使用 Matplotlib 进行合并排序的 3D 可视化

通过分析和比较为比较和交换元素而发生的操作数量，可视化算法可以更容易地理解它们。算法的 3D 可视化不太常见，为此我们将使用 matplotlib 绘制条形图并对其进行动画处理以表示数组的元素。

方法 ：

1. 我们将生成一个包含随机元素的数组。
2. 该算法将在该数组上调用，并且出于可视化目的，将使用 yield 语句而不是 return 语句。
3. 在比较和交换之后，我们将产生数组的当前状态。因此该算法将返回一个生成器对象。
4. Matplotlib 动画将用于可视化数组的比较和交换。
5. 然后我们将绘制图形，它将返回一个 Poly3dCollection 对象，使用该对象将完成进一步的动画。

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()

输出 ：

对于数组大小 20