From e01517d7915a7d44575c4052a9cabfb39e2a70d5 Mon Sep 17 00:00:00 2001
From: koba-e964 <3303362+koba-e964@users.noreply.github.com>
Date: Tue, 19 Sep 2023 10:44:07 +0900
Subject: [PATCH] Add yukicoder/1385.rs yukicoder/2455.rs yukicoder/2477.rs

---
 comm/Complex.rs   |  12 +++--
 yukicoder/1385.rs | 113 +++++++++++++++++++++++++++++++++++++++++
 yukicoder/2455.rs |  64 ++++++++++++++++++++++++
 yukicoder/2477.rs | 125 ++++++++++++++++++++++++++++++++++++++++++++++
 4 files changed, 311 insertions(+), 3 deletions(-)
 create mode 100644 yukicoder/1385.rs
 create mode 100644 yukicoder/2455.rs
 create mode 100644 yukicoder/2477.rs

diff --git a/comm/Complex.rs b/comm/Complex.rs
index cc579e9e..42bac7f1 100644
--- a/comm/Complex.rs
+++ b/comm/Complex.rs
@@ -1,7 +1,8 @@
-/// Complex numbers.
-/// Verified by: ATC001-C (http://atc001.contest.atcoder.jp/submissions/1175487)
+// Complex numbers.
+// Verified by: ATC001-C (http://atc001.contest.atcoder.jp/submissions/1175487)
+//              yukicoder 1385 (https://yukicoder.me/submissions/914070)
 mod complex {
-    use std::ops::{Add, Sub, Mul};
+    use std::ops::{Add, Sub, Mul, Neg};
     #[derive(Clone, Copy, Debug)]
     pub struct Complex<T = f64> {
         pub x: T,
@@ -35,4 +36,9 @@ mod complex {
                       self.x * other.y + self.y * other.x)
         }
     }
+    impl<T: Copy + Neg<Output = T>> Complex<T> {
+        pub fn conj(self) -> Self {
+            Self::new(self.x, -self.y)
+        }
+    }
 } // complex
diff --git a/yukicoder/1385.rs b/yukicoder/1385.rs
new file mode 100644
index 00000000..1bd1f0f1
--- /dev/null
+++ b/yukicoder/1385.rs
@@ -0,0 +1,113 @@
+// https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8
+macro_rules! input {
+    ($($r:tt)*) => {
+        let stdin = std::io::stdin();
+        let mut bytes = std::io::Read::bytes(std::io::BufReader::new(stdin.lock()));
+        let mut next = move || -> String{
+            bytes.by_ref().map(|r|r.unwrap() as char)
+                .skip_while(|c|c.is_whitespace())
+                .take_while(|c|!c.is_whitespace())
+                .collect()
+        };
+        input_inner!{next, $($r)*}
+    };
+}
+
+macro_rules! input_inner {
+    ($next:expr) => {};
+    ($next:expr,) => {};
+    ($next:expr, $var:ident : $t:tt $($r:tt)*) => {
+        let $var = read_value!($next, $t);
+        input_inner!{$next $($r)*}
+    };
+}
+
+macro_rules! read_value {
+    ($next:expr, [ $t:tt ; $len:expr ]) => {
+        (0..$len).map(|_| read_value!($next, $t)).collect::<Vec<_>>()
+    };
+    ($next:expr, $t:ty) => ($next().parse::<$t>().expect("Parse error"));
+}
+
+/// Complex numbers.
+/// Verified by: ATC001-C (http://atc001.contest.atcoder.jp/submissions/1175487)
+mod complex {
+    use std::ops::{Add, Sub, Mul, Neg};
+    #[derive(Clone, Copy, Debug)]
+    pub struct Complex<T = f64> {
+        pub x: T,
+        pub y: T,
+    }
+    
+    impl<T> Complex<T> {
+        pub fn new(x: T, y: T) -> Self { Complex { x: x, y: y } }
+    }
+    impl<T> Add for Complex<T>
+        where T: Add<Output = T> {
+        type Output = Self;
+        fn add(self, other: Self) -> Self { 
+            Self::new(self.x + other.x, self.y + other.y)
+        }
+    }
+    impl<T> Sub for Complex<T>
+        where T: Sub<Output = T> {
+        type Output = Self;
+        fn sub(self, other: Self) -> Self {
+            Self::new(self.x - other.x, self.y - other.y)
+        }
+    }
+    impl<T: Copy> Mul for Complex<T>
+        where T: Add<Output = T> +
+              Sub<Output = T> +
+              Mul<Output = T> {
+        type Output = Self;
+        fn mul(self, other: Self) -> Self {
+            Self::new(self.x * other.x - self.y * other.y,
+                      self.x * other.y + self.y * other.x)
+        }
+    }
+    impl<T: Copy + Neg<Output = T>> Complex<T> {
+        pub fn conj(self) -> Self {
+            Self::new(self.x, -self.y)
+        }
+    }
+} // complex
+
+// https://yukicoder.me/problems/no/1385 (3)
+// 三角形の面積は 点の座標に関する線形関数 + 定数 として表せるので、累積和ができる。
+// 具体的には、複素数 a, b, c に対してこれらを頂点とする三角形の面積は |Im((b-c)conj(a-c))|/2 である。
+// 絶対値の中身は a, b, c が反時計回りに並んでいる時に正。
+// 点列を時計回りに a[0], ..., a[N-1] として、j < k < i のときの a = a[j], b = a[k], c = a[i] としたときの和を計算することにする。
+// p[i] = \sum_{j < k < i} conj(a[j])a[k] が計算できていれば、c = a[i] のときの Im 内部の和は
+// (p[i] - conj(a[i]) \sum_{j < i} ja[j] - a[i] \sum_{j<i}(i - j - 1)conj(a[j]) + |a|^2 i(i-1)/2) / 2 である。
+// これの計算のためには q[i] = \sum_{j < i} ja[j] と r[i] = \sum_{j < i} a[j] がわかっていればよく、
+// これらを使うと (p[i] - conj(a[i]) q[i] + a[i]conj(q[j]) - a[i](i-1)conj(r[i]) + |a|^2 i(i-1)/2) / 2 である。
+fn main() {
+    input! {
+        n: usize, l: f64,
+        t: [f64; n],
+    }
+    use complex::*;
+    let mut a = vec![Complex::new(0.0, 0.0); n];
+    for i in 0..n {
+        let angle = std::f64::consts::PI * t[i] * 2.0 / l;
+        a[i] = Complex::new(angle.cos(), angle.sin());
+    }
+    let mut p = vec![Complex::new(0.0, 0.0); n + 1];
+    let mut q = vec![Complex::new(0.0, 0.0); n + 1];
+    let mut r = vec![Complex::new(0.0, 0.0); n + 1];
+    for i in 0..n {
+        r[i + 1] = r[i] + a[i];
+        q[i + 1] = q[i] + a[i] * Complex::new(i as f64, 0.0);
+        if i > 0 {
+            p[i + 1] = p[i] + a[i] * r[i].conj();
+        }
+    }
+    let mut ans = Complex::new(0.0, 0.0);
+    for i in 0..n {
+        ans = ans + p[i] - a[i].conj() * q[i] + a[i] * q[i].conj()
+            - a[i] * r[i].conj() * Complex::new(i as f64 - 1.0, 0.0);
+    }
+    let nn = n as f64;
+    println!("{}", ans.y * 3.0 / nn / (nn - 1.0) / (nn - 2.0));
+}
diff --git a/yukicoder/2455.rs b/yukicoder/2455.rs
new file mode 100644
index 00000000..c7a661a2
--- /dev/null
+++ b/yukicoder/2455.rs
@@ -0,0 +1,64 @@
+use std::cmp::*;
+use std::io::Read;
+
+fn get_word() -> String {
+    let stdin = std::io::stdin();
+    let mut stdin=stdin.lock();
+    let mut u8b: [u8; 1] = [0];
+    loop {
+        let mut buf: Vec<u8> = Vec::with_capacity(16);
+        loop {
+            let res = stdin.read(&mut u8b);
+            if res.unwrap_or(0) == 0 || u8b[0] <= b' ' {
+                break;
+            } else {
+                buf.push(u8b[0]);
+            }
+        }
+        if buf.len() >= 1 {
+            let ret = String::from_utf8(buf).unwrap();
+            return ret;
+        }
+    }
+}
+
+fn get<T: std::str::FromStr>() -> T { get_word().parse().ok().unwrap() }
+
+// If p10 = 10^k, this function returns a k-digit number
+// that is obtained as floor(n * 10^?).
+fn pick_digits(mut n: i64, p10: i64) -> i64 {
+    if n < p10 / 10 {
+        while n < p10 / 10 {
+            n *= 10;
+        }
+        return n;
+    }
+    while n >= p10 {
+        n /= 10;
+    }
+    n
+}
+
+fn main() {
+    let t: i32 = get();
+    for _ in 0..t {
+        let n: i64 = get();
+        let k: i64 = get();
+        let mut p = 1;
+        while p <= n {
+            p *= 10;
+        }
+        let mut ans = 0;
+        while p > 1 {
+            p /= 10;
+            // [p, cur)
+            let cur = pick_digits(k, 10 * p);
+            let l = p;
+            let r = min(cur + 1, min(n + 1, if cur > k { cur } else { cur + 1 }));
+            if l < r {
+                ans += r - l;
+            }
+        }
+        println!("{}", ans);
+    }
+}
diff --git a/yukicoder/2477.rs b/yukicoder/2477.rs
new file mode 100644
index 00000000..69cf1c7a
--- /dev/null
+++ b/yukicoder/2477.rs
@@ -0,0 +1,125 @@
+use std::cmp::*;
+use std::collections::*;
+// https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8
+macro_rules! input {
+    ($($r:tt)*) => {
+        let stdin = std::io::stdin();
+        let mut bytes = std::io::Read::bytes(std::io::BufReader::new(stdin.lock()));
+        let mut next = move || -> String{
+            bytes.by_ref().map(|r|r.unwrap() as char)
+                .skip_while(|c|c.is_whitespace())
+                .take_while(|c|!c.is_whitespace())
+                .collect()
+        };
+        input_inner!{next, $($r)*}
+    };
+}
+
+macro_rules! input_inner {
+    ($next:expr) => {};
+    ($next:expr,) => {};
+    ($next:expr, $var:ident : $t:tt $($r:tt)*) => {
+        let $var = read_value!($next, $t);
+        input_inner!{$next $($r)*}
+    };
+}
+
+macro_rules! read_value {
+    ($next:expr, ( $($t:tt),* )) => { ($(read_value!($next, $t)),*) };
+    ($next:expr, [ $t:tt ; $len:expr ]) => {
+        (0..$len).map(|_| read_value!($next, $t)).collect::<Vec<_>>()
+    };
+    ($next:expr, usize1) => (read_value!($next, usize) - 1);
+    ($next:expr, $t:ty) => ($next().parse::<$t>().expect("Parse error"));
+}
+
+fn divide_into_segment_ranges<F: FnMut(usize)>(n: usize, rng: std::ops::Range<usize>, mut f: F) {
+    assert!(n.is_power_of_two());
+    let (mut a, mut b) = (rng.start, rng.end);
+    a += n - 1;
+    b += n - 1;
+    while a < b {
+        if (a & 1) == 0 {
+            f(a);
+        }
+        if (b & 1) == 0 {
+            f(b - 1);
+        }
+        a = a / 2;
+        b = (b - 1) / 2;
+    }
+}
+
+// 範囲に辺を張りたいので、重み 0 の辺を使って ->->-> という流れを作ってそれの上に辺を張ることにする。
+// -> それだと (a, b) に対して複数の c がある場合にうまくいかないので、代わりにセグメント木を使う。
+// Tags: manual-segment-trees
+fn main() {
+    input! {
+        n: usize, m: usize,
+        uvw: [(usize1, usize1, i64); m],
+        k: usize,
+        abc: [(usize1, usize1, usize1); k],
+    }
+    let mut g = vec![vec![]; n];
+    for &(u, v, w) in &uvw {
+        g[u].push((v, w));
+    }
+    let mut offset = vec![0; n + 1];
+    for i in 0..n {
+        g[i].sort();
+        offset[i + 1] = offset[i] + g[i].len();
+    }
+    let mut map = vec![HashMap::new(); n];
+    for &(a, b, c) in &abc {
+        if let Ok(idx) = g[b].binary_search_by_key(&c, |x| x.0) {
+            map[a].entry(b).or_insert(vec![]).push(idx);
+        }
+    }
+    for i in 0..n {
+        for e in map[i].values_mut() {
+            e.sort();
+        }
+    }
+    let m2 = m.next_power_of_two();
+    let mut sup = vec![vec![]; 2 * m2]; // segment tree
+    for i in 0..m2 - 1 {
+        sup[i].push((2 * i + 1, 0));
+        sup[i].push((2 * i + 2, 0));
+    }
+    for a in 0..n {
+        for i in 0..g[a].len() {
+            let (b, w) = g[a][i];
+            let idx = offset[a] + i;
+            if let Some(v) = map[a].get(&b) {
+                if !v.is_empty() {
+                    for i in 0..v.len() - 1 {
+                        divide_into_segment_ranges(m2, offset[b] + v[i] + 1..offset[b] + v[i + 1], |x| sup[m2 + idx - 1].push((x, w)));
+                    }
+                    divide_into_segment_ranges(m2, offset[b]..offset[b] + v[0], |x| sup[m2 + idx - 1].push((x, w)));
+                    divide_into_segment_ranges(m2, offset[b] + v[v.len() - 1] + 1..offset[b + 1], |x| sup[m2 + idx - 1].push((x, w)));
+                }
+            } else {
+                if b == n - 1 {
+                    sup[m2 - 1 + idx].push((2 * m2 - 1, w));
+                } else {
+                    divide_into_segment_ranges(m2, offset[b]..offset[b + 1], |x| sup[m2 + idx - 1].push((x, w)));
+                }
+            }
+        }
+    }
+    let mut que = BinaryHeap::new();
+    for i in 0..g[0].len() {
+        que.push((Reverse(0), m2 - 1 + i));
+    }
+    const INF: i64 = 1 << 50;
+    let mut dist = vec![INF; 2 * m2];
+    while let Some((Reverse(d), v)) = que.pop() {
+        if dist[v] <= d { continue; }
+        dist[v] = d;
+        for &(w, c) in &sup[v] {
+            que.push((Reverse(d + c), w));
+        }
+    }
+    let ans = dist[2 * m2 - 1];
+    println!("{}", if ans >= INF { -1 } else { ans });
+}