找到集合 P 中的所有 ”最大“ 点的集合

题目描述

P为给定的二维平面整数点集。定义 P 中某点x，如果x满足 P 中任意点都不在 x 的右上方区域内（横纵坐标都大于x），则称其为“最大的”。求出所有“最大的”点的集合。（所有点的横坐标和纵坐标都不重复, 坐标轴范围在[0, 1e9) 内）

如下图：实心点为满足条件的点的集合。请实现代码找到集合 P 中的所有 ”最大“ 点的集合并输出。

例子：

input:

5
1 2
5 3
4 6
7 5
9 0

output:

4 6
7 5
9 0

代码实现

#!/usr/bin/env python
# -*- encoding: utf-8 -*-

class MaxPointDraw:
    def __init__(self):
        self.xy = []
        self.max_x = 0
        self.max_y = 0

    def generateCoordinateCollection(self):
        number = int(input('please input a number(1 <= number <= 10000):'))
        for i in range(number):
            input_xy = input()
            x = int(input_xy.split(' ')[0])
            y = int(input_xy.split(' ')[1])
            if x > self.max_x:
                self.max_x = x
            if y > self.max_y:
                self.max_y = y
            self.xy.append([x, y])

    def checkIsMaxPoint(self, xy_args):
        x = xy_args[0]
        y = xy_args[1]
        for xy_list in self.xy:
            x_value = xy_list[0]
            y_value = xy_list[1]
            if x_value > x and y_value > y:
                return False
        return True
    
    def Output(self):
        print('--------------------')
        for xy_list in self.xy:
            x_value = xy_list[0]
            y_value = xy_list[1]
            if self.checkIsMaxPoint(xy_list):
                print(' '.join(['%s'%xy for xy in xy_list]))

if __name__ == "__main__":
    mpd = MaxPointDraw()
    mpd.generateCoordinateCollection()
    mpd.Output()

输出：

please input a number(1 <= number <= 10000):5
1 2
5 3
4 6
7 5
9 0
--------------------
4 6
7 5
9 0

拓展

使用matplotlib来展示效果，以及随机生成一个点集合：

#!/usr/bin/env python
# -*- encoding: utf-8 -*-
from random import randint
import matplotlib.pyplot as plt


class MaxPointDraw:
    def __init__(self):
        self.xy = []
        self.max_x = 0
        self.max_y = 0
    # generate CoordinateCollection
    def generateCoordinateCollection(self):
        number = int(input('please input a number(1 <= number <= 10000):'))
        for i in range(number):
            x = randint(0, number)
            y = randint(0, number)
            if x > self.max_x:
                self.max_x = x
            if y > self.max_y:
                self.max_y = y
            self.xy.append([x, y])

    # check the point is Max or not
    def checkIsMaxPoint(self, xy_args):
        x = xy_args[0]
        y = xy_args[1]
        for xy_list in self.xy:
            x_value = xy_list[0]
            y_value = xy_list[1]
            if x_value > x and y_value > y:
                return False
        return True
    # show the MaxPoint result
    def DrawPaint(self):
        fig = plt.figure()
        ax = fig.add_subplot(111)
        ax.set(xlim=[0, self.max_x+self.max_x//2], ylim=[0, self.max_y+self.max_y//2], title='Max Point Set',
               ylabel='Y-Axis', xlabel='X-Axis')
        for xy_list in self.xy:
            x_value = xy_list[0]
            y_value = xy_list[1]
            if self.checkIsMaxPoint(xy_list):
                plt.scatter([x_value], [y_value], color='red')
            else:
                plt.scatter([x_value], [y_value], color='blue')
        plt.show()


if __name__ == "__main__":
    mpd = MaxPointDraw()
    mpd.generateCoordinateCollection()
    mpd.DrawPaint()

input1:

please input a number(1 <= number <= 10000):10

result1:

input2:

please input a number(1 <= number <= 10000):50

output2:

效果就是上面的样子，复制代码后运行前需要pip install matplotlib 不然会找不到这个包。