chore(CPlusPlus): add min-heap (#343)

algorithms/CPlusPlus/README.md

@@ -69,6 +69,7 @@
 6. [In order morris traversal](Trees/in-order-morris-traversal.cpp)
 7. [In order Predecessor and Successor](Trees/in-order-predecessor-and-successor.cpp)
 8. [Avl Tree](Trees/avl.cpp)
+9. [Min Heap](Trees/min-heap.cpp)
 
 # Maths
 1. [Kaprekar Number](Maths/Kaprekar-number.cpp)

algorithms/CPlusPlus/Trees/min-heap.cpp

@@ -0,0 +1,138 @@
+/*
+ Implementation of the min-heap using an array.
+
+ Min-Heap is a Binary tree where each child nodes value is greater 
+ than that of their parent. It is used when you need quick access to 
+ the smallest number in the array.
+*/
+
+#include <iostream>
+
+class Heap{
+	public:
+		void insert(const int& data);
+		void removemin();
+		void print();
+		Heap();
+		~Heap();
+
+	private:
+		// size - number of elements in the array
+		// capacity - number of elements the array can store
+		int size, capacity;
+		int *items;
+
+		int parent(unsigned index) const;
+		int child(unsigned index) const;
+
+		void heapifyUP(unsigned index);
+		void heapifyDOWN(unsigned index);
+		void growArray();
+
+};
+
+Heap::~Heap(){
+	delete[] items;
+	items = nullptr;
+}
+
+Heap::Heap(): size(0), capacity(2){
+	items = new int[capacity + 1];
+}
+
+int Heap::parent(unsigned index) const{ return index/2; }
+
+void Heap::growArray(){
+	/**
+	  * Inorder to accommodate more numbers in the array
+	  * Allocate memory in the heap 
+	  * Double the size of the old array up to (capacity*2) + 1
+	  * Copy the elements of the previous array into the new array
+	  */
+
+	// Doubling the size of the array
+	int* new_Array = new int[(capacity * 2) + 1];
+	// Copying the elements of the old array to the new array
+	for(int i=1; i<=size; i++){ new_Array[i] = items[i]; }
+	// Doubling the capacity
+	capacity *= 2;
+	// delete the items inorder to avoid any memory leak
+	delete[] items;
+	// set items to point to new_Array
+	items = new_Array;
+}
+
+void Heap::insert(const int& data){
+	// if size == capacity it means the array is full and need to grow
+	if(size == capacity){ growArray(); }
+	items[++size] = data;
+	heapifyUP(size);
+}
+
+void Heap::heapifyUP(unsigned index){
+	if(index > 1){
+		if(items[index] < items[parent(index)]){
+			std::swap(items[index], items[parent(index)]);
+			heapifyUP(parent(index));
+		}
+	}
+}
+
+void Heap::removemin(){
+	std::swap(items[1], items[size--]);
+	heapifyDOWN(1);
+}
+
+int Heap::child(unsigned index) const{
+	unsigned left = index * 2;
+	unsigned right = (index * 2) + 1;
+
+	if(right > size){ return left; }
+	else if(items[left] <= items[right]){ return left; }
+	return right;
+}
+
+void Heap::heapifyDOWN(unsigned index){
+	int childindex = child(index);
+	if(index*2 <= size){
+		if(items[index] > items[childindex]){
+			std::swap(items[index], items[childindex]);
+			heapifyDOWN(childindex);
+		}
+	}
+}
+
+void Heap::print(){
+	for(int i=1; i<=size; i++){ std::cout << items[i] << " "; }
+	std::cout << std::endl;
+}
+
+
+int main(){
+	Heap heap;
+
+	heap.insert(4);
+	heap.insert(10);
+	heap.insert(2);
+	heap.insert(22);
+	heap.insert(45);
+	heap.insert(18);
+	heap.insert(-8);
+	heap.insert(95);
+	heap.insert(13);
+	heap.insert(42);
+
+	heap.removemin();
+	heap.removemin();
+
+	heap.print();
+	/*
+	Output: 4 10 18 13 42 22 45 95
+	
+	Time complexity to build the heap: O(n)
+	Time complexity to remove min: O(log(n))
+	Time complexity to remove all elements: O(n*log(n))
+	*/
+	return 0;
+
+}