Add an example for ABC168-E

qryxip · qryxip · commit 90e66d3d774c · 2020-05-19T00:20:11.000+09:00
diff --git a/examples/abc168-e.rs b/examples/abc168-e.rs
@@ -0,0 +1,130 @@
+// https://atcoder.jp/contests/abc168/tasks/abc168_e
+//
+// 以下のクレートを使用。
+// - `maplit`
+// - `num`
+//     - `num-rational`
+// - `proconio`
+
+use maplit::hashmap;
+use num::{rational::Ratio, One, Signed as _};
+use proconio::input;
+use std::{
+    fmt,
+    iter::Product,
+    ops::{Add, Mul, Sub},
+};
+
+fn main() {
+    // `proconio::input!`。
+    //
+    // https://docs.rs/proconio/0.3.6/proconio/macro.input.html
+    input! {
+        n: usize,
+        abs: [(i64, i64); n],
+    }
+
+    // 有理数として`num_rational::Ratio<i64>`を使う。
+    //
+    // https://docs.rs/num-rational/0.2.4/num_rational/struct.Ratio.html
+
+    let mut zeros = 0;
+    let mut horz = 0;
+    let mut vert = 0;
+    let mut others = hashmap!();
+
+    for (a, b) in abs {
+        match (a.signum(), b.signum()) {
+            (0, 0) => zeros += 1,
+            (1, 0) | (-1, 0) => horz += 1,
+            (0, 1) | (0, -1) => vert += 1,
+            _ => *others.entry(Ratio::new(a, b)).or_insert(0) += 1usize,
+        }
+    }
+
+    let ans = others
+        .iter()
+        .map(|(grad, &num1)| {
+            // `Ratio::recip`で逆元を得ることができる。
+            //
+            // https://docs.rs/num-rational/0.2.4/num_rational/struct.Ratio.html#method.recip
+            let num2 = *others.get(&-grad.recip()).unwrap_or(&0);
+            if grad.is_negative() && num2 > 0 {
+                Zp::unchecked(1)
+            } else {
+                xor_combinations(num1, num2)
+            }
+        })
+        .product::<Zp>()
+        * xor_combinations(horz, vert)
+        + Zp::unchecked(zeros)
+        - Zp::unchecked(1);
+    println!("{}", ans);
+}
+
+fn xor_combinations(a: usize, b: usize) -> Zp {
+    return pow2(a) + pow2(b) - Zp::unchecked(1);
+
+    fn pow2(exp: usize) -> Zp {
+        num::pow(Zp::unchecked(2), exp)
+    }
+}
+
+const P: usize = 1_000_000_007;
+
+#[derive(Clone, Copy, Debug)]
+struct Zp {
+    repr: usize,
+}
+
+impl Zp {
+    fn new(val: usize) -> Self {
+        Self { repr: val % P }
+    }
+
+    fn unchecked(repr: usize) -> Self {
+        Self { repr }
+    }
+}
+
+impl One for Zp {
+    fn one() -> Self {
+        Self::unchecked(1)
+    }
+}
+
+impl fmt::Display for Zp {
+    fn fmt(&self, fmt: &mut fmt::Formatter) -> fmt::Result {
+        fmt::Display::fmt(&self.repr, fmt)
+    }
+}
+
+impl Add for Zp {
+    type Output = Self;
+
+    fn add(self, rhs: Self) -> Self {
+        Self::new(self.repr + rhs.repr)
+    }
+}
+
+impl Sub for Zp {
+    type Output = Self;
+
+    fn sub(self, rhs: Self) -> Self {
+        Self::new(P + self.repr - rhs.repr)
+    }
+}
+
+impl Mul for Zp {
+    type Output = Self;
+
+    fn mul(self, rhs: Self) -> Self {
+        Self::new(self.repr * rhs.repr)
+    }
+}
+
+impl Product for Zp {
+    fn product<I: Iterator<Item = Self>>(iter: I) -> Self {
+        iter.fold(Self::unchecked(1), Mul::mul)
+    }
+}
diff --git a/test-examples.toml b/test-examples.toml
@@ -268,6 +268,13 @@ url = "https://atcoder.jp/contests/abc168/tasks/abc168_c"
 matching = { FloatOr = { abs = 1e-9, rel = 1e-9 } }
 meta = { using = ["num", "proconio"] }
 
+[examples.abc168-e]
+type = "Normal"
+name = "ABC168 - E - ∙ (Bullet)"
+url = "https://atcoder.jp/contests/abc168/tasks/abc168_e"
+matching = "Words"
+meta = { using = ["maplit", "num", "proconio"] }
+
 [examples.agc020-c]
 type = "Normal"
 name = "AGC020: C - Median Sum"
