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>
#include <limits.h>

int merge(int *A, int left, int mid, int right){
	int i, j, k, c = 0, n1 = mid-left, n2 = right-mid;
	int L[n1+1], R[n2+1];

	for(i = 0; i < n1; i++)
		L[i] = A[left+i];
	L[n1] = INT_MAX;
	for(i = 0; i < n2; i++)
		R[i] = A[mid+i];
	R[n2] = INT_MAX;

	i = 0;
	j = 0;
	for(k = left; k < right; k++){
		c++;
		if(L[i] <= R[j]){
			A[k] = L[i];
			i++;
		}
		else{
			A[k] = R[j];
			j++;
		}
	}
	return c;
}

int mergeSort(int *A, int left, int right){
	static int c = 0;
	int mid;

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

int main(){
	int n, i, c;
	int *A;

	scanf("%d", &n);
	A = (int *)malloc(sizeof(int) * n);
	for(i = 0; i < n; i++)
		scanf("%d", &A[i]);

	c = mergeSort(A, 0, n);

	for(i = 0; i < n; i++){
		printf("%d", A[i]);
		if(i < n-1)
			printf(" ");
		else
			printf("\n");
	}
	printf("%d\n", c);

	free(A);
	return 0;
}