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 <iostream>
#include <cstdio>
#include <cstring>

using namespace std;

int n, count;
int *S;

inline void merge(int left, int mid, int right) {
//    printf("[merge] left = %d, mid = %d, right = %d\n",
//                    left,      mid,      right);
    int n1 = mid - left, n2 = right - mid;
    int *L = new int[n1 + 1], *R = new int[n2 + 1];
    memcpy(L, S + left, sizeof(int) * n1);
    memcpy(R, S + mid, sizeof(int) * n2);
    L[n1] = R[n2] = 1e9+1;      // sentinel 

    for (int i = 0, j = 0, k = left; k < right; ++k) {
        ++count;
        if (L[i] <= R[j]) {
            S[k] = L[i++];
        }
        else {
            S[k] = R[j++];
        }
    }
    delete[] L;
    delete[] R;
}

inline void merge_sort(int left, int right) {
    if (left + 1 < right) {
        int mid = (left + right) / 2;
//        printf("[merge_sort] left = %d, mid = %d, right = %d\n",
//                             left,      mid,      right);
        merge_sort(left, mid);
        merge_sort(mid, right);
        merge(left, mid, right);
    }
}

int main(void) {

    scanf("%d", &n);

    S = new int[n];
    for (int i = 0; i < n; ++i) {
        scanf("%d", S + i);
    }

    merge_sort(0, n);

    printf("%d", S[0]);
    for (int i = 1; i < n; ++i) {
        printf(" %d", S[i]);
    }
    printf("\n%d\n", count);

    delete[] S;

    return 0;
}