Prerequisites: Introduction to Matplotlib, Merge Sort
Visualizing algorithms makes it easier to understand them by analyzing and comparing the number of operations that took place to compare and swap the elements. For this we will use matplotlib, to plot bar graphs to represent the elements of the array,
Approach:
- We will generate an array with random elements.
- The algorithm will be called on that array and yield statement will be used instead of a return statement for visualization purposes.
- We will yield the current states of the array after comparing and swapping. Hence the algorithm will return a generator object.
- Matplotlib animation will be used to visualize the comparing and swapping of the array.
- The array will be stored in a matplotlib bar container object (‘bar_rects’), where the size of each bar will be equal to the corresponding value of the element in the array.
- The inbuilt FuncAnimation method of matplotlib animation will pass the container and generator objects to the function used to create animation. Each frame of the animation corresponds to a single iteration of the generator.
- The animation function is repeatedly called will set the height of the rectangle equal to the value of the elements.
Below is the implementation of the above approach.
Python3
# import all the modules import matplotlib.pyplot as plt from matplotlib.animation import FuncAnimation from mpl_toolkits.mplot3d import axes3d import matplotlib as mp import numpy as np import random # function to recursively divide the arra def mergesort(A, start, end): if end <= start: return mid = start + ((end - start + 1) // 2) - 1 # yield from statements have been used to yield # the array from the functions yield from mergesort(A, start, mid) yield from mergesort(A, mid + 1, end) yield from merge(A, start, mid, end) # function to merge the array def merge(A, start, mid, end): merged = [] leftIdx = start rightIdx = mid + 1 while leftIdx <= mid and rightIdx <= end: if A[leftIdx] < A[rightIdx]: merged.append(A[leftIdx]) leftIdx += 1 else: merged.append(A[rightIdx]) rightIdx += 1 while leftIdx <= mid: merged.append(A[leftIdx]) leftIdx += 1 while rightIdx <= end: merged.append(A[rightIdx]) rightIdx += 1 for i in range(len(merged)): A[start + i] = merged[i] yield A # function to plot bars def showGraph(): # for random unique values n=20 a=[i for i in range(1, n+1)] random.shuffle(a) datasetName='Random' # generator object returned by the function generator = mergesort(a, 0, len(a)-1) algoName='Merge Sort' # style of the chart plt.style.use('fivethirtyeight') # set colors of the bars data_normalizer = mp.colors.Normalize() color_map = mp.colors.LinearSegmentedColormap( "my_map", { "red": [(0, 1.0, 1.0), (1.0, .5, .5)], "green": [(0, 0.5, 0.5), (1.0, 0, 0)], "blue": [(0, 0.50, 0.5), (1.0, 0, 0)] } ) fig, ax = plt.subplots() # bar container bar_rects = ax.bar(range(len(a)), a, align="edge", color=color_map(data_normalizer(range(n)))) # setting the limits of x and y axes ax.set_xlim(0, len(a)) ax.set_ylim(0, int(1.1*len(a))) ax.set_title("ALGORITHM : "+algoName+"\n"+"DATA SET : "+datasetName, fontdict={'fontsize': 13, 'fontweight': 'medium', 'color' : '#E4365D'}) # the text to be shown on the upper left # indicating the number of iterations # transform indicates the position with # relevance to the axes coordinates. text = ax.text(0.01, 0.95, "", transform=ax.transAxes, color="#E4365D") iteration = [0] def animate(A, rects, iteration): for rect, val in zip(rects, A): # setting the size of each bar equal # to the value of the elements rect.set_height(val) iteration[0] += 1 text.set_text("iterations : {}".format(iteration[0])) # call animate function repeatedly anim = FuncAnimation(fig, func=animate, fargs=(bar_rects, iteration), frames=generator, interval=50, repeat=False) plt.show() showGraph() |
Output:
