Find the median at every step in log(n) time while inserting random integers .

Median.java

import java.util.*;
import java.lang.Math;


public class Median
{
    
    public static void main(String args[])
    {
        long sum = 0;
        Scanner sc  = new Scanner(System.in);
        
        MaxHeap mxh = new MaxHeap();
        MinHeap mnh = new MinHeap();
        sum = sc.nextInt()
        mxh.insert((int)sum);
        while(sc.hasNextInt())
        {
            int a = sc.nextInt();
            
            if(a <= mxh.getMax())
              mxh.insert(a);
            else
              mnh.insert(a);
            
            int mn = mnh.size();
            int mx = mxh.size();
            
            if(mn != mx)
            {
                if(mn > mx)
                mxh.insert(mnh.delete(0));
                
                else if(mx - mn >= 2)
                mnh.insert(mxh.delete(0)); // n/2 th element of n is even
            }

            sum = sum+mxh.getMax(); //make sure the value is not exceeding limit
        }
        
        
        
        System.out.print(sum);
    }
}

class MaxHeap {
    ArrayList<Integer> ar = new ArrayList<>();
    int size = 0;
    
    int delete(int pos)
    {
        int temp = ar.get(pos);
        ar.set(pos,ar.get(ar.size()-1));
        ar.remove(ar.size()-1);
        heapify(pos);
        return temp;
    }
    
    boolean check()
    {
        int size = ar.size();
        while(--size > 0)
        {
            if(ar.get(size) > ar.get((int)Math.ceil((float)size/2-1)) )
            return false;
        }
        return true;
    }
    int getMax(){return ar.get(0);}
    
    int size()
    {
        return ar.size();
    }
    
    void insert(int val)
    {
        int i = ar.size();
        ar.add(val);
        int parent = i -1;
        while(parent > 0)
        {
            parent = (int)Math.ceil((float)i/2 - 1);
            if(ar.get(i) > ar.get(parent))
            {
                int temp = ar.get(parent);
                ar.set(parent,ar.get(i));
                ar.set(i,temp);
                i = parent;
            }
            else break;
        }
        heapify(i);
    }
    
    void heapify(int i)
    {

        int size = ar.size()/2;
        int parent=0;
        int lchild=0;
        int rchild = 0;
        while(i < size)
        {
            lchild = 2*i+1;
            rchild = 2*i+2;
            parent = i;
            
            if(rchild < ar.size() && ar.get(rchild) > ar.get(i))
            i = rchild;
            
            if(ar.get(lchild) > ar.get(i))
            i = lchild;
            
            if(i==parent)break;
            
            int temp = ar.get(parent);
            ar.set(parent,ar.get(i));
            ar.set(i,temp);
            
        }
    }
    
    void buildHeap()
    {
        int n = ar.size()/2;
        while(n > 0)
        {
            
            heapify(--n);
            
        }
    }
    
    
    void print()
    {
        for(int x : ar)
        System.out.print(x+"  ");
        System.out.println();
    }
    
    
}


class MinHeap {
    ArrayList<Integer> ar = new ArrayList<>();
    int size = 0;
    
    int delete(int pos)
    {
        int temp = ar.get(pos);
        ar.set(pos,ar.get(ar.size()-1));
        ar.remove(ar.size()-1);
        heapify(pos);
        return temp;
    }
    
    int size()
    {
        return ar.size();
    }
    
    int getMin(){return ar.get(0);}
    
    boolean check()
    {
        int size = ar.size();
        while(--size > 0)
        {
            if(ar.get(size) < ar.get((int)Math.ceil((float)size/2-1)) )
            return false;
        }
        return true;
    }
    
    void insert(int val)
    {
        int i = ar.size();
        ar.add(val);
        int parent = i -1;
        while(parent > 0)
        {
            parent = (int)Math.ceil((float)i/2 - 1);
            if(ar.get(i) < ar.get(parent))
            {
                int temp = ar.get(parent);
                ar.set(parent,ar.get(i));
                ar.set(i,temp);
                i = parent;
            }
            else break;
        }
        heapify(i);
    }
    
    void heapify(int i)
    {

        int size = ar.size()/2;
        int parent=0;
        int lchild=0;
        int rchild = 0;
        while(i < size)
        {
            lchild = 2*i+1;
            rchild = 2*i+2;
            parent = i;
            
            if(rchild < ar.size() && ar.get(rchild) < ar.get(i))
            i = rchild;
            
            if(ar.get(lchild) < ar.get(i))
            i = lchild;
            
            if(i==parent)break;
            
            int temp = ar.get(parent);
            ar.set(parent,ar.get(i));
            ar.set(i,temp);
            
        }
    }
    
    void buildHeap()
    {
        int n = ar.size()/2;
        while(n > 0)
        {
            
            heapify(--n);
            
        }
    }
    
    
    void print()
    {
        for(int x : ar)
        System.out.print(x+"  ");
        System.out.println();
    }
  
}

Please comment if you have any doubts(s).I can explain what the program is doing . I dont have time to comment at every step what is happening in the program