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 <stdlib.h>
#include <memory.h>
  
#define SENTINEL (1000000001)
#define putChar(c) ; *p = (char)(c); ++p;
  
int c = 0;
int S[500000];
int L[250001];
int R[250001];
char str[5500010];
char *p = str;
  
int getNum(void) {
    int n = 0;
    while ((*p >= '0') && (*p <= '9')) {
        n = n * 10 + (int)(*p - '0');
        ++p;
    }
    ++p;
    return n;
}
  
void putNum(int n) {
    int d;
    if (n < 10) {
        putChar( '0' + n );
        return;
    }
    d = n / 10;
    if (d) putNum(d);
    putChar( '0' + (n % 10) );
}
  
void Merge(int A[], int left, int mid, int right) {
    int i = 0, j = 0, k = left;
    int n1 = mid - left;
    int n2 = right - mid;
    memcpy(L, A + left, n1 * sizeof(int));
    memcpy(R, A + mid, n2 * sizeof(int));
    L[n1] = R[n2] = SENTINEL;
    for (; k < right; ++k) {
        if (L[i] <= R[j]) {
            A[k] = L[i];
            ++i;
        } else {
            A[k] = R[j];
            ++j;
        }
    }
}
  
void MergeSort(int A[], int left, int right) {
    int mid;
    if (left + 1 < right) {
        mid = (left + right) >> 1;
        MergeSort(A, left, mid);
        MergeSort(A, mid, right);
        Merge(A, left, mid, right);
        c += right - left;
    }
}
  
int main(void) {
    register int i;
    int n;
      
    fread(str, 1, 5500000, stdin);
    n = getNum();
    for (i = 0; i < n; ++i) {
        S[i] = getNum();
    }
      
    MergeSort(S, 0, n);
      
    --n;
    p = str;
    for (i = 0; i < n; ++i) {
        putNum(S[i]);
        putChar( ' ' );
    }
    putNum(S[i]);
    putChar( '\n' );
      
    putNum(c);
    putChar( '\0' );
      
    puts(str);
  
    return 0;
}