Heap data structure is mainly used to represent a priority queue. In Python, it is available using “**heapq**” module. The property of this data structure in python is that each time the **smallest of heap element is popped(min heap)**. Whenever elements are pushed or popped, **heap structure in maintained**. The heap[0] element also returns the smallest element each time.

**Operations on heap :**

**1. heapify(iterable)** :- This function is used to** convert the iterable into a heap** data structure. i.e. in heap order.

**2. heappush(heap, ele)** :- This function is used to **insert the element** mentioned in its arguments into heap. The** order is adjusted**, so as **heap structure is maintained**.

**3. heappop(heap)** :- This function is used to **remove and return the smallest element** from heap. The** order is adjusted**, so as **heap structure is maintained**.

# Python code to demonstrate working of # heapify(), heappush() and heappop() # importing "heapq" to implement heap queue import heapq # initializing list li = [5, 7, 9, 1, 3] # using heapify to convert list into heap heapq.heapify(li) # printing created heap print ("The created heap is : ",end="") print (list(li)) # using heappush() to push elements into heap # pushes 4 heapq.heappush(li,4) # printing modified heap print ("The modified heap after push is : ",end="") print (list(li)) # using heappop() to pop smallest element print ("The popped and smallest element is : ",end="") print (heapq.heappop(li))

Output :

The created heap is : [1, 3, 9, 7, 5] The modified heap after push is : [1, 3, 4, 7, 5, 9] The popped and smallest element is : 1

**4. heappushpop(heap, ele) **:- This function **combines the functioning of both push and pop operations** in one statement, increasing efficiency. Heap order is maintained after this operation.

**5. heapreplace(heap, ele)** :- This function also inserts and pops element in one statement, but it is different from above function. In this, **element is first popped, then element is pushed.i.e, the value larger than the pushed value can be returned.**

# Python code to demonstrate working of # heappushpop() and heapreplce() # importing "heapq" to implement heap queue import heapq # initializing list 1 li1 = [5, 7, 9, 4, 3] # initializing list 2 li2 = [5, 7, 9, 4, 3] # using heapify() to convert list into heap heapq.heapify(li1) heapq.heapify(li2) # using heappushpop() to push and pop items simultaneously # pops 2 print ("The popped item using heappushpop() is : ",end="") print (heapq.heappushpop(li1, 2)) # using heapreplace() to push and pop items simultaneously # pops 3 print ("The popped item using heapreplace() is : ",end="") print (heapq.heapreplace(li2, 2))

Output :

The popped item using heappushpop() is : 2 The popped item using heapreplace() is : 3

**6. nlargest(k, iterable, key = fun) **:- This function is used to** return the k largest elements from the iterable specified and satisfying the key if mentioned.**

**7. nsmallest(k, iterable, key = fun) **:- This function is used to** return the k smallest elements from the iterable specified and satisfying the key if mentioned.**

# Python code to demonstrate working of # nlargest() and nsmallest() # importing "heapq" to implement heap queue import heapq # initializing list li1 = [6, 7, 9, 4, 3, 5, 8, 10, 1] # using heapify() to convert list into heap heapq.heapify(li1) # using nlargest to print 3 largest numbers # prints 10, 9 and 8 print("The 3 largest numbers in list are : ",end="") print(heapq.nlargest(3, li1)) # using nsmallest to print 3 smallest numbers # prints 1, 3 and 4 print("The 3 smallest numbers in list are : ",end="") print(heapq.nsmallest(3, li1))

Output :

The 3 largest numbers in list are : [10, 9, 8] The 3 smallest numbers in list are : [1, 3, 4]

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