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 INFTY 1000000000
int S[500000];

int merge(int A[500000],int left,int mid,int right){
    int n1,n2,i,j,k;
    n1=mid-left;
    n2=right-mid;
    int L[n1+1],R[n2+1];
    for(i=0;i<n1;i++)
        L[i]=A[left+i];
    for(i=0;i<n2;i++)
        R[i]=A[mid+i];
    L[n1]=INFTY;
    R[n2]=INFTY;
    i=0;
    j=0;
    for(k=left;k<right;k++){
        if(L[i]<=R[j]){
            A[k]=L[i];
            i+=1;
        }else{
            A[k]=R[j];
            j+=1;
        }
    }
    return i+j;
}

int mergeSort(int A[500000],int left,int right){
    int mid,sum=0;
    if(left+1<right){
        mid=(left+right)/2;
        sum+=mergeSort(A,left,mid);
        sum+=mergeSort(A,mid,right);
        sum+=merge(A,left,mid,right);
    }
    return sum;
}

int main(){
    int i,n,sum;
    scanf("%d",&n);
    for(i=0;i<n;i++){
        scanf("%d",&S[i]);
    }
    sum=mergeSort(S,0,n);
    for(i=0;i<n-1;i++)
        printf("%d ",S[i]);
    printf("%d\n%d\n",S[n-1],sum);
    
    return 0;
}