The below code comes from
https://www.geeksforgeeks.org/median-of-stream-of-integers-running-integers/
It's elegant except for the massive code duplication -- MaxHeap and MinHeap are copy-pastes of each other with only a single difference.
Any ideas?
My idea would probably be to make Heap a non-abstract class, and leave out
the inheritance. max and min heaps could then be distinguished by each
other by naming conventions rather than inheritance hierarchies.
Without using inheritance, and with just one non-abstract heap class, we write for example:
Heap *left = new Heap(&Greater);
Heap *right = new Heap(&Smaller);
This way code duplication can be completely avoided.
I'd be interested to hear others' opinions.
Thanks,
Paul
#include <iostream>
using namespace std;
// Heap capacity
#define MAX_HEAP_SIZE (128)
#define ARRAY_SIZE(a) sizeof(a)/sizeof(a[0])
//// Utility functions
// exchange a and b
inline
void Exch(int &a, int &b)
{
int aux = a;
a = b;
b = aux;
}
// Greater and Smaller are used as comparators
bool Greater(int a, int b)
{
return a > b;
}
bool Smaller(int a, int b)
{
return a < b;
}
int Average(int a, int b)
{
return (a + b) / 2;
}
// Signum function
// = 0 if a == b - heaps are balanced
// = -1 if a < b - left contains less elements than right
// = 1 if a > b - left contains more elements than right
int Signum(int a, int b)
{
if( a == b )
return 0;
return a < b ? -1 : 1;
}
// Heap implementation
// The functionality is embedded into
// Heap abstract class to avoid code duplication
class Heap
{
public:
// Initializes heap array and comparator required
// in heapification
Heap(int *b, bool (*c)(int, int)) : A(b), comp(c)
{
heapSize = -1;
}
// Frees up dynamic memory
virtual ~Heap()
{
if( A )
{
delete[] A;
}
}
// We need only these four interfaces of Heap ADT
virtual bool Insert(int e) = 0;
virtual int GetTop() = 0;
virtual int ExtractTop() = 0;
virtual int GetCount() = 0;
protected:
// We are also using location 0 of array
int left(int i)
{
return 2 * i + 1;
}
int right(int i)
{
return 2 * (i + 1);
}
int parent(int i)
{
if( i <= 0 )
{
return -1;
}
return (i - 1)/2;
}
// Heap array
int *A;
// Comparator
bool (*comp)(int, int);
// Heap size
int heapSize;
// Returns top element of heap data structure
int top(void)
{
int max = -1;
if( heapSize >= 0 )
{
max = A[0];
}
return max;
}
// Returns number of elements in heap
int count()
{
return heapSize + 1;
}
// Heapification
// Note that, for the current median tracing problem
// we need to heapify only towards root, always
void heapify(int i)
{
int p = parent(i);
// comp - differentiate MaxHeap and MinHeap
// percolates up
if( p >= 0 && comp(A[i], A[p]) )
{
Exch(A[i], A[p]);
heapify(p);
}
}
// Deletes root of heap
int deleteTop()
{
int del = -1;
if( heapSize > -1)
{
del = A[0];
Exch(A[0], A[heapSize]);
heapSize--;
heapify(parent(heapSize+1));
}
return del;
}
// Helper to insert key into Heap
bool insertHelper(int key)
{
bool ret = false;
if( heapSize < MAX_HEAP_SIZE )
{
ret = true;
heapSize++;
A[heapSize] = key;
heapify(heapSize);
}
return ret;
}
};
// Specilization of Heap to define MaxHeap
class MaxHeap : public Heap
{
private:
public:
MaxHeap() : Heap(new int[MAX_HEAP_SIZE], &Greater) { }
~MaxHeap() { }
// Wrapper to return root of Max Heap
int GetTop()
{
return top();
}
// Wrapper to delete and return root of Max Heap
int ExtractTop()
{
return deleteTop();
}
// Wrapper to return # elements of Max Heap
int GetCount()
{
return count();
}
// Wrapper to insert into Max Heap
bool Insert(int key)
{
return insertHelper(key);
}
};
// Specilization of Heap to define MinHeap
class MinHeap : public Heap
{
private:
public:
MinHeap() : Heap(new int[MAX_HEAP_SIZE], &Smaller) { }
~MinHeap() { }
// Wrapper to return root of Min Heap
int GetTop()
{
return top();
}
// Wrapper to delete and return root of Min Heap
int ExtractTop()
{
return deleteTop();
}
// Wrapper to return # elements of Min Heap
int GetCount()
{
return count();
}
// Wrapper to insert into Min Heap
bool Insert(int key)
{
return insertHelper(key);
}
};
// Function implementing algorithm to find median so far.
int getMedian(int e, int &m, Heap &l, Heap &r)
{
// Are heaps balanced? If yes, sig will be 0
int sig = Signum(l.GetCount(), r.GetCount());
switch(sig)
{
case 1: // There are more elements in left (max) heap
if( e < m ) // current element fits in left (max) heap
{
// Remore top element from left heap and
// insert into right heap
r.Insert(l.ExtractTop());
// current element fits in left (max) heap
l.Insert(e);
}
else
{
// current element fits in right (min) heap
r.Insert(e);
}
// Both heaps are balanced
m = Average(l.GetTop(), r.GetTop());
break;
case 0: // The left and right heaps contain same number of elements
if( e < m ) // current element fits in left (max) heap
{
l.Insert(e);
m = l.GetTop();
}
else
{
// current element fits in right (min) heap
r.Insert(e);
m = r.GetTop();
}
break;
case -1: // There are more elements in right (min) heap
if( e < m ) // current element fits in left (max) heap
{
l.Insert(e);
}
else
{
// Remove top element from right heap and
// insert into left heap
l.Insert(r.ExtractTop());
// current element fits in right (min) heap
r.Insert(e);
}
// Both heaps are balanced
m = Average(l.GetTop(), r.GetTop());
break;
}
// No need to return, m already updated
return m;
}
void printMedian(int A[], int size)
{
int m = 0; // effective median
Heap *left = new MaxHeap();
Heap *right = new MinHeap();
for(int i = 0; i < size; i++)
{
m = getMedian(A[i], m, *left, *right);
cout << m << endl;
}
// C++ more flexible, ensure no leaks
delete left;
delete right;
}
// Driver code
int main()
{
int A[] = {5, 15, 1, 3, 2, 8, 7, 9, 10, 6, 11, 4};
int size = ARRAY_SIZE(A);
// In lieu of A, we can also use data read from a stream
printMedian(A, size);
return 0;
}