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//! Implementation of [An all-substrings common subsequence algorithm](https://www.sciencedirect.com/science/article/pii/S0166218X07002727) //! //! Given two strings s1 and s2, it is possible construct, //! in O(|s1|\*|s2|) time and O(|s1|+|s2|) space, //! a structure that can be queried to find the length of //! all Longest Common Subsequences between s1 and all possible substrings of s2, //! each query requiring constant time. //! //! Some accessor functions are provided to retrieve the matrices and the vectors defined in the paper //! //! //! # Example //! //! ``` //! extern crate alcs; //! use alcs::Alcs; //! //! fn main() { //! let a = "word"; //! let b = "hello world"; //! let va = a.chars().collect::<Vec<char>>(); //! let vb = b.chars().collect::<Vec<char>>(); //! let alcs = Alcs::new(&va, &vb); //! for i in 0..b.len() { //! for (i, j, cij) in alcs.suffix(i) { //! println!(r#"LCS between "{}" and "{}" has length {}"#,a,&b[i..j],cij); //! } //! } //! } //! ``` //! //! Output: //! //! ``` //! //! LCS between "word" and "h" has length 0 //! LCS between "word" and "he" has length 0 //! LCS between "word" and "hel" has length 0 //! ... //! LCS between "word" and " world" has length 4 //! LCS between "word" and "w" has length 1 //! LCS between "word" and "wo" has length 2 //! LCS between "word" and "wor" has length 3 //! ... //! LCS between "word" and "d" has length 1 //! //! ``` //! //! Also, it is defined a trait that allows to fuzzy search a string: //! //! ``` //! //! extern crate alcs; //! use alcs::FuzzyStrstr; //! //! fn main() { //! let tsh = 0.7; //! let tests = [ //! ("he.llo.wor.ld.!", "world"), //! ("he.llo.word", "world"), //! ("hello world", "word"), //! ("hello world", "banana"), //! ]; //! for &(h, n) in &tests { //! match h.fuzzy_find_str(n, tsh) { //! None => { //! println!(r#""{}" does not contain "{}""#, h, n); //! } //! Some((score, sub)) => { //! println!(r#""{}" contains "{}" ("{}") with score {}"#, h, n, sub, score); //! } //! } //! } //! } //! //! ``` //! //!Output: //! //! ``` //! //! "he.llo.wor.ld.!" contains "world" ("wor.ld") with score 0.8333333 //! "he.llo.word" contains "world" ("word") with score 0.8 //! "hello world" contains "word" ("world") with score 0.8 //! "hello world" does not contain "banana" //! //! ``` use std::cmp::{max, min}; /// Constructs the full matrices i_h and i_v /// /// It requires O(|a|\*|b|) space and O(|a|\*|b|) time /// /// ``` /// /// let a = "word"; /// let b = "hello world"; /// let va = a.chars().collect::<Vec<char>>(); /// let vb = b.chars().collect::<Vec<char>>(); /// let (ih,iv) = alcs::compute_mat_ih_iv(&va,&vb); /// println!("{:?}\n{:?}",ih,iv); /// /// ``` /// pub fn compute_mat_ih_iv<T>(a: &[T], b: &[T]) -> (Vec<Vec<usize>>, Vec<Vec<usize>>) where T: Eq, { let na = a.len(); let nb = b.len(); let mut ih = vec![vec![0; nb + 1]; na + 1]; let mut iv = vec![vec![0; nb + 1]; na + 1]; for j in 0..(nb + 1) { ih[0][j] = j; } for l in 0..(na + 1) { iv[l][0] = 0; } for l in 1..(na + 1) { for j in 1..(nb + 1) { if a[l - 1] != b[j - 1] { ih[l][j] = max(iv[l][j - 1], ih[l - 1][j]); iv[l][j] = min(iv[l][j - 1], ih[l - 1][j]); } else { ih[l][j] = iv[l][j - 1]; iv[l][j] = ih[l - 1][j]; } } } (ih, iv) } /// Constructs the vector I<sub>G</sub> /// /// It requires O(|a|+|b|) space and O(|a|*|b|) time /// /// ``` /// /// let a = "word"; /// let b = "hello world"; /// let va = a.chars().collect::<Vec<char>>(); /// let vb = b.chars().collect::<Vec<char>>(); /// let ig = alcs::compute_vec_ig(&va,&vb); /// println!("{:?}",ig); /// /// ``` pub fn compute_vec_ig<T>(a: &[T], b: &[T]) -> Vec<usize> where T: Eq, { let na = a.len(); let nb = b.len(); let mut ih = vec![vec![0; nb + 1], vec![0; nb + 1]]; let mut iv = vec![vec![0; nb + 1], vec![0; nb + 1]]; for j in 0..(nb + 1) { ih[0][j] = j; } for l in 1..(na + 1) { iv[1][0] = 0; for j in 1..(nb + 1) { if a[l - 1] != b[j - 1] { ih[1][j] = max(iv[1][j - 1], ih[0][j]); iv[1][j] = min(iv[1][j - 1], ih[0][j]); } else { ih[1][j] = iv[1][j - 1]; iv[1][j] = ih[0][j]; } } ih.swap(0, 1); iv.swap(0, 1); } ih.into_iter().next().unwrap() } /// Constructs the vectors D<sub>G</sub><sup>0</sup> and V<sub>G</sub> using I<sub>G</sub> /// /// ``` /// /// let a = "word"; /// let b = "hello world"; /// let va = a.chars().collect::<Vec<char>>(); /// let vb = b.chars().collect::<Vec<char>>(); /// let ig = alcs::compute_vec_ig(&va,&vb); /// let (vg,dg) = alcs::compute_vg_dg_from_ig(&va,&vb,&ig); /// println!("{:?}\n{:?}\n{:?}",ig,vg,dg); /// /// ``` pub fn compute_vg_dg_from_ig<T>( a: &[T], b: &[T], ig: &Vec<usize>, ) -> (Vec<Option<usize>>, Vec<Option<usize>>) where T: Eq, { let na = a.len(); let nb = b.len(); let mut vg = vec![None; nb + 1]; let mut dg = vec![Some(0); na + 1]; let mut i = 1; for j in 1..(nb + 1) { if ig[j] == 0 { dg[i] = Some(j); i += 1; } else { vg[ig[j]] = Some(j); } } for l in i..(na + 1) { dg[l] = None; } (vg, dg) } /// Constructs the vectors D<sub>G</sub><sup>0</sup> and V<sub>G</sub> using the matrix i<sub>h</sub> /// /// ``` /// /// let a = "word"; /// let b = "hello world"; /// let va = a.chars().collect::<Vec<char>>(); /// let vb = b.chars().collect::<Vec<char>>(); /// let (ih,iv) = alcs::compute_mat_ih_iv(&va,&vb); /// let (ig,vg,dg) = alcs::compute_ig_vg_dg_from_ih_mat(&va,&vb,&ih); /// println!("{:?}\n{:?}",ih,iv); /// println!("{:?}\n{:?}\n{:?}",ig,vg,dg); /// /// ``` pub fn compute_ig_vg_dg_from_ih_mat<T>( a: &[T], b: &[T], ih: &Vec<Vec<usize>>, ) -> (Vec<usize>, Vec<Option<usize>>, Vec<Option<usize>>) where T: Eq, { let ig = ih[ih.len() - 1].clone(); let (vg, dg) = compute_vg_dg_from_ig(a, b, &ih[ih.len() - 1]); (ig, vg, dg) } /// Constructs the vectors I<sub>G</sub>, V<sub>G</sub>, D<sub>G</sub><sup>0<sup> /// /// ``` /// /// let a = "word"; /// let b = "hello world"; /// let va = a.chars().collect::<Vec<char>>(); /// let vb = b.chars().collect::<Vec<char>>(); /// let (ig,vg,dg) = alcs::alcs(&va,&vb); /// println!("{:?}\n{:?}\n{:?}",ig,vg,dg); /// /// ``` pub fn alcs<T>(a: &[T], b: &[T]) -> (Vec<usize>, Vec<Option<usize>>, Vec<Option<usize>>) where T: Eq, { let ig = compute_vec_ig(a, b); let (vg, dg) = compute_vg_dg_from_ig(a, b, &ig); (ig, vg, dg) } /// Constructs the matrices i<sub>h</sub>, i<sub>v</sub>, and the vectors I<sub>G</sub>, V<sub>G</sub>, D<sub>G</sub><sup>0</sub> /// /// ``` /// /// let a = "word"; /// let b = "hello world"; /// let va = a.chars().collect::<Vec<char>>(); /// let vb = b.chars().collect::<Vec<char>>(); /// let (ih,iv,ig,vg,dg) = alcs::alcs_mat(&va,&vb); /// println!("{:?}\n{:?}\n{:?}\n{:?}\n{:?}",ih,iv,ig,vg,dg); /// /// ``` pub fn alcs_mat<T>( a: &[T], b: &[T], ) -> ( Vec<Vec<usize>>, Vec<Vec<usize>>, Vec<usize>, Vec<Option<usize>>, Vec<Option<usize>>, ) where T: Eq, { let (ih, iv) = compute_mat_ih_iv(a, b); let (ig, vg, dg) = compute_ig_vg_dg_from_ih_mat(a, b, &ih); (ih, iv, ig, vg, dg) } pub struct Alcs { ig: Vec<usize>, } impl Alcs { /// Constructs a structure able to return all the Longest Common Subsequences between a and each substring of b /// /// It requires O(|a|+|b|) space and O(|a|*|b|) time /// /// ``` /// /// let a = "word"; /// let b = "hello world"; /// let va = a.chars().collect::<Vec<char>>(); /// let vb = b.chars().collect::<Vec<char>>(); /// let alcs = Alcs::new(&va, &vb); /// // this will actually take O(|b|^2) /// for i in 0..b.len() { /// for (i, j, cij) in alcs.suffix(i) { /// println!("LCS between '{}' and '{}' has length {}",a,&b[i..j],cij); /// } /// } /// /// ``` pub fn new<T>(a: &[T], b: &[T]) -> Self where T: Eq, { Alcs { ig: compute_vec_ig(a, b), } } /// Returns an iterator yielding the LCS length for all substrings starting from position `i` /// pub fn suffix(&self, pos: usize) -> AlcsIterator { AlcsIterator::new(&self, pos) } } pub struct AlcsIterator<'a> { alcs: &'a Alcs, i: usize, j: usize, prev: usize, } impl<'a> AlcsIterator<'a> { fn new(alcs: &'a Alcs, pos: usize) -> Self { AlcsIterator { alcs, i: pos, j: pos + 1, prev: 0, } } } impl<'a> Iterator for AlcsIterator<'a> { type Item = (usize, usize, usize); fn next(&mut self) -> Option<Self::Item> { if self.j >= self.alcs.ig.len() { return None; } let cur = self.prev + (self.alcs.ig[self.j] <= self.i) as usize; self.prev = cur; self.j += 1; Some((self.i, self.j - 1, cur)) } } fn score(b: &str, a: &str, tsh: Option<f32>) -> (f32, usize, usize) { let va = a.chars().collect::<Vec<char>>(); let vb = b.chars().collect::<Vec<char>>(); let alcs = Alcs::new(&va, &vb); let na = a.len(); let nb = b.len(); let many = match tsh { None => nb, Some(tsh) => (na as f32 / tsh) as usize, }; let mut best = (0., 0, 0); for i in 0..nb { let mut maxrow = (0., 0, 0); for (i, j, cij) in alcs.suffix(i).take(many) { let cur = cij as f32 / max(j - i, na) as f32; if cur > maxrow.0 { maxrow = (cur, i, j); } } if maxrow >= best { best = maxrow; } } best } pub trait FuzzyStrstr<T: AsRef<str>>: AsRef<str> { /// Searches s inside self, /// /// It returns: /// /// `Some(score,start,end)` if there is a substring s[start..end] achieving a score that is at least the threshold /// /// `None` otherwise /// /// For "not too small" values of tsh, /// /// it requires O(|self|+|s|) space and O(|self|*|s|) time fn fuzzy_find_pos(&self, s: T, tsh: f32) -> Option<(f32, usize, usize)> { let s = score(self.as_ref(), s.as_ref(), Some(tsh)); if s.0 > tsh { Some(s) } else { None } } /// Searches s inside self, /// /// It returns: /// /// `Some(score,substring)` if there is a substring achieving a score that is at least the threshold /// /// `None` otherwise /// /// For "not too small" values of tsh, /// /// it requires O(|self|+|s|) space and O(|self|*|s|) time fn fuzzy_find_str<'a>(&'a self, s: T, tsh: f32) -> Option<(f32, &'a str)> { let r = self.fuzzy_find_pos(s, tsh); r.map(|(tsh, start, end)| (tsh, &self.as_ref()[start..end])) } /// Searches s inside self, /// /// It returns: /// /// `true` if there is a substring achieving a score that is at least the threshold /// /// `false` otherwise /// /// For "not too small" values of tsh, /// /// it requires O(|self|+|s|) space and O(|self|*|s|) time fn fuzzy_contains(&self, s: T, tsh: f32) -> bool { self.fuzzy_find_pos(s, tsh).is_some() } } impl<S, T> FuzzyStrstr<T> for S where S: AsRef<str>, T: AsRef<str>, { } #[cfg(test)] mod tests { #[test] fn it_works() { assert_eq!(2 + 2, 4); } }