[Leetcode] 1232. Check If It Is a Straight Line (Easy)

概述

題目

https://leetcode.com/problems/check-if-it-is-a-straight-line/
給予數個點，確認此些點是否都在同一直線上

心得

應該也是滿直覺的數學題，透過平面座標求兩點求直線，再看餘下點是否都經過此線即可，唯一需注意除數為 0 的狀況

Math

思路

取兩點求直線，餘下點帶入後等式成立則同直線、否則非直線

程式

class Solution(object):
    def checkStraightLine(self, coordinates):
        """
        :type coordinates: List[List[int]]
        :rtype: bool
        """
        n = len(coordinates)
        if n < 3:
            return True

        x0, y0 = coordinates[0]
        x1, y1 = coordinates[1]

        # 先確認水平線之狀況
        if y1 == y0:
            for i in range(n):
                x, y = coordinates[i]
                if y != y0:
                    return False

        # 餘下的情況
        else:
            for i in range(2, n):
                x, y = coordinates[i]
                if y-y0 != 0:
                    if (x1-x0)/(y1-y0) != (x-x0)/(y-y0):
                        return False
                else:
                    return False
        return True

除數有可能是零的狀況，則轉換 a/b vs c/d => a*d vs c*b

class Solution(object):
    def checkStraightLine(self, coordinates):
        """
        :type coordinates: List[List[int]]
        :rtype: bool
        """
        n = len(coordinates)
        if n < 3:
            return True

        x0, y0 = coordinates[0]
        x1, y1 = coordinates[1]

        dx = x1-x0
        dy = y1-y0

        for x, y in coordinates:
            if dx * (y-y1) != dy * (x-x1):
                return False
        return True