3D Visualisation of Merge Sort using Matplotlib

Last Updated : 19 Jan, 2022

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. 3D visualization of algorithms is less common, for this we will use matplotlib to plot bar graphs and animate them 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 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.
We will then plot the graph, which will return an object of Poly3dCollection using which further animation will be done.

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

# merge sort function to divide the array
def mergesort(A, start, end):
    if end <= start:
        return

    mid = start + ((end - start + 1) // 2) - 1

    # yield from statement is used to 
    # yield the array from the merge function
    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 = int(input("enter array size\n"))
    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 = plt.figure()
    ax = fig.add_subplot(projection = '3d')

    # z values and positions of the bars 
    z = np.zeros(n)
    dx = np.ones(n)
    dy = np.ones(n)
    dz = [i for i in range(len(a))]

    # Poly3dCollection returned into variable rects
    rects = ax.bar3d(range(len(a)), a, z, dx, dy, dz, 
                     color = color_map(data_normalizer(range(n))))

    # setting and x and y limits equal to the length of the array
    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'})

    # text to plot on the chart
    text = ax.text2D(0.1, 0.95, "", horizontalalignment ='center', 
                     verticalalignment ='center',
                     transform = ax.transAxes, color ="#E4365D")
    iteration = [0]

    # animation function to be repeatedly called
    def animate(A, rects, iteration):

        # to clear the bars from the Poly3DCollection object
        ax.collections.clear()
        ax.bar3d(range(len(a)), A, z, dx, dy, dz, 
                 color = color_map(data_normalizer(range(n))))
        iteration[0] += 1
        text.set_text("iterations : {}".format(iteration[0]))
            
    # animate function is called here and the generator object is passed
    anim = FuncAnimation(fig, func = animate,
        fargs =(rects, iteration), frames = generator, interval = 50,
        repeat = False)
    plt.show()

showGraph()

Output :

For array size 20

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