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 <math.h>


#define N 500000
#define SENTINEL 1000000000

int num,L[N/2+2],R[N/2+2];
int cnt=0;

void merge(int [],int,int,int);
void mergeSort(int [],int,int);

int main(){
    int i,j;
    int l,m,r;
    int A[N];

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

    mergeSort(A,0,num);
    for(i=0;i<num;i++){
        if(i) printf(" ");
        printf("%d",A[i]);
    }
    printf("\n");
    printf("%d\n",cnt);
    return 0;
}

void merge(int A[],int l,int m,int r){
    int n1,n2;
    int i,j,k;

    n1 = m-l;
    n2 = r-m;

    for(i=0;i<n1;i++){
        L[i] = A[l+i];
    }
    for(j=0;j<n2;j++){
        R[j] = A[m+j];
    }
    L[n1] = SENTINEL;
    R[n2] = SENTINEL;

    i=j=0;
    for(k=l;k<r;k++){
        cnt++;
        if(L[i] <= R[j]){
            A[k] = L[i];
            i++;
        }
        else{
            A[k] = R[j];
            j++;
        }
    }
}

void mergeSort(int A[],int l,int r){
    int mid;
    if(l+1<r){
        mid = (l+r)/2;
        mergeSort(A,l,mid);
        mergeSort(A,mid,r);
        merge(A,l,mid,r);
    }
}