結果
問題 | No.2177 Recurring ab |
ユーザー | atcoder8 |
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 |
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testcase_00 | AC | 1 ms
5,248 KB |
testcase_01 | AC | 1 ms
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testcase_02 | AC | 1 ms
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testcase_03 | AC | 1 ms
5,248 KB |
testcase_04 | AC | 1 ms
5,376 KB |
testcase_05 | AC | 1 ms
5,376 KB |
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
5,376 KB |
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
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 ); } }