backtrack-rs 🦀

backtrack-rs lets you define and solve backtracking problems succinctly.

Problems are defined by their scope and checks against possible solutions. The Scope determines length and allowed values for possible solution. The Check or CheckInc trait determines whether a particular combination of values is satisfactory.

Usage

It is required that partial solutions, i.e. shorter solutions than in scope must satisfy if a complete solutions should as well. Solvers borrow the problem for the duration of their search for candidate solutions.

Checks

We define the problem of counting down with a limited set of numbers and solve iteratively.

use backtrack_rs::problem::{Check, Scope};
use backtrack_rs::solvers::IterSolveNaive;
// helper trait to filter solutions of interest
use backtrack_rs::solve::IterSolveExt;

/// Obtain permutations of some 3 descending numbers
struct CountDown {}

impl Scope for CountDown {
    fn size(&self) -> usize { 3 }
    fn domain(&self) -> Vec<usize> { (0..=3).collect() }
}

impl Check for CountDown{
    fn extends_sat(&self, solution: &[usize], x_l: usize) -> bool {
        solution.last().map_or(true, |last| *last > x_l)
    }
}

let solver = IterSolveNaive::new(&CountDown{});
let mut sats = solver.sat_iter();

assert_eq!(sats.next(), Some(vec![2, 1, 0]));
assert_eq!(sats.next(), Some(vec![3, 1, 0]));
assert_eq!(sats.next(), Some(vec![3, 2, 0]));
assert_eq!(sats.next(), Some(vec![3, 2, 1]));
assert_eq!(sats.next(), None);

Incremental Checks

If your checks can be formulated with a reduced solution, implement CheckInc instead.

The same result as above can be formulated by "computing" the last item at each step. This approach makes more sense if actual work on more than one prior value needs to be peformed for any given sat check.

use backtrack_rs::problem::{CheckInc, Scope};
// ...
impl CheckInc for CountDown{
    type Accumulator = usize;

    fn fold_acc(&self, accu: Option<Self::Accumulator>, x: &usize) -> Self::Accumulator {
        // only last value is of interest for checking
        *x
    }

    fn accu_sat(&self, accu: Option<&Self::Accumulator>, x: &usize, index: usize) -> bool {
       accu.map_or(true, |last| last > x)
    }
}
// since `CheckInc` impls `Check`, the same solver as in example above can be used
// todo: specialize solver to actually realize performance advantage
// ...

Examples

Checkout the examples folder for example problems.

# 4-queens solution
cargo run --example n_queens 4 | grep Sat
## n_queens.rs: NQueens { n: 4 }
## Sat([1, 3, 0, 2])
## Sat([2, 0, 3, 1])

# sequence of numbers which sum up to a minimum value but not more
cargo run --example total_sum | grep Sat

Benchmarks

backtrack-rs uses criterion for benches.

cargo benches

Todos

• CheckInc solver
• generic domain values
• parallelize search