competitive_library/algorithm/
convex_hull_trick.rs

1// 線形で処理できるもの
2
3// 追加する直線の傾きが単調減少(増加)
4// 計算する最小値(最大値)の座標xが単調増加(減少)
5
6use std::collections::VecDeque;
7
8pub struct LinearFunction(i64, i64);
9
10pub struct ConvexHullTrick {
11    d: VecDeque<LinearFunction>,
12    f: fn(&LinearFunction, i64) -> i64,
13}
14fn f(f: &LinearFunction, x: i64) -> i64 {
15    f.0 * x + f.1
16}
17
18impl ConvexHullTrick {
19    pub fn new() -> Self {
20        ConvexHullTrick {
21            d: VecDeque::new(),
22            f,
23        }
24    }
25    pub fn from(f: fn(&LinearFunction, i64) -> i64) -> Self {
26        ConvexHullTrick {
27            d: VecDeque::new(),
28            f,
29        }
30    }
31    fn check(f1: &LinearFunction, f2: &LinearFunction, f3: &LinearFunction) -> bool {
32        (f2.0 - f1.0) * (f3.1 - f2.1) >= (f2.1 - f1.1) * (f3.0 - f2.0)
33    }
34
35    // a_{prev} >= a
36
37    pub fn add_line(&mut self, a: i64, b: i64) {
38        let f = LinearFunction(a, b);
39
40        while self.d.len() >= 2
41            && ConvexHullTrick::check(&self.d[self.d.len() - 2], &self.d[self.d.len() - 1], &f)
42        {
43            self.d.pop_back();
44        }
45        self.d.push_back(f);
46    }
47
48    // x_{prev} <= x
49    pub fn query(&mut self, x: i64) -> i64 {
50        while self.d.len() >= 2 && (self.f)(&(self.d)[0], x) >= (self.f)(&(self.d)[1], x) {
51            self.d.pop_front();
52        }
53        (self.f)(&(self.d)[0], x)
54    }
55}
56impl Default for ConvexHullTrick {
57    fn default() -> Self {
58        ConvexHullTrick::new()
59    }
60}
61
62#[cfg(test)]
63mod tests {
64    use super::*;
65    #[test]
66    fn test_cht() {
67        let mut cht = ConvexHullTrick::new();
68        for (a, b) in &[(2, 0), (1, 1), (0, -1), (-1, 0)] {
69            cht.add_line(*a, *b);
70        }
71        let ans: Vec<_> = (0..10).map(|i| cht.query(-5 + i)).collect();
72        assert_eq!(ans, [-10, -8, -6, -4, -2, -1, -1, -2, -3, -4]);
73    }
74}
competitive_library/algorithm/convex_hull_trick.rs

competitive_library/algorithm/
convex_hull_trick.rs
