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 SENTINEL 1000000010

int cnt = 0;

void Merge(int A[], int left, int mid, int right){
    int n1 = mid - left;
    int n2 = right - mid;
    int L[n1 + 1], R[n2 + 1];
    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 = j = 0;

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

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);
    }
}

int main(){
    int n, A[500000 + 10];
    int i, j;

    scanf("%d", &n);
    for(i=0; i<n; i++){
        scanf("%d", &A[i]);
    }

    MergeSort(A, 0, n);

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

}