			 i++;
		 }
		 else{
			 A[k] = R[j];
			 j++;
		 }
	 }
 }

 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);
	 }
 }