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#182 in Algorithms


559 lines

backtrack-rs 🦀

Documentation crates.io CI License

backtrack lets you solve backtracking problems simply and generically.

Problems are defined by their scope and checks against possible solutions.

A Scope determines length and allowed values of a solution. The domain defaults to usize, but any T works if it lives as long as its Scope, including references.

The Check or CheckInc trait determines whether a particular combination of values is satisfying.


It is required that solutions shorter than the entire scope, i.e. partial solutions must satisfy if the completed solutions should as well.

Solvers borrow a problem in search for candidate solutions.


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

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

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

impl Scope<'_> for CountDown {
    fn size(&self) -> usize { 3 }
    fn value(&self, index: usize) -> usize { index }
    fn len(&self) -> usize { 4 }

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

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 against a reduced solution, implement CheckInc instead.

The same result as above can be obtained by first computing intermediate values for any given sat check. Such an approach makes sense if work between prior candidate values should be reused.

use backtrack::problem::{CheckInc, Scope};
use backtrack::solvers::{IterSolveCached};
// ...
impl CheckInc for CountDown{
    type Accumulator = (usize, bool);

    fn fold_acc(&self, accu: Option<Self::Accumulator>, x: &usize, _position: usize) -> Self::Accumulator {
        // remember last value and if it was larger than current one
        accu.map_or_else(||(*x, true), |last| (*x, last.0 > *x))

    fn accu_sat(&self, accu: &Self::Accumulator, _x: &usize, _position: usize) -> bool {
// since `CheckInc` works from accumulated state, a solver that caches them should be used
let mut sats = IterSolveCached::new(&CountDown{}).sat_iter();
// ... gives the same results as above


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


backtrack-rs uses criterion for benches.

cargo bench


  • planning / ordered solutions
  • parallelize search

No runtime deps