結果

問題 No.2177 Recurring ab
ユーザー atcoder8atcoder8
提出日時 2023-01-06 23:00:29
言語 Rust
(1.77.0 + proconio)
結果
AC  
実行時間 1 ms / 2,000 ms
コード長 22,421 bytes
コンパイル時間 26,101 ms
コンパイル使用メモリ 378,032 KB
実行使用メモリ 5,376 KB
最終ジャッジ日時 2024-05-07 22:43:56
合計ジャッジ時間 17,070 ms
ジャッジサーバーID
(参考情報)
judge2 / judge3
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テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 AC 1 ms
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testcase_01 AC 1 ms
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testcase_02 AC 1 ms
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testcase_03 AC 1 ms
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testcase_04 AC 1 ms
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testcase_05 AC 1 ms
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testcase_06 AC 1 ms
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testcase_07 AC 1 ms
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testcase_08 AC 1 ms
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testcase_09 AC 1 ms
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testcase_10 AC 1 ms
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testcase_11 AC 0 ms
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testcase_12 AC 1 ms
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testcase_13 AC 1 ms
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testcase_14 AC 1 ms
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testcase_15 AC 1 ms
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testcase_16 AC 1 ms
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testcase_17 AC 1 ms
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testcase_18 AC 1 ms
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testcase_19 AC 1 ms
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testcase_20 AC 1 ms
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ソースコード

diff #

use atcoder8_library::binary_search::BinarySearchWithUsize;

fn main() {
    let n = {
        let mut line = String::new();
        std::io::stdin().read_line(&mut line).unwrap();
        line.trim().parse::<usize>().unwrap()
    };

    let mut ans = 0;

    for a in 0..=9 {
        for b in 0..=9 {
            if a == b {
                continue;
            }

            let is_ok = |x| (x * x - 1) / n < x * a + b;

            let max_p = (2..=10_usize.pow(9)).binary_search(is_ok, true);

            if let Some(max_p) = max_p {
                if max_p > a && max_p > b {
                    ans += max_p - a.max(b);
                }
            }
        }
    }

    println!("{}", ans);
}

pub mod atcoder8_library {
    pub mod binary_search {
        //! Implements binary search for range represented by the Rust's built-in range type.

        use std::ops::{
            Range, RangeBounds, RangeFrom, RangeFull, RangeInclusive, RangeTo, RangeToInclusive,
        };

        macro_rules! impl_binary_search_with_integer {
            ($int_type: ident, $fn_name_for_inc: ident, $fn_name_for_dec: ident, $fn_name: ident, $trait_name: ident) => {
                fn $fn_name_for_inc<R, F>(rng: R, mut is_ok: F) -> Option<$int_type>
                where
                    R: RangeBounds<$int_type>,
                    F: FnMut($int_type) -> bool,
                {
                    let mut left = match rng.start_bound() {
                        std::ops::Bound::Included(&start) => start,
                        std::ops::Bound::Excluded(&start) => {
                            if start == std::$int_type::MAX {
                                return None;
                            }

                            start + 1
                        }
                        std::ops::Bound::Unbounded => std::$int_type::MIN,
                    };

                    let mut right = match rng.end_bound() {
                        std::ops::Bound::Included(&end) => {
                            if end == std::$int_type::MAX {
                                if !is_ok(end) {
                                    return None;
                                }

                                end
                            } else {
                                end + 1
                            }
                        }
                        std::ops::Bound::Excluded(&end) => end,
                        std::ops::Bound::Unbounded => std::$int_type::MAX,
                    };

                    if left >= right {
                        return None;
                    }

                    if is_ok(left) {
                        return Some(left);
                    }

                    if left + 1 == right || !is_ok(right - 1) {
                        return None;
                    }

                    while right - left > 1 {
                        let mid = left + (right - left) / 2;

                        if is_ok(mid) {
                            right = mid;
                        } else {
                            left = mid;
                        }
                    }

                    Some(right)
                }

                fn $fn_name_for_dec<R, F>(rng: R, mut is_ok: F) -> Option<$int_type>
                where
                    R: RangeBounds<$int_type>,
                    F: FnMut($int_type) -> bool,
                {
                    let mut left = match rng.start_bound() {
                        std::ops::Bound::Included(&start) => start,
                        std::ops::Bound::Excluded(&start) => {
                            if start == std::$int_type::MAX {
                                return None;
                            }

                            start + 1
                        }
                        std::ops::Bound::Unbounded => std::$int_type::MIN,
                    };

                    let mut right = match rng.end_bound() {
                        std::ops::Bound::Included(&end) => {
                            if end == std::$int_type::MAX {
                                if is_ok(end) {
                                    return Some(end);
                                }

                                end
                            } else {
                                end + 1
                            }
                        }
                        std::ops::Bound::Excluded(&end) => end,
                        std::ops::Bound::Unbounded => std::$int_type::MAX,
                    };

                    if left >= right {
                        return None;
                    }

                    if is_ok(right - 1) {
                        return Some(right - 1);
                    }

                    if left + 1 == right || !is_ok(left) {
                        return None;
                    }

                    while right - left > 1 {
                        let mid = left + (right - left) / 2;

                        if is_ok(mid) {
                            left = mid;
                        } else {
                            right = mid;
                        }
                    }

                    Some(left)
                }

                /// If `is_ok` is monotonically increasing, returns the smallest integer `x`
                /// that satisfies `is_ok(x) = true` as the value of `Some`.
                ///
                /// If `is_ok` is monotonically decreasing, returns the largest integer `x`
                /// that satisfies `is_ok(x) = true` as the value of `Some`.
                ///
                /// Returns `None` if no such integer exists in both of the above cases.
                ///
                /// # Arguments
                ///
                /// * `rng` - Domain of function `is_ok`.
                /// * `is_ok` - Monotonic function.
                /// * `dec` - Represents that `is_ok` is a monotonically decreasing function if true,
                /// or a monotonically increasing function if false.
                ///
                /// # Examples
                ///
                /// ```
                /// use atcoder8_library::binary_search::binary_search_with_i64;
                ///
                /// let is_ok = |x: i64| { x.pow(2) >= 400 };
                /// assert_eq!(binary_search_with_i64(0..100, is_ok, false), Some(20));
                ///
                /// let is_ok = |x: i64| { x.pow(2) >= 400 };
                /// assert_eq!(binary_search_with_i64(0..10, is_ok, false), None);
                ///
                /// let is_ok = |x: i64| { x.pow(3) < -8000 };
                /// assert_eq!(binary_search_with_i64(-100..0, is_ok, true), Some(-21));
                /// ```
                pub fn $fn_name<R, F>(rng: R, is_ok: F, dec: bool) -> Option<$int_type>
                where
                    R: RangeBounds<$int_type>,
                    F: FnMut($int_type) -> bool,
                {
                    if dec {
                        $fn_name_for_dec(rng, is_ok)
                    } else {
                        $fn_name_for_inc(rng, is_ok)
                    }
                }

                pub trait $trait_name: Sized + RangeBounds<$int_type> {
                    /// Performs a binary search on the domain specified by the Rust's built-in range type.
                    ///
                    /// If `is_ok` is monotonically increasing, returns the smallest integer `x`
                    /// that satisfies `is_ok(x) = true` as the value of `Some`.
                    ///
                    /// If `is_ok` is monotonically decreasing, returns the largest integer `x`
                    /// that satisfies `is_ok(x) = true` as the value of `Some`.
                    ///
                    /// Returns `None` if no such integer exists in both of the above cases.
                    ///
                    /// # Arguments
                    ///
                    /// * `is_ok` - Monotonic function.
                    /// * `dec` - Represents that `is_ok` is a monotonically decreasing function if true,
                    /// or a monotonically increasing function if false.
                    ///
                    /// # Examples
                    ///
                    /// ```
                    /// use atcoder8_library::binary_search::BinarySearchWithI64;
                    ///
                    /// let is_ok = |x: i64| { x.pow(2) >= 400 };
                    /// assert_eq!((0..100).binary_search(is_ok, false), Some(20));
                    ///
                    /// let is_ok = |x: i64| { x.pow(2) >= 400 };
                    /// assert_eq!((0..10).binary_search(is_ok, false), None);
                    ///
                    /// let is_ok = |x: i64| { x.pow(3) < -8000 };
                    /// assert_eq!((-100..0).binary_search(is_ok, true), Some(-21));
                    /// ```
                    fn binary_search<F>(self, is_ok: F, dec: bool) -> Option<$int_type>
                    where
                        F: FnMut($int_type) -> bool,
                    {
                        $fn_name(self, is_ok, dec)
                    }
                }

                impl $trait_name for RangeFull {}

                impl $trait_name for RangeTo<$int_type> {}

                impl $trait_name for RangeToInclusive<$int_type> {}

                impl $trait_name for RangeFrom<$int_type> {}

                impl $trait_name for Range<$int_type> {}

                impl $trait_name for RangeInclusive<$int_type> {}
            };
        }

        impl_binary_search_with_integer!(
            i8,
            binary_search_with_i8_for_inc,
            binary_search_with_i8_for_dec,
            binary_search_with_i8,
            BinarySearchWithI8
        );

        impl_binary_search_with_integer!(
            i16,
            binary_search_with_i16_for_inc,
            binary_search_with_i16_for_dec,
            binary_search_with_i16,
            BinarySearchWithI16
        );

        impl_binary_search_with_integer!(
            i32,
            binary_search_with_i32_for_inc,
            binary_search_with_i32_for_dec,
            binary_search_with_i32,
            BinarySearchWithI32
        );

        impl_binary_search_with_integer!(
            i64,
            binary_search_with_i64_for_inc,
            binary_search_with_i64_for_dec,
            binary_search_with_i64,
            BinarySearchWithI64
        );

        impl_binary_search_with_integer!(
            i128,
            binary_search_with_i128_for_inc,
            binary_search_with_i128_for_dec,
            binary_search_with_i128,
            BinarySearchWithI128
        );

        impl_binary_search_with_integer!(
            isize,
            binary_search_with_isize_for_inc,
            binary_search_with_isize_for_dec,
            binary_search_with_isize,
            BinarySearchWithIsize
        );

        impl_binary_search_with_integer!(
            u8,
            binary_search_with_u8_for_inc,
            binary_search_with_u8_for_dec,
            binary_search_with_u8,
            BinarySearchWithU8
        );

        impl_binary_search_with_integer!(
            u16,
            binary_search_with_u16_for_inc,
            binary_search_with_u16_for_dec,
            binary_search_with_u16,
            BinarySearchWithU16
        );

        impl_binary_search_with_integer!(
            u32,
            binary_search_with_u32_for_inc,
            binary_search_with_u32_for_dec,
            binary_search_with_u32,
            BinarySearchWithU32
        );

        impl_binary_search_with_integer!(
            u64,
            binary_search_with_u64_for_inc,
            binary_search_with_u64_for_dec,
            binary_search_with_u64,
            BinarySearchWithU64
        );

        impl_binary_search_with_integer!(
            u128,
            binary_search_with_u128_for_inc,
            binary_search_with_u128_for_dec,
            binary_search_with_u128,
            BinarySearchWithU128
        );

        impl_binary_search_with_integer!(
            usize,
            binary_search_with_usize_for_inc,
            binary_search_with_usize_for_dec,
            binary_search_with_usize,
            BinarySearchWithUsize
        );

        macro_rules! impl_binary_search_with_float {
            ($float_type: ident, $fn_name_for_inc: ident, $fn_name_for_dec: ident, $fn_name: ident, $trait_name: ident) => {
                fn $fn_name_for_inc<R, F>(
                    rng: R,
                    mut is_ok: F,
                    eps: $float_type,
                ) -> Option<$float_type>
                where
                    R: RangeBounds<$float_type>,
                    F: FnMut($float_type) -> bool,
                {
                    let mut left = match rng.start_bound() {
                        std::ops::Bound::Included(&start) => start,
                        std::ops::Bound::Excluded(&start) => start,
                        std::ops::Bound::Unbounded => std::$float_type::MIN,
                    };

                    let mut right = match rng.end_bound() {
                        std::ops::Bound::Included(&end) => end,
                        std::ops::Bound::Excluded(&end) => end,
                        std::ops::Bound::Unbounded => std::$float_type::MAX,
                    };

                    assert!(
                        eps > 0.0,
                        "Allowable margin of error must be a positive number."
                    );

                    if left >= right {
                        return None;
                    }

                    if is_ok(left) {
                        return Some(left);
                    }

                    if !is_ok(right) {
                        return None;
                    }

                    while right - left > eps {
                        let mid = right - (right - left) / 2.0;

                        if mid <= left || right <= mid {
                            return None;
                        }

                        if is_ok(mid) {
                            right = mid;
                        } else {
                            left = mid;
                        }
                    }

                    Some(right)
                }

                fn $fn_name_for_dec<R, F>(
                    rng: R,
                    mut is_ok: F,
                    eps: $float_type,
                ) -> Option<$float_type>
                where
                    R: RangeBounds<$float_type>,
                    F: FnMut($float_type) -> bool,
                {
                    let mut left = match rng.start_bound() {
                        std::ops::Bound::Included(&start) => start,
                        std::ops::Bound::Excluded(&start) => start,
                        std::ops::Bound::Unbounded => std::$float_type::MIN,
                    };

                    let mut right = match rng.end_bound() {
                        std::ops::Bound::Included(&end) => end,
                        std::ops::Bound::Excluded(&end) => end,
                        std::ops::Bound::Unbounded => std::$float_type::MAX,
                    };

                    assert!(
                        eps > 0.0,
                        "Allowable margin of error must be a positive number."
                    );

                    if left >= right {
                        return None;
                    }

                    if is_ok(right) {
                        return Some(right);
                    }

                    if !is_ok(left) {
                        return None;
                    }

                    while (right - left) > eps {
                        let mid = right - (right - left) / 2.0;

                        if mid <= left || right <= mid {
                            return None;
                        }

                        if is_ok(mid) {
                            left = mid;
                        } else {
                            right = mid;
                        }
                    }

                    Some(left)
                }

                /// If `is_ok` is monotonically increasing,
                /// returns the smallest floating point number `x`
                /// that satisfies `is_ok(x) = true` as the value of `Some`.
                ///
                /// If `is_ok` is monotonically decreasing,
                /// returns the largest floating point number `x`
                /// that satisfies `is_ok(x) = true` as the value of `Some`.
                ///
                /// Returns `None` if no such floating point number exists in both of the above cases.
                /// This includes the case where the absolute error cannot be determined
                /// to be less than or equal to `eps`.
                ///
                /// # Arguments
                ///
                /// * `rng` - Domain of function `is_ok`.
                /// * `is_ok` - Monotonic function.
                /// * `eps` - The allowable absolute error. It must be a positive number.
                /// * `dec` - Represents that `is_ok` is a monotonically decreasing function if true,
                /// or a monotonically increasing function if false.
                ///
                /// # Examples
                ///
                /// ```
                /// use atcoder8_library::binary_search::binary_search_with_f64;
                ///
                /// let is_ok = |x: f64| { x.powi(2) >= 400.0 };
                /// let ans = binary_search_with_f64(0.0..100.0, is_ok, 1e-6, false).unwrap();
                /// assert!((ans - 20.0).abs() <= 1e-6);
                ///
                /// let is_ok = |x: f64| { x.powi(2) >= 400.0 };
                /// assert_eq!(binary_search_with_f64(0.0..10.0, is_ok, 1e-6, false), None);
                ///
                /// let is_ok = |x: f64| { x.powi(3) <= -8000.0 };
                /// let ans = binary_search_with_f64(-100.0..0.0, is_ok, 1e-6, true).unwrap();
                /// assert!((ans - (-20.0)).abs() <= 1e-6);
                /// ```
                pub fn $fn_name<R, F>(
                    rng: R,
                    is_ok: F,
                    eps: $float_type,
                    dec: bool,
                ) -> Option<$float_type>
                where
                    R: RangeBounds<$float_type>,
                    F: FnMut($float_type) -> bool,
                {
                    if dec {
                        $fn_name_for_dec(rng, is_ok, eps)
                    } else {
                        $fn_name_for_inc(rng, is_ok, eps)
                    }
                }

                pub trait $trait_name: Sized + RangeBounds<$float_type> {
                    /// Performs a binary search on the domain specified by the Rust's built-in range type.
                    ///
                    /// If `is_ok` is monotonically increasing,
                    /// returns the smallest floating point number `x`
                    /// that satisfies `is_ok(x) = true` as the value of `Some`.
                    ///
                    /// If `is_ok` is monotonically decreasing,
                    /// returns the largest floating point number `x`
                    /// that satisfies `is_ok(x) = true` as the value of `Some`.
                    ///
                    /// Returns `None` if no such floating point number exists in both of the above cases.
                    /// This includes the case where the absolute error cannot be determined
                    /// to be less than or equal to `eps`.
                    ///
                    /// # Arguments
                    ///
                    /// * `is_ok` - Monotonic function.
                    /// * `eps` - The allowable absolute error. It must be a positive number.
                    /// * `dec` - Represents that `is_ok` is a monotonically decreasing function if true,
                    /// or a monotonically increasing function if false.
                    ///
                    /// # Examples
                    ///
                    /// ```
                    /// use atcoder8_library::binary_search::BinarySearchWithF64;
                    ///
                    /// let is_ok = |x: f64| { x.powi(2) >= 400.0 };
                    /// let ans = (0.0..100.0).binary_search(is_ok, 1e-6, false).unwrap();
                    /// assert!((ans - 20.0).abs() <= 1e-6);
                    ///
                    /// let is_ok = |x: f64| { x.powi(2) >= 400.0 };
                    /// assert_eq!((0.0..10.0).binary_search(is_ok, 1e-6, false), None);
                    ///
                    /// let is_ok = |x: f64| { x.powi(3) <= -8000.0 };
                    /// let ans = (-100.0..0.0).binary_search(is_ok, 1e-6, true).unwrap();
                    /// assert!((ans - (-20.0)).abs() <= 1e-6);
                    /// ```
                    fn binary_search<F>(
                        self,
                        is_ok: F,
                        eps: $float_type,
                        dec: bool,
                    ) -> Option<$float_type>
                    where
                        F: FnMut($float_type) -> bool,
                    {
                        $fn_name(self, is_ok, eps, dec)
                    }
                }

                impl $trait_name for RangeFull {}

                impl $trait_name for RangeTo<$float_type> {}

                impl $trait_name for RangeToInclusive<$float_type> {}

                impl $trait_name for RangeFrom<$float_type> {}

                impl $trait_name for Range<$float_type> {}

                impl $trait_name for RangeInclusive<$float_type> {}
            };
        }

        impl_binary_search_with_float!(
            f32,
            binary_search_with_f32_for_inc,
            binary_search_with_f32_for_dec,
            binary_search_with_f32,
            BinarySearchWithF32
        );

        impl_binary_search_with_float!(
            f64,
            binary_search_with_f64_for_inc,
            binary_search_with_f64_for_dec,
            binary_search_with_f64,
            BinarySearchWithF64
        );
    }
}
0