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 MAX 500000
#define SENTINEL 2000000000
int L[MAX/2+2], R[MAX/2+2];
int cnt;
void merge(int A[],int n,int left,int mid,int right){
    int n1 = mid - left;
    int n2 = right - mid;
    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] = R[n2] = SENTINEL;
    i = j = 0;
    for(k = left;k < right;k++){
        cnt++;
        if(L[i] <= R[j]){
            A[k] = L[i++];
        }
        else{
            A[k] =R[j++]; 
        }
    }
    
}

void mergeSort(int A[],int n,int left,int right){
    if((left + 1) < right){
        int mid = (left + right) / 2;
        mergeSort(A,n,left,mid);
        mergeSort(A,n,mid,right);
        merge(A,n,left,mid,right);
    }
}
int main(void){
    int A[MAX],n,i;
    cnt = 0;
    scanf("%d",&n);
    for(i=0;i<n;i++) scanf("%d",&A[i]);
    mergeSort(A,n,0,n);
    for(i=0;i<n;i++){
        if(i>=1) printf(" ");
        printf("%d",A[i]);
    }
    printf("\n");
    printf("%d\n",cnt);
    return 0;
}