make the ReadAtImpl enum variants private

[pxar.git] / src / binary_tree_array.rs

//! Helpers to generate a binary search tree stored in an array from a
//! sorted array.
//!
//! Specifically, for any given sorted array 'input' permute the
//! array so that the following rule holds:
//!
//! For each array item with index i, the item at 2i+1 is smaller and
//! the item 2i+2 is larger.
//!
//! This structure permits efficient (meaning: O(log(n)) binary
//! searches: start with item i=0 (i.e. the root of the BST), compare
//! the value with the searched item, if smaller proceed at item
//! 2i+1, if larger proceed at item 2i+2, and repeat, until either
//! the item is found, or the indexes grow beyond the array size,
//! which means the entry does not exist.
//!
//! Effectively this implements bisection, but instead of jumping
//! around wildly in the array during a single search we only search
//! with strictly monotonically increasing indexes.
//!
//! Algorithm is from casync (camakebst.c), simplified and optimized
//! for rust. Permutation function originally by L. Bressel, 2017. We
//! pass permutation info to user provided callback, which actually
//! implements the data copy.
//!
//! The Wikipedia Artikel for [Binary
//! Heap](https://en.wikipedia.org/wiki/Binary_heap) gives a short
//! intro howto store binary trees using an array.

use std::cmp::Ordering;

#[allow(clippy::many_single_char_names)]
fn copy_inner<F: FnMut(usize, usize)>(
    copy_func: &mut F,
    // we work on input array input[o..o+n]
    n: usize,
    o: usize,
    e: usize,
    i: usize,
) {
    let p = 1 << e;

    let t = p + (p >> 1) - 1;

    let m = if n > t {
        // |...........p.............t....n........(2p)|
        p - 1
    } else {
        // |...........p.....n.......t.............(2p)|
        p - 1 - (t - n)
    };

    (copy_func)(o + m, i);

    if m > 0 {
        copy_inner(copy_func, m, o, e - 1, i * 2 + 1);
    }

    if (m + 1) < n {
        copy_inner(copy_func, n - m - 1, o + m + 1, e - 1, i * 2 + 2);
    }
}

/// This function calls the provided `copy_func()` with the permutaion information required to
/// build a binary search tree array.
///
/// ```
/// # use pxar::binary_tree_array;
/// # let mut i = 0;
/// # const EXPECTED: &[(usize, usize)] = &[(3, 0), (1, 1), (0, 3), (2, 4), (4, 2)];
/// binary_tree_array::copy(5, |src, dest| {
///    # assert_eq!((src, dest), EXPECTED[i]);
///    # i += 1;
///    println!("Copy {} to {}", src, dest);
/// });
/// ```
///
/// This will produce the folowing output:
///
/// ```no-compile
/// Copy 3 to 0
/// Copy 1 to 1
/// Copy 0 to 3
/// Copy 2 to 4
/// Copy 4 to 2
/// ```
///
/// So this generates the following permuation: `[3,1,4,0,2]`.
pub fn copy<F>(n: usize, mut copy_func: F)
where
    F: FnMut(usize, usize),
{
    if n == 0 {
        return;
    };

    let e = (64 - n.leading_zeros() - 1) as usize; // fast log2(n)

    copy_inner(&mut copy_func, n, 0, e, 0);
}

/// This function searches for the index where the comparison by the provided
/// `compare()` function returns `Ordering::Equal`.
/// The order of the comparison matters (noncommutative) and should be search
/// value compared to value at given index as shown in the examples.
/// The parameter `skip` defines the number of matches to ignore while
/// searching before returning the index in order to lookup duplicate entries in
/// the tree.
///
/// ```
/// # use pxar::binary_tree_array;
/// let mut vals = vec![0,1,2,2,2,3,4,5,6,6,7,8,8,8];
///
/// let clone = vals.clone();
/// binary_tree_array::copy(vals.len(), |s, d| {
///     vals[d] = clone[s];
/// });
/// let should_be = vec![5,2,8,1,3,6,8,0,2,2,4,6,7,8];
/// assert_eq!(vals, should_be);
///
/// let find = 8;
/// let skip = 0;
/// let idx = binary_tree_array::search_by(&vals, 0, skip, |el| find.cmp(el));
/// assert_eq!(idx, Some(2));
///
/// let find = 8;
/// let skip = 1;
/// let idx = binary_tree_array::search_by(&vals, 2, skip, |el| find.cmp(el));
/// assert_eq!(idx, Some(6));
///
/// let find = 8;
/// let skip = 1;
/// let idx = binary_tree_array::search_by(&vals, 6, skip, |el| find.cmp(el));
/// assert_eq!(idx, Some(13));
///
/// let find = 5;
/// let skip = 1;
/// let idx = binary_tree_array::search_by(&vals, 0, skip, |el| find.cmp(el));
/// assert!(idx.is_none());
///
/// let find = 5;
/// let skip = 0;
/// // if start index is equal to the array length, `None` is returned.
/// let idx = binary_tree_array::search_by(&vals, vals.len(), skip, |el| find.cmp(el));
/// assert!(idx.is_none());
///
/// // if start index is larger than length, `None` is returned.
/// let idx = binary_tree_array::search_by(&vals, vals.len() + 1, skip, |el| find.cmp(el));
/// assert!(idx.is_none());
/// ```
pub fn search_by<F, T>(tree: &[T], start: usize, skip: usize, f: F) -> Option<usize>
where
    F: Copy + Fn(&T) -> Ordering,
{
    let mut i = start;

    while i < tree.len() {
        match f(&tree[i]) {
            Ordering::Less => i = 2 * i + 1,
            Ordering::Greater => i = 2 * i + 2,
            Ordering::Equal if skip == 0 => return Some(i),
            Ordering::Equal => {
                i = 2 * i + 1;
                return search_by(tree, i, skip - 1, f)
                    .or_else(move || search_by(tree, i + 1, skip - 1, f));
            }
        }
    }

    None
}

#[test]
fn test_binary_search_tree() {
    fn run_test(len: usize) -> Vec<usize> {
        const MARKER: usize = 0xfffffff;
        let mut output = vec![];
        for _i in 0..len {
            output.push(MARKER);
        }
        copy(len, |s, d| {
            assert!(output[d] == MARKER);
            output[d] = s;
        });
        if len < 32 {
            println!("GOT:{}:{:?}", len, output);
        }
        for i in 0..len {
            assert!(output[i] != MARKER);
        }
        output
    }

    assert!(run_test(0).len() == 0);
    assert!(run_test(1) == [0]);
    assert!(run_test(2) == [1, 0]);
    assert!(run_test(3) == [1, 0, 2]);
    assert!(run_test(4) == [2, 1, 3, 0]);
    assert!(run_test(5) == [3, 1, 4, 0, 2]);
    assert!(run_test(6) == [3, 1, 5, 0, 2, 4]);
    assert!(run_test(7) == [3, 1, 5, 0, 2, 4, 6]);
    assert!(run_test(8) == [4, 2, 6, 1, 3, 5, 7, 0]);
    assert!(run_test(9) == [5, 3, 7, 1, 4, 6, 8, 0, 2]);
    assert!(run_test(10) == [6, 3, 8, 1, 5, 7, 9, 0, 2, 4]);
    assert!(run_test(11) == [7, 3, 9, 1, 5, 8, 10, 0, 2, 4, 6]);
    assert!(run_test(12) == [7, 3, 10, 1, 5, 9, 11, 0, 2, 4, 6, 8]);
    assert!(run_test(13) == [7, 3, 11, 1, 5, 9, 12, 0, 2, 4, 6, 8, 10]);
    assert!(run_test(14) == [7, 3, 11, 1, 5, 9, 13, 0, 2, 4, 6, 8, 10, 12]);
    assert!(run_test(15) == [7, 3, 11, 1, 5, 9, 13, 0, 2, 4, 6, 8, 10, 12, 14]);
    assert!(run_test(16) == [8, 4, 12, 2, 6, 10, 14, 1, 3, 5, 7, 9, 11, 13, 15, 0]);
    assert!(run_test(17) == [9, 5, 13, 3, 7, 11, 15, 1, 4, 6, 8, 10, 12, 14, 16, 0, 2]);

    for len in 18..1000 {
        run_test(len);
    }
}