5
\$\begingroup\$

This problem is taken from the book Introduction to Algorithms, Third Edition By Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest and Clifford Stein:

In order to transform one source string of text x[1..m] to a target string y[1..n], we can perform various transformation operations. Our goal is, given x and y, to produce a series of transformations that change x to y. We use an array ́z—assumed to be large enough to hold all the characters it will need—to hold the intermediate results. Initially, z is empty, and at termination, we should have z[j] = y[j] for j = 1, 2,..., n. We maintain current indices i into x and j into z, and the operations are allowed to alter z and these indices. Initially, i = j = 1. We are required to examine every character in x during the transformation, which means that at the end of the sequence of transformation operations, we must have i = m + 1.

We may choose from among six transformation operations:

Copy a character from x to z by setting ́z[j] = x[i] and then incrementing both i and j. This operation examines x[i].

Replace a character from x by another character c, by setting z[j] = c, and then incrementing both i and j . This operation examines x[i].

Delete a character from x by incrementing i but leaving j alone. This operation examines x[i].

Insert the character c into z by setting z[j] = c and then incrementing j , but leaving i alone. This operation examines no characters of x.

Twiddle (i.e., exchange) the next two characters by copying them from x to z but in the opposite order; we do so by setting z[j] = x[i + 1] and ́z[j + 1] = x[i] and then setting i = i + 2 and j = j + 2. This operation examines x[i] and x[i + 1].

Kill the remainder of x by setting i = m + 1. This operation examines all characters in x that have not yet been examined. This operation, if performed, must be the final operation.

a. Given two sequences x[1..m] and y[1..n] and set of transformation operation costs, the edit distance from x to y is the cost of the least expensive operation sequence that transforms x to y. Describe a dynamic-programming algorithm that finds the edit distance from x[1..m] to y[1..n] and prints an optimal operation sequence. Analyze the running time and space requirements of your algorithm

My solution is \$O(nm + m+n)\$.

Code:

extern crate rand;

use std::collections::HashMap;
use std::collections::VecDeque;

#[derive(Debug, Copy, Clone, PartialEq, Eq, Hash)]
enum EditOp {
    Copy,
    Replace,
    Delete,
    Insert,
    Twiddle,
    Kill,
}

impl EditOp {
    fn valid(&self,
             i       : usize,
             j       : usize,
             iprev   : char,
             jprev   : char,
             icurrent: char,
             jcurrent: char) -> bool {

        let threshold = |p| i != p || j == p; 
        match *self {
            EditOp::Copy    => threshold(1) 
                                && icurrent == jcurrent,

            EditOp::Replace => threshold(1),
            EditOp::Delete  => i > 1,

            EditOp::Twiddle => i > 1 && j > 1
                                && threshold(2)
                                && icurrent == jprev
                                && iprev == jcurrent,
            _ => true,                                                          
        }
    }

    fn displacement(&self) -> (usize, usize) {
        match *self {
            EditOp::Copy    => (1, 1),
            EditOp::Replace => (1, 1),
            EditOp::Delete  => (1, 0),
            EditOp::Insert  => (0, 1),
            EditOp::Twiddle => (2, 2),
            EditOp::Kill    => (0, 0),    
        }
    }

    fn apply(&self, 
             from_itr: &mut std::str::Chars, 
             to_itr  : &mut std::str::Chars, 
             result  : &mut String) {
        match *self {
            EditOp::Copy    => { 
                result.push(from_itr.next().unwrap());
                to_itr.next();

            },
            EditOp::Replace => {
                result.push(to_itr.next().unwrap());
                from_itr.next();
            },
            EditOp::Delete  => {
                from_itr.next();
            },
            EditOp::Insert  => {
                result.push(to_itr.next().unwrap());
            },
            EditOp::Twiddle => {
                let second = from_itr.next().unwrap();
                let first = from_itr.next().unwrap();
                result.push(first);
                result.push(second);
                to_itr.next();
                to_itr.next();
            },
            EditOp::Kill => {},
        }
    }
}


fn create_tables(from_len: usize, 
                 to_len  : usize, 
                 costs   : &HashMap<EditOp, usize>) 
-> (Vec<Vec<EditOp>>, Vec<Vec<usize>>) {    

    let mut op_table   = vec![ vec![EditOp::Kill; to_len]; from_len ];
    let mut cost_table = vec![ vec![0usize; to_len]; from_len ];
    let delete_cost    = costs.get(&EditOp::Delete).map(|c| *c).unwrap_or(0);

    for (i, c) in (1.. from_len).map(|i|(i, i * delete_cost)) {
        cost_table[i][0] = c;
        op_table[i][0]   = EditOp::Delete;
    } 
    (op_table , cost_table)
}

fn edit_distance(from : &str, 
                 to   : &str, 
                 costs: &HashMap<EditOp, usize>) 
-> (usize, VecDeque<EditOp>){

    if costs.is_empty() {
        panic!("map of costs is empty");
    }

    let from_len = from.chars().count(); 
    let to_len   = to.chars().count();

    let (mut op_table, mut cost_table) = create_tables(from_len + 1, 
                                                       to_len + 1, 
                                                       costs);
    let (mut lasti, mut lastj)         = (' ', ' ');

    for (i, ichar) in from.chars().enumerate() {
        for (j, jchar) in to.chars().enumerate() {
            let (i, j) = (i + 1, j + 1);
            let (op, cost) = costs.iter()
                .filter(|&(x, _)| !x.eq(&EditOp::Kill))
                .filter(|&(x, _)| x.valid(i, j, lasti, lastj, 
                                          ichar, jchar))
                .map(|(x, c)| {
                    let (di, dj) = x.displacement();
                    (x, cost_table[i - di][j - dj] + c)
                })
                .min_by_key(|&(_, c)| c)
                .unwrap(); 

            cost_table[i][j] = cost;
            op_table[i][j] = *op;
            lastj = jchar;
        }
        lasti = ichar;
    }


    let no_kill_cost    = cost_table[from_len][to_len];
    let (i, cost, kill) = costs.get(&EditOp::Kill)
                               .map(|kc| min_with_kill(&cost_table, 
                                                       from_len, 
                                                       to_len, *kc))
                               .unwrap_or((from_len, no_kill_cost, None));

    (cost, build_operations(kill, &op_table, i, to_len))
}


fn edit(from: &str, to: &str, ops: &VecDeque<EditOp>) -> String {   
    let mut result   = String::new();
    let mut from_itr = from.chars();
    let mut to_itr   = to.chars();

    for op in ops {
        op.apply(&mut from_itr, &mut to_itr, &mut result);      
    }
    result
}



fn min_with_kill(cost_table: &Vec<Vec<usize>>, 
                 from_size : usize, 
                 to_size   : usize, 
                 kill_cost : usize ) -> (usize, usize, Option<EditOp>) {

    let no_kill_cost  = cost_table[from_size][to_size];
    (1..from_size).map(|i|(i, cost_table[i][to_size] + kill_cost) )
                  .map(|(i, c)|(i, c, Some(EditOp::Kill)))
                  .chain(Some((from_size, no_kill_cost, None)).into_iter())
                  .min_by_key(|&(_, cost, _)| cost).unwrap() 
}

fn build_operations(kill    : Option<EditOp>, 
                    op_table: &Vec<Vec<EditOp>>, 
                    i       : usize, 
                    j       : usize) -> VecDeque<EditOp> {

    let itr = std::iter::repeat(()).scan((i, j), |s,_| {
            let op       = op_table[s.0][s.1]; 
            let (id, jd) = op.displacement();
            *s = (s.0 - id, s.1 - jd); 
            Some(op)
    }).take_while(|op| !op.eq(&EditOp::Kill));

    let mut stack = VecDeque::new();
    for op in kill.into_iter().chain(itr) {
        stack.push_front(op);
    }
    stack
}




fn main() {

 let mut map = HashMap::new();
    map.insert(EditOp::Copy, 2);
    map.insert(EditOp::Replace, 3);
    map.insert(EditOp::Delete, 2);
    map.insert(EditOp::Insert, 4);
    map.insert(EditOp::Twiddle, 1);
    map.insert(EditOp::Kill, 1);


    let from = "▓▓▓▓\n\
                ▒▒▒▓▓\n\
                ▒▒▒▒▒▓\n\
                ▒▒▒▒▒▒▓\n\
                ▒▒▒▒▒▒▓\n\
                ▒▒▒▒▒▒▒▓\n\
                ▒▒▒▒▒▒▒▓▓▓\n\
                ▒▓▓▓▓▓▓░░░▓\n\
                ▒▓░░░░▓░░░░▓\n\
                ▓░░░░░░▓░▓░▓\n\
                ▓░░░░░░▓░░░▓\n\
                ▓░░▓░░░▓▓▓▓\n\
                ▒▓░░░░▓▒▒▒▒▓\n\
                ▒▒▓▓▓▓▒▒▒▒▒▓\n\
                ▒▒▒▒▒▒▒▒▓▓▓▓\n\
                ▒▒▒▒▒▓▓▓▒▒▒▒▓\n\
                ▒▒▒▒▓▒▒▒▒▒▒▒▒▓\n\
                ▒▒▒▓▒▒▒▒▒▒▒▒▒▓\n\
                ▒▒▓▒▒▒▒▒▒▒▒▒▒▒▓\n\
                ▒▓▒▓▒▒▒▒▒▒▒▒▒▓\n\
                ▒▓▒▓▓▓▓▓▓▓▓▓▓\n\
                ▒▓▒▒▒▒▒▒▒▓\n\
                ▒▒▓▒▒▒▒▒▓";


    let to = "│▒│ /▒/\n\
              │▒│/▒/\n\
              │▒/▒/─┬─┐\n\
              │▒│▒|▒│▒│\n\
              ┌┴─┴─┐-┘─┘\n\
              │▒┌──┘▒▒▒│\n\
              └┐▒▒▒▒▒▒  ";

    let (c, s) = edit_distance(&from, &to, &map);  
    let result = edit(&from, &to, &s);


    println!("cost = {}", c);
    println!("{:?}", s);
    println!("{}", result);
}

Test:

use rand::Rng;

fn random_string(size: usize) -> String {
    (0..size).map(|_|rand::random::<char>()).collect()
}
#[test]
fn test_for_accurate_edition(){

    let mut map = HashMap::new();
    map.insert(EditOp::Copy, 2);
    map.insert(EditOp::Replace, 3);
    map.insert(EditOp::Delete, 2);
    map.insert(EditOp::Insert, 4);
    map.insert(EditOp::Twiddle, 1);
    map.insert(EditOp::Kill, 1);

    let size_generator = || rand::thread_rng().gen_range(100, 500);
    for _ in 0..100 {
        let from = random_string(size_generator());
        let to = random_string(size_generator());
        let (_, s) = edit_distance(&from, &to, &map);  
        let result = edit(&from, &to, &s);
        assert_eq!(to, result);          
     }
}
\$\endgroup\$
1
3
\$\begingroup\$

Here's a lightweight review...

  1. You can combine imports with {}: use std::collections::{HashMap, VecDeque};
  2. Consider importing enum variants in methods that exhaustively match on a lot of them. This helps avoid duplication and rightward pushing of code.
  3. Accept a generic type that implements an iterator, instead of the specific std::str::Chars.
  4. Introduce more and unique types, especially when you have repeated parallel names (i, iprev, icurrent). This also allows you to move functionality into methods.
  5. Introduce type aliases. This is a tiny step towards official types, but gives an opportunity to introduce names and shorten them.
  6. Instead of VecDeque, use a normal Vec, then you can use Iterator::collect and reverse it.
  7. Use a == &b instead of a.eq(&b).
  8. I always recommend using expect instead of unwrap. When the panic happens, you will be much happier having some context of where the failure is.
  9. Maybe introduce a dedicated struct for the cost mapping. Then you can implement Default, and there's no chance of missing a key.
  10. Use &[T] instead of &Vec<T>. Faster and more usable.
  11. [Clippy] Combine identical match arms with Foo | Bar.
  12. [Clippy] Use map_or instead of map().unwrap_or.
  13. [Clippy] Can use cloned instead of |x| *x.
  14. [Clippy] Calls to edit and edit_distance have extra references.
  15. Check out rustfmt, which, let's say disagrees, with some of your style choices.

Unfortunately, I found the code very dense, which made reading over it fairly difficult. It's possible some more verbose names could help. Here's a cherry-picked sample of code that takes a second to mentally process :

.map(|(x, c)| {
    let (di, dj) = x.displacement();
    (x, cost_table[i - di][j - dj] + c)
})

extern crate rand;

use std::collections::HashMap;

#[derive(Debug, Copy, Clone, PartialEq, Eq, Hash)]
enum EditOp {
    Copy,
    Replace,
    Delete,
    Insert,
    Twiddle,
    Kill,
}

#[derive(Debug, Copy, Clone)]
struct FindBetterName {
    idx: usize,
    prev: char,
    current: char,
}

impl FindBetterName {
    fn valid_twiddle(&self, other: &FindBetterName) -> bool {
        self.idx > 1 && other.idx > 1 && self.current == other.prev && self.prev == other.current
    }
}

impl EditOp {
    fn valid(&self, i: FindBetterName, j: FindBetterName) -> bool {
        use EditOp::*;

        let threshold = |p| i.idx != p || j.idx == p;

        match *self {
            Copy => threshold(1) && i.current == j.current,
            Replace => threshold(1),
            Delete => i.idx > 1,
            Twiddle => threshold(2) && i.valid_twiddle(&j),
            _ => true,
        }
    }

    fn displacement(&self) -> (usize, usize) {
        use EditOp::*;

        match *self {
            Copy | Replace => (1, 1),
            Delete => (1, 0),
            Insert => (0, 1),
            Twiddle => (2, 2),
            Kill => (0, 0),
        }
    }

    fn apply<F, T>(&self, mut from_itr: F, mut to_itr: T, result: &mut String)
        where F: Iterator<Item = char>,
              T: Iterator<Item = char>
    {
        use EditOp::*;

        match *self {
            Copy => {
                result.push(from_itr.next().unwrap());
                to_itr.next();
            }
            Replace => {
                result.push(to_itr.next().unwrap());
                from_itr.next();
            }
            Delete => {
                from_itr.next();
            }
            Insert => {
                result.push(to_itr.next().unwrap());
            }
            Twiddle => {
                let second = from_itr.next().unwrap();
                let first = from_itr.next().unwrap();
                result.push(first);
                result.push(second);
                to_itr.next();
                to_itr.next();
            }
            Kill => {}
        }
    }
}

type CostMap = HashMap<EditOp, usize>;

fn create_tables(from_len: usize,
                 to_len: usize,
                 costs: &CostMap)
                 -> (Vec<Vec<EditOp>>, Vec<Vec<usize>>) {
    let mut op_table = vec![ vec![EditOp::Kill; to_len]; from_len ];
    let mut cost_table = vec![ vec![0usize; to_len]; from_len ];
    let delete_cost = costs.get(&EditOp::Delete).cloned().unwrap_or(0);

    for (i, c) in (1..from_len).map(|i| (i, i * delete_cost)) {
        cost_table[i][0] = c;
        op_table[i][0] = EditOp::Delete;
    }

    (op_table, cost_table)
}

fn edit_distance(from: &str, to: &str, costs: &CostMap) -> (usize, Operations) {
    if costs.is_empty() {
        panic!("map of costs is empty");
    }

    let from_len = from.chars().count();
    let to_len = to.chars().count();

    let (mut op_table, mut cost_table) = create_tables(from_len + 1, to_len + 1, costs);
    let (mut lasti, mut lastj) = (' ', ' ');

    for (i, ichar) in from.chars().enumerate() {
        for (j, jchar) in to.chars().enumerate() {
            let (i, j) = (i + 1, j + 1);
            let ii = FindBetterName {
                idx: i,
                prev: lasti,
                current: ichar,
            };
            let jj = FindBetterName {
                idx: j,
                prev: lastj,
                current: jchar,
            };

            let (op, cost) = costs.iter()
                .filter(|&(x, _)| x != &EditOp::Kill)
                .filter(|&(x, _)| x.valid(ii, jj))
                .map(|(x, c)| {
                    let (di, dj) = x.displacement();
                    (x, cost_table[i - di][j - dj] + c)
                })
                .min_by_key(|&(_, c)| c)
                .unwrap();

            cost_table[i][j] = cost;
            op_table[i][j] = *op;
            lastj = jchar;
        }
        lasti = ichar;
    }

    let no_kill_cost = cost_table[from_len][to_len];
    let (i, cost, kill) = costs.get(&EditOp::Kill)
        .map_or((from_len, no_kill_cost, None), |kc| {
            min_with_kill(&cost_table, from_len, to_len, *kc)
        });

    (cost, build_operations(kill, &op_table, i, to_len))
}

type Operations = Vec<EditOp>;
type OperationsSlice<'a> = &'a [EditOp];

fn edit(from: &str, to: &str, ops: OperationsSlice) -> String {
    let mut result = String::new();
    let mut from_itr = from.chars();
    let mut to_itr = to.chars();

    for op in ops {
        op.apply(&mut from_itr, &mut to_itr, &mut result);
    }
    result
}

fn min_with_kill(cost_table: &[Vec<usize>],
                 from_size: usize,
                 to_size: usize,
                 kill_cost: usize)
                 -> (usize, usize, Option<EditOp>) {

    let no_kill_cost = cost_table[from_size][to_size];
    (1..from_size)
        .map(|i| (i, cost_table[i][to_size] + kill_cost))
        .map(|(i, c)| (i, c, Some(EditOp::Kill)))
        .chain(Some((from_size, no_kill_cost, None)).into_iter())
        .min_by_key(|&(_, cost, _)| cost)
        .unwrap()
}

fn build_operations(kill: Option<EditOp>,
                    op_table: &[Vec<EditOp>],
                    i: usize,
                    j: usize)
                    -> Operations {

    let itr = std::iter::repeat(())
        .scan((i, j), |s, _| {
            let op = op_table[s.0][s.1];
            let (id, jd) = op.displacement();
            *s = (s.0 - id, s.1 - jd);
            Some(op)
        })
        .take_while(|op| op != &EditOp::Kill);

    let mut stack: Vec<_> = kill.into_iter().chain(itr).collect();
    stack.reverse();
    stack
}


fn main() {
    let mut cost_map = HashMap::new();
    cost_map.insert(EditOp::Copy, 2);
    cost_map.insert(EditOp::Replace, 3);
    cost_map.insert(EditOp::Delete, 2);
    cost_map.insert(EditOp::Insert, 4);
    cost_map.insert(EditOp::Twiddle, 1);
    cost_map.insert(EditOp::Kill, 1);


    let from = "▓▓▓▓\n\
                ▒▒▒▓▓\n\
                ▒▒▒▒▒▓\n\
                ▒▒▒▒▒▒▓\n\
                ▒▒▒▒▒▒▓\n\
                ▒▒▒▒▒▒▒▓\n\
                ▒▒▒▒▒▒▒▓▓▓\n\
                ▒▓▓▓▓▓▓░░░▓\n\
                ▒▓░░░░▓░░░░▓\n\
                ▓░░░░░░▓░▓░▓\n\
                ▓░░░░░░▓░░░▓\n\
                ▓░░▓░░░▓▓▓▓\n\
                ▒▓░░░░▓▒▒▒▒▓\n\
                ▒▒▓▓▓▓▒▒▒▒▒▓\n\
                ▒▒▒▒▒▒▒▒▓▓▓▓\n\
                ▒▒▒▒▒▓▓▓▒▒▒▒▓\n\
                ▒▒▒▒▓▒▒▒▒▒▒▒▒▓\n\
                ▒▒▒▓▒▒▒▒▒▒▒▒▒▓\n\
                ▒▒▓▒▒▒▒▒▒▒▒▒▒▒▓\n\
                ▒▓▒▓▒▒▒▒▒▒▒▒▒▓\n\
                ▒▓▒▓▓▓▓▓▓▓▓▓▓\n\
                ▒▓▒▒▒▒▒▒▒▓\n\
                ▒▒▓▒▒▒▒▒▓";


    let to = "│▒│ /▒/\n\
              │▒│/▒/\n\
              │▒/▒/─┬─┐\n\
              │▒│▒|▒│▒│\n\
              ┌┴─┴─┐-┘─┘\n\
              │▒┌──┘▒▒▒│\n\
              └┐▒▒▒▒▒▒  ";

    let (c, s) = edit_distance(from, to, &cost_map);
    let result = edit(from, to, &s);

    println!("cost = {}", c);
    println!("{:?}", s);
    println!("{}", result);
}
\$\endgroup\$
2
\$\begingroup\$

It seems my solution is incorrect for some inputs.

The main problem is in the valid and create_tables functions.

For some reason I added a several conditions in valid so that i will reach zero always after j and this is wrong. For example "a" -> "ha" with insert and copy should be valid. But for this to work properly all j so that i == 0 most have insert in the table (The only way to edit an empty string is with insert).

So valid and create_table will end up like this:

fn create_tables(from_len: usize, 
                 to_len  : usize, 
                 costs   : &HashMap<EditOp, usize>) 
-> (Vec<Vec<EditOp>>, Vec<Vec<usize>>) {    

    let mut op_table   = vec![ vec![EditOp::Kill; to_len]; from_len ];
    let mut cost_table = vec![ vec![0usize; to_len]; from_len ];
    let delete_cost    = *costs.get(&EditOp::Delete).expect("delete most be in costs");
    let insert_cost    = *costs.get(&EditOp::Insert).expect("insert most be in costs");

    for (i, c) in (1.. from_len).map(|i|(i, i * delete_cost)) {
        cost_table[i][0] = c;
        op_table[i][0]   = EditOp::Delete;
    }
    for (j, c) in (1.. to_len).map(|j|(j, j * insert_cost)) {
        cost_table[0][j] = c;
        op_table[0][j]   = EditOp::Insert;
    }  
    (op_table , cost_table)
}

 fn valid(&self,
             i       : usize,
             j       : usize,
             iprev   : char,
             jprev   : char,
             icurrent: char,
             jcurrent: char) -> bool {

        match *self {
            EditOp::Copy    => icurrent == jcurrent,
            EditOp::Twiddle => i > 1 && j > 1
                                && icurrent == jprev
                                && iprev == jcurrent,
            _ => true,                                                          
        }
    }
\$\endgroup\$

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