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 N1 500000
#define N2 1000000000
            
int Merge(int S[], int, int, int);
int Merge_sort(int S[], int, int);
 
int sum=0;
 
 
 
int main(){
 
int S[N1];
int i, n;
 
scanf("%d",&n);
 
for(i = 0; i < n; i++){
scanf("%d",&S[i]);
}
 
Merge_sort(S, 0, n);
 
 
for(i = 0; i<n; i++){
printf("%d",S[i]);
 
if(i<n-1) printf(" ");
 
}
printf("\n%d\n",sum);
return 0;
 
}
 
int Merge(int S[], int left, int mid, int right){
 
int n1 = mid - left;
int n2 = right - mid;
int L[n1], R[n2];
int i, j, k;
 
for(i = 0; i < n1; i++){
L[i] = S[left + i];
}
 
for(i = 0; i < n2; i++){
R[i] = S[mid + i];
}
 
L[n1] = N2;
R[n2] = N2;
 
i=0;
j=0;
 
for(k=left; k < right; k++){
 
if(L[i] <= R[j]){
S[k] = L[i];
i++;
}
 
else {
S[k] = R[j];
j++;
}
sum++;
}
 
}
 
int Merge_sort(int S[], int left, int right){
 
int mid;
 
if(left + 1 < right){
 mid = (left + right)/2;
        Merge_sort(S,left,mid);
        Merge_sort(S,mid,right);
        Merge(S,left,mid,right);
}
 
}