Skewed Sorting

Description

Farmer John has 2^N (1 <= N <= 10) cows, each conveniently labeled
with paint on her flank with a number in the range 1..2^N. They are
standing in a line in some random order. The first cow in line is
cow_1; the second cow in line is cow_2; and so on (1 <= cow_i <=
2^N). Of course, cow_1 is unlikely to carry the painted label 1.

He performs the following algorithm to put them in order.

    1. If there is more than one cow, then partition the cows into
       two equal-sized sub-groups. Sort the first sub-group using
       this algorithm and then sort the second sub-group, also using
       this algorithm.

    2. Consider the current set of cows to be sorted as an equal-length
       pair of (potentially huge) base 2^N numbers. If the second
       number is smaller than the first one, then swap all the
       elements of the second one with those elements of the first
       one.

The cows would like to know how much distance they cover while
moving around during this 'sorting' procedure.

Given the initial configuration of the cows, process the list
according to the algorithm above and then print out:

    * the sum of the total distances traveled by all cows and

    * the final configuration of the cows after this 'sorting'
      procedure.

By way of example, consider this line of 2^3=8 cows:

        8 5 2 3 4 7 1 6

First, Farmer John will sort each half of the line separately:

        8 5 2 3 | 4 7 1 6

Since each half still has more than one cow, Farmer John will sort
those halves separately; starting with the 'first' half:

        8 5 | 2 3

Partitioning again, FJ makes

        8 | 5      and        2 | 3

each of which can be sorted by second rule, ultimately yielding:

        5 | 8      and        2 | 3 (<--unchanged)

The distance traveled by each cow during the first subgroup's sort
is 1, so total_distance_moved becomes 2. The second half is already
sorted, so the total_distance_moved stays at 2. The new configuration
of this sub-group is:

        5 8 | 2 3

For step 2 of the algorithm on the subgroup above, we compare the
two sides lexicographically (5 8 vs. 2 3). Since the 2 comes before
5, we swap the two elements of the first half with the corresponding
elements of the second half, yielding:

        2 3 5 8

Each of the four cows moved two spaces in this swap, contributing
a total of 8 moves, so total_distance_moved becomes 10.

Consider the other half of the cows; we divide the list of four
into two sub-groups:

        4 7 | 1 6

Each pair (4, 7) and (1, 6) is already sorted.

Comparing (4 7) to (1 6), since 1 comes before 4, we must swap the
two sub-groups:

        1 6 4 7

which contributes a total of 8 more moves, bringing total_distanced_move
to 18.

After the operations above, the list looks like this (and it's time
for step 2 to be performed on the two groups of 4):

        2 3 5 8 | 1 6 4 7

Since 1 comes before 2, we must swap the halves, this yielding this
configuration:

        1 6 4 7 2 3 5 8

Since each of 8 cows moved four units, this contributes a total of
32 more moves, making total_distance_moved become 50

Therefore, the answer is 50 and 1 6 4 7 2 3 5 8.

Input

* Line 1: A single integer: N

* Lines 2..2^N + 1: Line i+1 contains a single integer: cow_i

Output

* Line 1: One integer, the total distance traveled by all the cows

* Lines 2..2^N + 1: Line i+1 will contain one integer: the ith cow in
        the final configuration

• Sample
  Input
• Raw

3
8
5
2
3
4
7
1
6

• Sample
  Output
• Raw

50
1
6
4
7
2
3
5
8

#include<iostream>
#include<cstdio>
#include<algorithm>
const int maxn=1025;
int a[maxn],b[maxn];
int ans,k;
void a_array(int a[],int begin,int mid,int end,int b[])
{
    k=0;
    if(a[begin]>a[mid+1]){
        ans+=(mid+1-begin)*(end-begin+1);
        for(int i=mid+1;i<=end;i++)
            b[k++]=a[i];
        for(int i=begin;i<=mid;i++)
            b[k++]=a[i];
    }
    else {
        for(int i=begin;i<=mid;i++)
            b[k++]=a[i];
        for(int i=mid+1;i<=end;i++)
            b[k++]=a[i];
    }
    for(int i=0;i<k;i++)
        a[begin+i]=b[i];
}
void a_sort (int a[],int begin,int end,int b[])
{
    int mid;
    if(begin<end){
        mid=(begin+end)/2;
    a_sort(a,begin,mid,b);
    a_sort(a, mid+1, end, b);
    a_array(a, begin, mid, end, b);
    }
}
int main ()
{
    int n,t=1;
    while(~scanf("%d",&n)){
        ans=0;t=1;t<<=n;
        for(int i=0;i<t;i++)
            scanf("%d",&a[i]);
        a_sort(a, 0, t-1, b);
        printf("%d\n",ans);
        for(int i=0;i<t;i++)
            printf("%d\n",a[i]);
    }
    return 0;
}