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<limits.h>

int INF = 999999999;

int count;

void merge(int S[], int left, int mid, int right){
	int i=0, j=0;
	int n1 = mid-left;
	int n2 = right - mid;
	int L[n1], R[n2];
	for(i=0; i<n1; i++){
		L[i] = S[left + i];
	}
	for(i=0; i<n2; i++){
		R[i] = S[mid + i];
	}
	L[n1] = INF;
	R[n2] = INF;
	i=0; j=0;
	for(int k=left; k<right; k++){
		count++;
		if(L[i]<=R[j]){
			S[k] = L[i];
			i++;
		}
		else{
			S[k] = R[j];
			j++;
		}
	}
}

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

int main(void){
	int n, i, S[500000];
	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[i]);
	printf("%d\n", count);
	return 0;
}