分治法（快包法）解決凸包問題，並使用matplotlib繪製凸包

這是算法設計課程學到分治法的一個作業，網上找了不少博客，但都沒咋看懂=_=（其實是因爲自己沒有認真去看），晚上吃過晚飯自己動手寫了寫，大約兩個小時後，它誕生了。

凸包的繪製是使用python中的matplotlib.pyplot庫實現的，也僅僅是爲了直觀和可視化，也爲了老師給更高的分數，誠然真正刷算法題還得是C++ or C

自己動動手，才發現真的很簡單，每次上方選面積最大的，下方選面積最小的畫線即可。

import random
import numpy
import matplotlib.pyplot as plt


def caculate(x1, y1, x2, y2, x3, y3):
    return x1 * y2 + x3 * y1 + x2 * y3 - x1 * y3 - x2 * y1 - x3 * y2


def findUpperMax(x1, y1, x2, y2, points):
    flag = False
    upperMax = 0
    upperx = uppery = 0
    for i in points:
        if i[0] == x1 and i[1] == y1 or i[0] == x2 and i[1] == y2:
            continue
        areaData = caculate(x1, y1, x2, y2, i[0], i[1])
        if areaData > 0:
            if areaData > upperMax:
                flag = True
                upperMax = areaData
                upperx = i[0]
                uppery = i[1]
    if flag == False:
        plt.plot([x1, x2], [y1, y2], color='r')
        plt.text(x1, y1 + 0.3, (x1, y1), ha='center', va='bottom', fontsize=10.5)
        plt.text(x2, y2 + 0.3, (x2, y2), ha='center', va='bottom', fontsize=10.5)
        return
    plt.plot([x1, upperx], [y1, uppery], color='k')
    plt.plot([x2, upperx], [y2, uppery], color='k')
    findUpperMax(x1, y1, upperx, uppery, points)
    findUpperMax(upperx, uppery, x2, y2, points)

def findBottomMin(x1, y1, x2, y2, points):
    flag = False
    lowerMax = 0
    lowerx = lowery = 0
    for i in points:
        if i[0] == x1 and i[1] == y1 or i[0] == x2 and i[1] == y2:
            continue
        areaData = caculate(x1, y1, x2, y2, i[0], i[1])
        if areaData < 0:
            if areaData < lowerMax:
                flag = True
                lowerMax = areaData
                lowerx = i[0]
                lowery = i[1]
    if flag == False:
        plt.plot([x1, x2], [y1, y2], color='r')
        plt.text(x1, y1 + 0.3, (x1, y1), ha='center', va='bottom', fontsize=10.5)
        plt.text(x2, y2 + 0.3, (x2, y2), ha='center', va='bottom', fontsize=10.5)
        return
    plt.plot([x1, lowerx], [y1, lowery], color='k')
    plt.plot([x2, lowerx], [y2, lowery], color='k')
    findBottomMin(x1, y1, lowerx, lowery, points)
    findBottomMin(lowerx, lowery, x2, y2, points)

#以下數值可以自行修改

pointsSize = 30  # 30個點
upper = 100  # 點的座標上限爲100
lower = -100  # 點的座標下限爲-100
xx = [random.randint(lower, upper) for i in range(pointsSize)]
yy = [random.randint(lower, upper) for i in range(pointsSize)]
points = []
for i in range(pointsSize):
    points.append([xx[i], yy[i]])
for i in range(0, pointsSize):
    plt.scatter(xx[i], yy[i], color='k', s=20)
points.sort(key=lambda x: (x[0], x[1]))
plt.plot([points[0][0], points[pointsSize - 1][0]], [points[0][1], points[pointsSize - 1][1]], color='k')
findUpperMax(points[0][0], points[0][1], points[pointsSize - 1][0], points[pointsSize - 1][1], points)
findBottomMin(points[0][0], points[0][1], points[pointsSize - 1][0], points[pointsSize - 1][1], points)
plt.show()

每次運行生成的點都在-100到+100之間，30個點，然後find answer

明天，一定解決最近對問題的分治法

^ ^另外，這是我第一篇用Markdown寫的筆記，紀念一hia hia hia hia~~~~

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