diff options
Diffstat (limited to 'max_points_line.rs')
-rw-r--r-- | max_points_line.rs | 91 |
1 files changed, 0 insertions, 91 deletions
diff --git a/max_points_line.rs b/max_points_line.rs deleted file mode 100644 index ee9c03d..0000000 --- a/max_points_line.rs +++ /dev/null @@ -1,91 +0,0 @@ -use std::collections::HashMap; -struct Solution; - -/* -* 'Line' is represented as y = m * x + c -* m & c are rational numbers because of integer coordinates, -* but in general floating point numbers can be insufficient to -* guarantee uniqueness as they are still finite precision. -* so for most real irl cases we use numerator and denominator -* to represent m & c. decimal precision!!! -* if m -> +- infinity then use x-int to identify line -* if m == 0 then use y-int to identify line -*/ -#[derive(Debug, Clone, Copy, PartialEq, Eq, Hash)] -enum Line { - Inf(i32), //x-int - MC((i32, i32), (i32, i32)), //numerator, denominator tuples for m & c - Zero(i32) //y-int -} - -impl Solution { - pub fn max_points(points: Vec<Vec<i32>>) -> i32 { - if points.len() == 1 { - return 1; - } - //y - y0 = (y1 - y0) / (x1 - x0) * (x - x0) - //y = dy / dx x + (dx * y0 - dy * x0) / dx - let mut fm: HashMap<Line, i32> = HashMap::new(); - points.iter().enumerate().flat_map(|(i, pt1)| { - points.iter().skip(i + 1).map(move |pt2| { - //swap points arounto make sure dy >= 0 since we are storing - //fraction numerator & denominator separately. - let (x0, y0, x1, y1) = if pt2[1] > pt1[1] || (pt2[1] == pt1[1] && pt2[0] > pt2[1]) { - (pt1[0], pt1[1], pt2[0], pt2[1]) - } else { - (pt2[0], pt2[1], pt1[0], pt1[1]) - }; - let mut dy = y1 - y0; - let mut dx = x1 - x0; - let g = Self::gcd(dy.abs(), dx.abs()); - if g != 0 { - dy /= g; - dx /= g; - } - if dx != 0 && dy != 0 { - /* - * slope is non-zero and finite so consistent line representation - * can be achieved using numerator & denominator representation - * because we have already preprocessed dy & dx for sign consistency - * and removed gcd from dy & dx - */ - Line::MC((dy, dx), (dx * y0 - dy * x0, dx)) - } else if dx == 0 { - //x-int is enough to identify common lines - Line::Inf(x0) - } else { - //y-int is enough to identify common lines - Line::Zero(y0) - } - }) - }).for_each(|k| { - *fm.entry(k).or_insert(0) += 1; - }); - let n = fm.values().max().cloned().unwrap(); - /* - * if 'm' points lie on a line & all points have been processed pairwise - * then n = m * (m - 1) / 2 pairs of points would have matched to same - * line m^2 - m - 2 * n = 0 => m = (1 + sqrt(8 * n + 1)) / 2 - */ - (1 + (8f64 * n as f64 + 1f64).sqrt() as i32) / 2 - } - fn gcd(a: i32, b: i32) -> i32 { - if a == 0 || b == 0 { - return 0; - } - let (mut a, mut b) = (a, b); - while b > 0 { - let tmp = a % b; - a = b; - b = tmp; - } - a - } -} - -fn main() { - let points1 = vec![vec![1,1],vec![2,2],vec![3,3]]; - let points2 = vec![vec![1,1],vec![3,2],vec![5,3],vec![4,1],vec![2,3],vec![1,4]]; - println!("{}", Solution::max_points(points1)); //expect: 3 - println!("{}", Solution::max_points(points2)); //expect: 3 -} |