1232. Patches into lines (mathematical straight line problems)

LeetCode: 1232. Dotted into a line

Ideas provided: Interview Question 16.14. Best straight line (mathematical vector collinear)

Ideas:

1. First move to the origin according to the first point, so that the straight line becomes a straight line passing through the origin. (Straight line general equation Ax + By + C == 0)
2. The method of vector collinearity
   2.1 Three points collinear: Two points (x1, y1) (x2, y2) minus the third point (x0, y0) respectively, if $x1\ast y2==x2\ast y1$ is the three points collinear.

AC Code straight line general equation

class Solution {
    
    
    public boolean checkStraightLine(int[][] cd) {
    
    
        // 把直线变成过原点的 -> 查看后面点的 b 是不是为 0， 不是 0 的话就返回 false
        int len = cd.length;
        int a = cd[0][0], b = cd[0][1];
        int x0 = cd[1][0] - a, y0 = cd[1][1] - b;
        // 移动
        for(int i = 2; i < len; i++) {
    
    
            cd[i][0] -= a;
            cd[i][1] -= b;
            // 直线的一般方程： Ax + By + C = 0 >> 过原点 C == 0
            // 然后代入 x0 and y0 --> 得 A = y0, B = -x0
            if(y0 * cd[i][0] + -x0 * cd[i][1] != 0) return false;
        }
        
        return true;
    }
}

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AC Code vector collinear method

class Solution {
    
    
    public boolean checkStraightLine(int[][] cd) {
    
    
        int len = cd.length;
        int x0 = cd[1][0] - cd[0][0];
        int y0 = cd[1][1] - cd[0][1];
        for(int i = 2; i < len; i++) {
    
    
            int x1 = cd[i][0] - cd[0][0];
            int y1 = cd[i][1] - cd[0][1];
            if(x0 * y1 != y0 * x1) return false;
        }

        return true;
    }
}