Python Code for time Complexity plot of Heap Sort

Prerequisite : HeapSort

Heap sort is a comparison based sorting technique based on Binary Heap data structure. It is similar to selection sort where we first find the maximum element and place the maximum element at the end. We repeat the same process for remaining element.

We implement Heap Sort here, call it for different sized random lists, measure time taken for different sizes and generate a plot of input size vs time taken.

Python

# Python Code for Implementation and running time Algorithm
# Complexity plot of Heap Sort
# by Ashok Kajal
# This python code intends to implement Heap Sort Algorithm
# Plots its time Complexity on list of different sizes

# ---------------------Important Note -------------------
# numpy, time and matplotlib.pyplot are required to run this code
import time
from numpy.random import seed
from numpy.random import randint
import matplotlib.pyplot as plt


# find left child of node i
def left(i):
    return 2 * i + 1

# find right child of node i
def right(i):
    return 2 * i + 2

# calculate and return array size
def heapSize(A):
    return len(A)-1


# This function takes an array and Heapyfies
# the at node i
def MaxHeapify(A, i):
    # print("in heapy", i)
    l = left(i)
    r = right(i)

    # heapSize = len(A)
    # print("left", l, "Rightt", r, "Size", heapSize)
    if l<= heapSize(A) and A[l] > A[i] :
        largest = l
    else:
        largest = i
    if r<= heapSize(A) and A[r] > A[largest]:
        largest = r
    if largest != i:
       # print("Largest", largest)
        A[i], A[largest]= A[largest], A[i]
       # print("List", A)
        MaxHeapify(A, largest)

# this function makes a heapified array
def BuildMaxHeap(A):
    for i in range(int(heapSize(A)/2)-1, -1, -1):
        MaxHeapify(A, i)

# Sorting is done using heap of array
def HeapSort(A):
    BuildMaxHeap(A)
    B = list()
    heapSize1 = heapSize(A)
    for i in range(heapSize(A), 0, -1):
        A[0], A[i]= A[i], A[0]
        B.append(A[heapSize1])
        A = A[:-1]
        heapSize1 = heapSize1-1
        MaxHeapify(A, 0)


# randomly generates list of different
# sizes and call HeapSort function
elements = list()
times = list()
for i in range(1, 10):

    # generate some integers
    a = randint(0, 1000 * i, 1000 * i)
    # print(i)
    start = time.clock()
    HeapSort(a)
    end = time.clock()

    # print("Sorted list is ", a)
    print(len(a), "Elements Sorted by HeapSort in ", end-start)
    elements.append(len(a))
    times.append(end-start)

plt.xlabel('List Length')
plt.ylabel('Time Complexity')
plt.plot(elements, times, label ='Heap Sort')
plt.grid()
plt.legend()
plt.show()
# This code is contributed by Ashok Kajal

Output : 

Input : Unsorted Lists of Different sizes are Generated Randomly
Output :
1000 Elements Sorted by HeapSort in  0.023797415087301488
2000 Elements Sorted by HeapSort in  0.053856713614550245
3000 Elements Sorted by HeapSort in  0.08474737185133563
4000 Elements Sorted by HeapSort in  0.13578669978414837
5000 Elements Sorted by HeapSort in  0.1658182863213824
6000 Elements Sorted by HeapSort in  0.1875901601906662
7000 Elements Sorted by HeapSort in  0.21982946862249264
8000 Elements Sorted by HeapSort in  0.2724293921580738
9000 Elements Sorted by HeapSort in  0.30996323029421546

Complexity PLot for Heap Sort is Given  Below