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 <memory.h>

#define SENTINEL (1000000001)
#define putChar(c) ; *p = (c); ++p;

int c = 0;
int S[500000];
int L[250001];
int R[250001];
char str[5500010];
char *p = str;

static void Merge(int A[], int left, int mid, int right);
static void MergeSort(int A[], int left, int right);
static int getNum(void);
static void putNum(int n);

int main(void) {
	register int i;
	int n;
	
	fread(str, sizeof(char), 5500000, stdin);
	n = getNum();
	for (i = 0; i < n; ++i) {
		S[i] = getNum();
	}
	
	MergeSort(S, 0, n);
	
	--n;
	p = str;
	for (i = 0; i < n; ++i) {
		putNum(S[i]);
		putChar( ' ' );
	}
	putNum(S[i]);
	putChar( '\n' );
	
	putNum(c);
	putChar( '\0' );
	
	puts(str);

	return 0;
}

int getNum(void) {
	int n = 0;
	while ((*p >= '0') && (*p <= '9')) {
		n = n * 10 + (int)(*p - '0');
		++p;
	} 
	++p;
	return n;
}

void putNum(int n) {
	int d = n / 10;
	if (n < 10) {
		putChar( '0' + (char)n );
		return;
	}
	if (d) putNum(d);
	putChar( '0' + (char)(n % 10) );
}

void Merge(int A[], int left, int mid, int right) {
	int i, j, k;
	int n1 = mid - left;
	int n2 = right - mid;
	memcpy(L, A + left, n1 * sizeof(int));
	memcpy(R, A + mid, n2 * sizeof(int));
	L[n1] = R[n2] = SENTINEL;
	i = j = 0;
	for (k = left; k < right; ++k) {
		if (L[i] <= R[j]) {
			A[k] = L[i];
			++i;
		} else {
			A[k] = R[j];
			++j;
		}
	}
	c += k - left;
}

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);
	}
}