LeetCode 1037. Effective boomerang (vector cross product)

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subject

• 1037. Effective boomerang

solution ： Vector cross product

「 The three points are different and not in a straight line 」 Equivalent to 「 The cross product of two vectors is not zero 」：
$${\vec{v}}_1\times {\vec{v}}_2\ne 0$$

The cross product of two vectors equals zero , Then they are parallel

Algorithm flow ：

• from points[0] and points[1] Calculate the vector ${\vec{v}}_1$, from points[0] and points[2] Calculate the vector ${\vec{v}}_2$
• Calculating the cross product of two vectors

class Solution {
    
    public boolean isBoomerang(int[][] points) {
    
        int[] v1 = {
    points[0][0] - points[1][0], points[0][1] - points[1][1]};
        int[] v2 = {
    points[0][0] - points[2][0], points[0][1] - points[2][1]};

        return v1[0] * v2[1] != v1[1] * v2[0];
    }
}

• Time complexity ：$O(1)$
• Spatial complexity ：$O(1)$

Reference

• Effective boomerang