向量点积和向量叉积的对比：求解《1037. 有效的回旋镖》

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2022-06-08 17:53:39

向量点积和向量叉积的对比，求解《1037. 有效的回旋镖》

向量积和数量积的区别

平面向量叉积的计算

(x2 - x1) * (y3 - y1) - (x3 - x1) * (y2 - y1)
萨吕法则：x1y2 + x2y3 + x3y1 - x1y3 - x2y1 - x3y2

向量点积和叉积的对比

如上图所示

例题

1037. 有效的回旋镖

给定一个数组 points ，其中 points[i] = [xi, yi] 表示 X-Y 平面上的一个点，如果这些点构成一个回旋镖则返回 true 。
回旋镖定义为一组三个点，这些点各不相同且不在一条直线上。

答案

向量叉积

var isBoomerang = function(points) {  // (x2 - x1) * (y3 - y1) - (x3 - x1) * (y2 - y1)
  return (points[1][0] - points[0][0]) * (points[2][1] - points[0][1]) - (points[2][0] - points[0][0]) * (points[1][1] - points[0][1]) !== 0
};

function isBoomerang(points: number[][]): boolean { // 萨吕法则
  return (points[0][0] * points[1][1] + points[1][0] * points[2][1] + points[2][0] * points[0][1] - points[0][0] * points[2][1] - points[1][0] * points[0][1] - points[2][0] * points[1][1]) !== 0
};

func isBoomerang(points [][]int) bool {
  return (points[1][0] - points[0][0]) * (points[2][1] - points[0][1]) - (points[2][0] - points[0][0]) * (points[1][1] - points[0][1]) != 0
}

class Solution {
  function isBoomerang($points) {
    return ($points[0][0] * $points[1][1] + $points[1][0] * $points[2][1] + $points[2][0] * $points[0][1] - $points[0][0] * $points[2][1] - $points[1][0] * $points[0][1] - $points[2][0] * $points[1][1]) !== 0;
  }
}

class Solution {
  public boolean isBoomerang(int[][] points) {
    return (points[1][0] - points[0][0]) * (points[2][1] - points[0][1]) - (points[2][0] - points[0][0]) * (points[1][1] - points[0][1]) != 0;
  }
}

class Solution:
  def isBoomerang(self, points: List[List[int]]) -> bool:
    return (points[1][0] - points[0][0]) * (points[2][1] - points[0][1]) - (points[2][0] - points[0][0]) * (points[1][1] - points[0][1]) != 0

bool isBoomerang(int** points, int pointsSize, int* pointsColSize){
  return (points[1][0] - points[0][0]) * (points[2][1] - points[0][1]) - (points[2][0] - points[0][0]) * (points[1][1] - points[0][1]) != 0;
}

public class Solution {
  public bool IsBoomerang(int[][] points) {
    return (points[1][0] - points[0][0]) * (points[2][1] - points[0][1]) - (points[2][0] - points[0][0]) * (points[1][1] - points[0][1]) != 0;
  }
}

class Solution {
public:
  bool isBoomerang(vector<vector<int>>& points) {
    return (points[1][0] - points[0][0]) * (points[2][1] - points[0][1]) - (points[2][0] - points[0][0]) * (points[1][1] - points[0][1]) != 0;
  }
};

Shon

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