Maximum and Minimum difference (greedy algorithm) - c++

Question

Problem:
You are given an array A ,of n elements.You have to remove exactly n/2 elements from an array and add it to another array B
(intially empty).Find the maximum and minimum values of difference
between these two arrays.The difference between those two arrays is
sum(abs(A[i]-B[i]).
The code only works if the size of the array(N) is even.
Can someone provide a solution which works when the size of array is odd as well.
#include <bits/stdc++.h>
using namespace std;
//This code only works for even number of elements
int main(){
int n;
cin>>n;
vector<int> a(n);
for(int i=0;i<n;i++){
cin>>a[i];
}
sort(a.begin(), a.end());
long long mn = 0,mx = 0;
for(int i=0;i<n/2;i++){
mx+=a[i+n/2]-a[i];
mn+=a[2*i+1]-a[2*i];
}
cout<<abs(mn)<<" "<<abs(mx)<<" ";
return 0;
}

Answer 1

For me, I like to split up the work to easily visualize where efficiencies can be made in the algorithm. The following is very similar to your solution, but works fine for both even and odd length vectors. The average runtime is O(nlogn) for sort with space complexity as O(n) for the vectors.
// Given two arrays of equal length, returns their "Difference", O(n) runtime
int ArrayDiff(vector<int> A, vector<int> B)
{
if (A.size() != B.size() || A.size() == 0) return -1;
int sum = 0;
for (int i = 0; i < A.size(); i++)
{
sum += abs(A[i] - B[i]);
}
return sum;
}
// Given a vector arr, find the max and min "Difference"
void PrintMaxAndMin(vector<int> arr)
{
int n = arr.size();
if (n <= 0) return;
vector<int> Amax, Amin, Bmax, Bmin {};
// for each iteration of removing n/2 elements, we find the max and min of the arrays
sort(arr.begin(), arr.end());
for (int i = 0; i < n/2; i++)
{
Amax.push_back(arr[i]);
Bmax.push_back(arr[n-i-1]);
Amin.push_back(arr[n-i-1]);
Bmin.push_back(arr[n-i-2]);
}
cout << ArrayDiff(Amax, Bmax) << " " << ArrayDiff(Amin, Bmin) << endl;
}
// Run the above functions on a vector of odd and even sizes
int main(){
vector<int> arr_even = { 4,3,2,1 };
cout << "Even Length Vector: ";
PrintMaxAndMin(arr_even);
vector<int> arr_odd = { 5,4,3,2,1 };
cout << "Odd Length Vector: ";
PrintMaxAndMin(arr_odd);
return 0;
}
Here's the working example: live example. Hope this helped.
Program output:
Program stdout
Even Length Vector: 4 2
Odd Length Vector: 6 2