Add yukicoder/2544.rs yukicoder/2545.rs yukicoder/2582.rs

koba-e964 · Dec 13, 2023 · 60b0eb1 · 60b0eb1
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diff --git a/yukicoder/2544.rs b/yukicoder/2544.rs
@@ -0,0 +1,172 @@
+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() }
+
+/// Verified by https://atcoder.jp/contests/abc198/submissions/21774342
+mod mod_int {
+    use std::ops::*;
+    pub trait Mod: Copy { fn m() -> i64; }
+    #[derive(Copy, Clone, Hash, PartialEq, Eq, PartialOrd, Ord)]
+    pub struct ModInt<M> { pub x: i64, phantom: ::std::marker::PhantomData<M> }
+    impl<M: Mod> ModInt<M> {
+        // x >= 0
+        pub fn new(x: i64) -> Self { ModInt::new_internal(x % M::m()) }
+        fn new_internal(x: i64) -> Self {
+            ModInt { x: x, phantom: ::std::marker::PhantomData }
+        }
+        pub fn pow(self, mut e: i64) -> Self {
+            debug_assert!(e >= 0);
+            let mut sum = ModInt::new_internal(1);
+            let mut cur = self;
+            while e > 0 {
+                if e % 2 != 0 { sum *= cur; }
+                cur *= cur;
+                e /= 2;
+            }
+            sum
+        }
+        #[allow(dead_code)]
+        pub fn inv(self) -> Self { self.pow(M::m() - 2) }
+    }
+    impl<M: Mod> Default for ModInt<M> {
+        fn default() -> Self { Self::new_internal(0) }
+    }
+    impl<M: Mod, T: Into<ModInt<M>>> Add<T> for ModInt<M> {
+        type Output = Self;
+        fn add(self, other: T) -> Self {
+            let other = other.into();
+            let mut sum = self.x + other.x;
+            if sum >= M::m() { sum -= M::m(); }
+            ModInt::new_internal(sum)
+        }
+    }
+    impl<M: Mod, T: Into<ModInt<M>>> Sub<T> for ModInt<M> {
+        type Output = Self;
+        fn sub(self, other: T) -> Self {
+            let other = other.into();
+            let mut sum = self.x - other.x;
+            if sum < 0 { sum += M::m(); }
+            ModInt::new_internal(sum)
+        }
+    }
+    impl<M: Mod, T: Into<ModInt<M>>> Mul<T> for ModInt<M> {
+        type Output = Self;
+        fn mul(self, other: T) -> Self { ModInt::new(self.x * other.into().x % M::m()) }
+    }
+    impl<M: Mod, T: Into<ModInt<M>>> AddAssign<T> for ModInt<M> {
+        fn add_assign(&mut self, other: T) { *self = *self + other; }
+    }
+    impl<M: Mod, T: Into<ModInt<M>>> SubAssign<T> for ModInt<M> {
+        fn sub_assign(&mut self, other: T) { *self = *self - other; }
+    }
+    impl<M: Mod, T: Into<ModInt<M>>> MulAssign<T> for ModInt<M> {
+        fn mul_assign(&mut self, other: T) { *self = *self * other; }
+    }
+    impl<M: Mod> Neg for ModInt<M> {
+        type Output = Self;
+        fn neg(self) -> Self { ModInt::new(0) - self }
+    }
+    impl<M> ::std::fmt::Display for ModInt<M> {
+        fn fmt(&self, f: &mut ::std::fmt::Formatter) -> ::std::fmt::Result {
+            self.x.fmt(f)
+        }
+    }
+    impl<M: Mod> ::std::fmt::Debug for ModInt<M> {
+        fn fmt(&self, f: &mut ::std::fmt::Formatter) -> ::std::fmt::Result {
+            let (mut a, mut b, _) = red(self.x, M::m());
+            if b < 0 {
+                a = -a;
+                b = -b;
+            }
+            write!(f, "{}/{}", a, b)
+        }
+    }
+    impl<M: Mod> From<i64> for ModInt<M> {
+        fn from(x: i64) -> Self { Self::new(x) }
+    }
+    // Finds the simplest fraction x/y congruent to r mod p.
+    // The return value (x, y, z) satisfies x = y * r + z * p.
+    fn red(r: i64, p: i64) -> (i64, i64, i64) {
+        if r.abs() <= 10000 {
+            return (r, 1, 0);
+        }
+        let mut nxt_r = p % r;
+        let mut q = p / r;
+        if 2 * nxt_r >= r {
+            nxt_r -= r;
+            q += 1;
+        }
+        if 2 * nxt_r <= -r {
+            nxt_r += r;
+            q -= 1;
+        }
+        let (x, z, y) = red(nxt_r, r);
+        (x, y - q * z, z)
+    }
+} // mod mod_int
+
+macro_rules! define_mod {
+    ($struct_name: ident, $modulo: expr) => {
+        #[derive(Copy, Clone, PartialEq, Eq, PartialOrd, Ord, Hash)]
+        pub struct $struct_name {}
+        impl mod_int::Mod for $struct_name { fn m() -> i64 { $modulo } }
+    }
+}
+const MOD: i64 = 998_244_353;
+define_mod!(P, MOD);
+type MInt = mod_int::ModInt<P>;
+
+// Depends on MInt.rs
+fn fact_init(w: usize) -> (Vec<MInt>, Vec<MInt>) {
+    let mut fac = vec![MInt::new(1); w];
+    let mut invfac = vec![0.into(); w];
+    for i in 1..w {
+        fac[i] = fac[i - 1] * i as i64;
+    }
+    invfac[w - 1] = fac[w - 1].inv();
+    for i in (0..w - 1).rev() {
+        invfac[i] = invfac[i + 1] * (i as i64 + 1);
+    }
+    (fac, invfac)
+}
+
+// https://yukicoder.me/problems/no/2544 (3.5)
+// L, R を固定した時の min の期待値は、x = R-L+1 <= N として C(N+1,x+1)/C(N,x) である。
+// - min >= i となる確率 (1 <= i <= N-x+1) は C(N+1-i,x)/C(N,x) であり、それの総和を取れば良い。
+// 1 <= x <= N であり、x ごとに (L,R) の組は N-x+1 通りある。
+// なので 1 クエリーの期待値は \sum xC(N+1,x+1)/C(N,x) / {N(N+1)/2} である。
+// 問題の答えは (期待値) * Q * (ありえるケースの個数) である。{N(N+1)/2} の指数は最終的に Q-1 乗になることに注意。
+fn main() {
+    let n: usize = get();
+    let q: i64 = get();
+    let (fac, invfac) = fact_init(n + 2);
+    let mut tot = MInt::new(0);
+    for x in 1..n + 1 {
+        tot += fac[n + 1] * invfac[x + 1] * invfac[n] * fac[x] * (n - x + 1) as i64;
+    }
+    let nn = n as i64;
+    let tri = nn * (nn + 1) / 2;
+    tot *= fac[n] * MInt::new(tri).pow(q - 1) * q;
+    println!("{}", tot);
+}
diff --git a/yukicoder/2545.rs b/yukicoder/2545.rs
@@ -0,0 +1,40 @@
+// https://yukicoder.me/problems/no/2545 (3.5)
+// https://nu50218.dev/posts/integer-division-by-multiplication/ の議論を使うことで、
+// (x * 0x5555_5556) >> 32 が答えであることがわかる。
+// x * 0x5555_5556 は常に 2^62 以下であるため問題ない。
+fn main() {
+    println!("67");
+
+    // A[4] = 5x
+    println!("plus 5 1 1");
+    println!("plus 5 5 5");
+    println!("plus 4 1 5");
+
+    // A[4] = 0x55 * x
+    println!("plus 5 4 4");
+    println!("plus 5 5 5");
+    println!("plus 5 5 5");
+    println!("plus 5 5 5");
+    println!("plus 4 4 5");
+
+    // A[4] = 0x5555 * x
+    println!("plus 5 4 4");
+    for _ in 1..8 {
+        println!("plus 5 5 5");
+    }
+    println!("plus 4 4 5");
+
+    // A[4] = 0x55555555 * x
+    println!("plus 5 4 4");
+    for _ in 1..16 {
+        println!("plus 5 5 5");
+    }
+    println!("plus 4 4 5");
+
+    // A[3] = 0x55555556 * x
+    println!("plus 3 4 1");
+
+    for _ in 0..32 {
+        println!("div 3 3");
+    }
+}
diff --git a/yukicoder/2582.rs b/yukicoder/2582.rs
@@ -0,0 +1,173 @@
+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() }
+
+/// Verified by https://atcoder.jp/contests/abc198/submissions/21774342
+mod mod_int {
+    use std::ops::*;
+    pub trait Mod: Copy { fn m() -> i64; }
+    #[derive(Copy, Clone, Hash, PartialEq, Eq, PartialOrd, Ord)]
+    pub struct ModInt<M> { pub x: i64, phantom: ::std::marker::PhantomData<M> }
+    impl<M: Mod> ModInt<M> {
+        // x >= 0
+        pub fn new(x: i64) -> Self { ModInt::new_internal(x % M::m()) }
+        fn new_internal(x: i64) -> Self {
+            ModInt { x: x, phantom: ::std::marker::PhantomData }
+        }
+        pub fn pow(self, mut e: i64) -> Self {
+            debug_assert!(e >= 0);
+            let mut sum = ModInt::new_internal(1);
+            let mut cur = self;
+            while e > 0 {
+                if e % 2 != 0 { sum *= cur; }
+                cur *= cur;
+                e /= 2;
+            }
+            sum
+        }
+        #[allow(dead_code)]
+        pub fn inv(self) -> Self { self.pow(M::m() - 2) }
+    }
+    impl<M: Mod> Default for ModInt<M> {
+        fn default() -> Self { Self::new_internal(0) }
+    }
+    impl<M: Mod, T: Into<ModInt<M>>> Add<T> for ModInt<M> {
+        type Output = Self;
+        fn add(self, other: T) -> Self {
+            let other = other.into();
+            let mut sum = self.x + other.x;
+            if sum >= M::m() { sum -= M::m(); }
+            ModInt::new_internal(sum)
+        }
+    }
+    impl<M: Mod, T: Into<ModInt<M>>> Sub<T> for ModInt<M> {
+        type Output = Self;
+        fn sub(self, other: T) -> Self {
+            let other = other.into();
+            let mut sum = self.x - other.x;
+            if sum < 0 { sum += M::m(); }
+            ModInt::new_internal(sum)
+        }
+    }
+    impl<M: Mod, T: Into<ModInt<M>>> Mul<T> for ModInt<M> {
+        type Output = Self;
+        fn mul(self, other: T) -> Self { ModInt::new(self.x * other.into().x % M::m()) }
+    }
+    impl<M: Mod, T: Into<ModInt<M>>> AddAssign<T> for ModInt<M> {
+        fn add_assign(&mut self, other: T) { *self = *self + other; }
+    }
+    impl<M: Mod, T: Into<ModInt<M>>> SubAssign<T> for ModInt<M> {
+        fn sub_assign(&mut self, other: T) { *self = *self - other; }
+    }
+    impl<M: Mod, T: Into<ModInt<M>>> MulAssign<T> for ModInt<M> {
+        fn mul_assign(&mut self, other: T) { *self = *self * other; }
+    }
+    impl<M: Mod> Neg for ModInt<M> {
+        type Output = Self;
+        fn neg(self) -> Self { ModInt::new(0) - self }
+    }
+    impl<M> ::std::fmt::Display for ModInt<M> {
+        fn fmt(&self, f: &mut ::std::fmt::Formatter) -> ::std::fmt::Result {
+            self.x.fmt(f)
+        }
+    }
+    impl<M: Mod> ::std::fmt::Debug for ModInt<M> {
+        fn fmt(&self, f: &mut ::std::fmt::Formatter) -> ::std::fmt::Result {
+            let (mut a, mut b, _) = red(self.x, M::m());
+            if b < 0 {
+                a = -a;
+                b = -b;
+            }
+            write!(f, "{}/{}", a, b)
+        }
+    }
+    impl<M: Mod> From<i64> for ModInt<M> {
+        fn from(x: i64) -> Self { Self::new(x) }
+    }
+    // Finds the simplest fraction x/y congruent to r mod p.
+    // The return value (x, y, z) satisfies x = y * r + z * p.
+    fn red(r: i64, p: i64) -> (i64, i64, i64) {
+        if r.abs() <= 10000 {
+            return (r, 1, 0);
+        }
+        let mut nxt_r = p % r;
+        let mut q = p / r;
+        if 2 * nxt_r >= r {
+            nxt_r -= r;
+            q += 1;
+        }
+        if 2 * nxt_r <= -r {
+            nxt_r += r;
+            q -= 1;
+        }
+        let (x, z, y) = red(nxt_r, r);
+        (x, y - q * z, z)
+    }
+} // mod mod_int
+
+macro_rules! define_mod {
+    ($struct_name: ident, $modulo: expr) => {
+        #[derive(Copy, Clone, PartialEq, Eq, PartialOrd, Ord, Hash)]
+        pub struct $struct_name {}
+        impl mod_int::Mod for $struct_name { fn m() -> i64 { $modulo } }
+    }
+}
+const MOD: i64 = 998_244_353;
+define_mod!(P, MOD);
+type MInt = mod_int::ModInt<P>;
+
+// Depends on MInt.rs
+fn fact_init(w: usize) -> (Vec<MInt>, Vec<MInt>) {
+    let mut fac = vec![MInt::new(1); w];
+    let mut invfac = vec![0.into(); w];
+    for i in 1..w {
+        fac[i] = fac[i - 1] * i as i64;
+    }
+    invfac[w - 1] = fac[w - 1].inv();
+    for i in (0..w - 1).rev() {
+        invfac[i] = invfac[i + 1] * (i as i64 + 1);
+    }
+    (fac, invfac)
+}
+
+// https://yukicoder.me/problems/no/2582 (3.5)
+// The author read the editorial before implementing this.
+// K = u_1 + ... + u_N の分割ごとに K!/N^K / (u_1+1)! / ... / (u_N + 1)! を足せばよい。
+// これは [x^{N+K}](e^x-1)^N を計算すれば計算できる。
+fn main() {
+    let n: usize = get();
+    let k: i64 = get();
+    let (fac, invfac) = fact_init(n + k as usize + 1);
+    let mut tot = MInt::new(0);
+    for i in 0..n + 1 {
+        let tmp = fac[n] * invfac[i] * invfac[n - i] * MInt::new(i as i64).pow(n as i64 + k);
+        if (n + i) % 2 == 0 {
+            tot += tmp;
+        } else {
+            tot -= tmp;
+        }
+    }
+    tot *= fac[k as usize] * MInt::new(n as i64).pow(k).inv() * invfac[n + k as usize];
+    println!("{}", tot);
+}