Question

1232. 缀点成线

English Version

题目描述

给定一个数组 coordinates ，其中 coordinates[i] = [x, y] ，

 [x, y] 表示横坐标为 x、纵坐标为 y 的点。请你来判断，这些点是否在该坐标系中属于同一条直线上。

 

示例 1：

输入：coordinates = [[1,2],[2,3],[3,4],[4,5],[5,6],[6,7]]
输出：true

示例 2：

输入：coordinates = [[1,1],[2,2],[3,4],[4,5],[5,6],[7,7]]
输出：false

 

提示：

• 2 <= coordinates.length <= 1000
• coordinates[i].length == 2
• -10^4 <= coordinates[i][0], coordinates[i][1] <= 10^4
• coordinates 中不含重复的点

解法

方法一：数学

时间复杂度 $O(n)$，其中 $n$ 表示 coordinates 数组的长度。空间复杂度 $O(1)$。

class Solution:
  def checkStraightLine(self, coordinates: List[List[int]]) -> bool:
    x1, y1 = coordinates[0]
    x2, y2 = coordinates[1]
    for x, y in coordinates[2:]:
      if (x - x1) * (y2 - y1) != (y - y1) * (x2 - x1):
        return False
    return True

class Solution {
  public boolean checkStraightLine(int[][] coordinates) {
    int x1 = coordinates[0][0], y1 = coordinates[0][1];
    int x2 = coordinates[1][0], y2 = coordinates[1][1];
    for (int i = 2; i < coordinates.length; ++i) {
      int x = coordinates[i][0], y = coordinates[i][1];
      if ((x - x1) * (y2 - y1) != (y - y1) * (x2 - x1)) {
        return false;
      }
    }
    return true;
  }
}

class Solution {
public:
  bool checkStraightLine(vector<vector<int>>& coordinates) {
    int x1 = coordinates[0][0], y1 = coordinates[0][1];
    int x2 = coordinates[1][0], y2 = coordinates[1][1];
    for (int i = 2; i < coordinates.size(); ++i) {
      int x = coordinates[i][0], y = coordinates[i][1];
      if ((x - x1) * (y2 - y1) != (y - y1) * (x2 - x1)) {
        return false;
      }
    }
    return true;
  }
};

func checkStraightLine(coordinates [][]int) bool {
  x1, y1 := coordinates[0][0], coordinates[0][1]
  x2, y2 := coordinates[1][0], coordinates[1][1]
  for i := 2; i < len(coordinates); i++ {
    x, y := coordinates[i][0], coordinates[i][1]
    if (x-x1)*(y2-y1) != (y-y1)*(x2-x1) {
      return false
    }
  }
  return true
}