【leetcode】1232. Check If It Is a Straight Line

题目如下：

You are given an array coordinates, coordinates[i] = [x, y], where [x, y] represents the coordinate of a point. Check if these points make a straight line in the XY plane.

Example 1:

Input: coordinates = [[1,2],[2,3],[3,4],[4,5],[5,6],[6,7]]
Output: true

Example 2:

Input: coordinates = [[1,1],[2,2],[3,4],[4,5],[5,6],[7,7]]
Output: false

Constraints:

• 2 <= coordinates.length <= 1000
• coordinates[i].length == 2
• -10^4 <= coordinates[i][0], coordinates[i][1] <= 10^4
• coordinates contains no duplicate point.

解题思路：初中几何知识，任意取两个点，解出方程y = k*x + b，然后判断其余点是否满足方程。

代码如下：

class Solution(object):
    def checkStraightLine(self, coordinates):
        """
        :type coordinates: List[List[int]]
        :rtype: bool
        """
        x1,y1 = coordinates[0]
        x2,y2 = coordinates[1]
        k_numerator = (y1-y2)
        k_denominator = (x1-x2)
        if k_denominator == 0:
            k_denominator = 1
        b = y1 - k_numerator/k_denominator*x1

        for i in range(2,len(coordinates)):
            x,y = coordinates[i]
            if y != k_numerator/k_denominator*x + b:
                return False
        return True