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/************************************************************************************************** * Copyright 2018 GrayJack * All rights reserved. * * This Source Code Form is subject to the terms of the BSD 3-Clause License. **************************************************************************************************/ //! A module for using searching algorithms. //! //! The array **must** be crescent ordered. use std::cmp::*; /// **Linear Search:** Search for the value 'x' in an array. /// /// Returns `Err` holding the last iterator if 'x' not found and array[i] > x. /// /// /// | Case | Time complexity | Space complexity | /// |:----------|:---------------:|:----------------:| /// | Best: | Ω(1) | | /// | Avrg: | θ(n) | | /// | Worst: | O(n) | O(1) | /// /// # Example /// ```rust /// use algos::search; /// /// let v = [1, 3, 4, 8, 11, 17, 23]; /// /// let find = search::linear(&v, &11); /// assert_eq!(find, Ok(4)); /// /// let find2 = search::linear(&v, &19); /// assert_eq!(find2, Err(6)); /// ``` pub fn linear<T: Ord>(a: &[T], x: &T) -> Result<usize,usize> { for (i, e) in a.iter().enumerate() { if e == x { return Ok(i); } else if e > x { return Err(i); } } Err(0) } /// **Binary Search:** Search for the value 'x' in an array. /// /// Returns `Err` holding the leftmost term if 'x' not found. /// /// /// | Case | Time complexity | Space complexity | /// |:----------|:---------------:|:----------------:| /// | Best: | Ω(1) | | /// | Avrg: | θ(log(n)) | | /// | Worst: | O(log(n)) | O(1) | /// /// # Example /// ```rust /// use algos::search; /// /// let v = [1, 3, 4, 8, 11, 17, 23]; /// /// let find = search::binary(&v, &11); /// assert_eq!(find, Ok(4)); /// /// let find2 = search::binary(&v, &19); /// assert_eq!(find2, Err(6)); /// ``` pub fn binary<T: Ord>(a: &[T], x: &T) -> Result<usize,usize> { let (mut l, mut r) = (0, a.len()); // Looks like I'm unable to make a recursive implementation, so I made interative. while l <= r { // This has the same result as (l+r)/2, but it's probably the same or faster. let mid = l+r >> 1; if &a[mid] > x { r = mid - 1; } else if &a[mid] < x { l = mid + 1; } else { return Ok(mid); } } Err(l) } /// **Exponential Search:** Search for the value 'x' in an array. /// /// Returns `Err` holding the leftmost term if 'x' not found. /// /// **Obs.:** Variation of binary search. /// /// | Case | Time complexity | Space complexity | /// |:----------|:---------------:|:----------------:| /// | Best: | Ω(1) | | /// | Avrg: | θ(log(n)) | | /// | Worst: | O(log(n)) | O(1) | /// /// # Example /// ```rust /// use algos::search; /// /// let v = [1, 3, 4, 8, 11, 17, 23]; /// /// let find = search::exponential(&v, &11); /// assert_eq!(find, Ok(4)); /// /// let find2 = search::exponential(&v, &19); /// assert_eq!(find2, Err(6)); /// ``` pub fn exponential<T: Ord>(a: &[T], x: &T) -> Result<usize,usize> { if &a[0] == x { return Ok(0); } let mut range = 1; while range < a.len() && &a[range] <= x { range *= 2; } let (mut l, mut r) = (range/2, range.min(a.len())); while l <= r { // This has the same result as (l+r)/2, but it's probably the same or faster. let mid = l+r >> 1; if &a[mid] > x { r = mid - 1; } else if &a[mid] < x { l = mid + 1; } else { return Ok(mid); } } Err(l) } /// **Fibonacci Search:** Search for the value 'x' in an array. /// /// Returns `Err` holding the leftmost term if 'x' not found. /// /// **Obs.:** Variation of binary search. /// /// | Case | Time complexity | Space complexity | /// |:----------|:---------------:|:----------------:| /// | Best: | Ω(1) | | /// | Avrg: | θ(log(n)) | | /// | Worst: | O(log(n)) | O(1) | /// /// # Example /// ```rust /// use algos::search; /// /// let v = [1, 3, 4, 8, 11, 17, 23]; /// /// let find = search::fibonacci(&v, &11); /// assert_eq!(find, Ok(4)); /// /// let find2 = search::fibonacci(&v, &19); /// assert_eq!(find2, Err(3)); /// ``` pub fn fibonacci<T: Ord>(a: &[T], x: &T) -> Result<usize,usize> { let (mut fib1, mut fib2) = (0, 1); let mut fibn = fib1 + fib2; // We are recalculating numbers, we can do better using dynamic programming. // Stores the smallest Fibonacci Number greater than or equal to a.len(). while fibn < a.len() { fib1 = fib2; fib2 = fibn; fibn = fib1 + fib2; } let mut off = 0; while fibn > 1 { let i = (off+fib1-1).min(a.len()); if &a[i] < x { fibn = fib2; fib2 = fib1; fib1 = fibn - fib2; off = i; } else if &a[i] > x { fibn = fib1; fib2 -= fib1; fib1 = fibn - fib2; } else { return Ok(i) } } if fib2 == 1 && &a[off+1] == x { return Ok(off+1) } Err(off) } #[cfg(test)] pub mod test { use search::*; #[test] pub fn linear_test() { let v = [1, 3, 4, 8, 11, 17, 23]; let find = linear(&v, &11); assert_eq!(find, Ok(4)); let find2 = linear(&v, &19); assert_eq!(find2, Err(6)); } #[test] pub fn binary_test() { let v = [1, 3, 4, 8, 11, 17, 23]; let find = binary(&v, &11); assert_eq!(find, Ok(4)); let find2 = binary(&v, &19); assert_eq!(find2, Err(6)); } #[test] pub fn exponential_test() { let v = [1, 3, 4, 8, 11, 17, 23]; let find = exponential(&v, &11); assert_eq!(find, Ok(4)); let find2 = exponential(&v, &19); assert_eq!(find2, Err(6)); } #[test] pub fn fibonacci_test() { let v = [1, 3, 4, 8, 11, 17, 23]; let find = fibonacci(&v, &11); assert_eq!(find, Ok(4)); let find2 = fibonacci(&v, &19); assert_eq!(find2, Err(3)); } }