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//! Count the total number of possible paths to reach a destination.

use std::hash::Hash;

use rustc_hash::FxHashMap;

fn cached_count_paths<T, FN, IN, FS>(
    start: T,
    successors: &mut FN,
    success: &mut FS,
    cache: &mut FxHashMap<T, usize>,
) -> usize
where
    T: Eq + Hash,
    FN: FnMut(&T) -> IN,
    IN: IntoIterator<Item = T>,
    FS: FnMut(&T) -> bool,
{
    if let Some(&n) = cache.get(&start) {
        return n;
    }

    let count = if success(&start) {
        1
    } else {
        successors(&start)
            .into_iter()
            .map(|successor| cached_count_paths(successor, successors, success, cache))
            .sum()
    };

    cache.insert(start, count);

    count
}

/// Count the total number of possible paths to reach a destination. There must be no loops
/// in the graph, or the function will overflow its stack.
///
/// # Example
///
/// On a 8x8 board, find the total paths from the bottom-left square to the top-right square.
///
/// ```
/// use pathfinding::prelude::count_paths;
///
/// let n = count_paths(
///     (0, 0),
///     |&(x, y)| {
///         [(x + 1, y), (x, y + 1)]
///             .into_iter()
///             .filter(|&(x, y)| x < 8 && y < 8)
///     },
///     |&c| c == (7, 7),
/// );
/// assert_eq!(n, 3432);
/// ```
pub fn count_paths<T, FN, IN, FS>(start: T, mut successors: FN, mut success: FS) -> usize
where
    T: Eq + Hash,
    FN: FnMut(&T) -> IN,
    IN: IntoIterator<Item = T>,
    FS: FnMut(&T) -> bool,
{
    cached_count_paths(
        start,
        &mut successors,
        &mut success,
        &mut FxHashMap::default(),
    )
}