dsalgo 0.3.10

A package for Datastructures and Algorithms.
Documentation 
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//! Longest Common Subsequence
//! not confused with Longest Common Substring

/// compute dp table.
#[allow(dead_code)]

pub(crate) fn dp<T: PartialEq>(
    a: &[T],
    b: &[T],
) -> Vec<Vec<usize>> {
    let n = a.len();

    let m = b.len();

    let mut l = vec![vec![0; m + 1]; n + 1]; // l
    for i in 0..n {
        for j in 0..m {
            if a[i] == b[j] {
                debug_assert!(l[i + 1][j + 1] <= l[i][j] + 1);

                l[i + 1][j + 1] = l[i][j] + 1;

                continue;
            }

            l[i + 1][j + 1] = l[i][j + 1].max(l[i + 1][j]);
        }
    }

    l
}

/// lcs length.

pub fn len<T: PartialEq>(
    a: &[T],
    b: &[T],
) -> usize {
    dp(a, b)[a.len()][b.len()]
}

/// compute lcs length with O(N) space.

pub fn len_lowmem<T: PartialEq>(
    a: &[T],
    b: &[T],
) -> usize {
    let m = b.len();

    let mut l = vec![0; m + 1];

    for x in a {
        for j in (0..m).rev() {
            if x == &b[j] {
                debug_assert!(l[j + 1] <= l[j] + 1);

                l[j + 1] = l[j] + 1;
            }
        }

        for j in 0..m {
            l[j + 1] = l[j].max(l[j + 1]);
        }
    }

    l[m]
}

/// restore one of the transtion histories.

pub(crate) fn restore(dp: &[Vec<usize>]) -> Vec<(usize, usize)> {
    let mut idx = vec![];

    let mut i = dp.len() - 1;

    let mut j = dp[0].len() - 1;

    while i > 0 && j > 0 {
        let l = dp[i][j];

        if dp[i][j - 1] == l {
            j -= 1;

            continue;
        }

        if dp[i - 1][j] == l {
            i -= 1;

            continue;
        }

        i -= 1;

        j -= 1;

        idx.push((i, j));
    }

    idx.reverse();

    idx
}

pub fn struct_one<T: PartialEq + Clone>(
    a: &[T],
    b: &[T],
) -> Vec<T> {
    restore(&dp(a, b)).into_iter().map(|(i, _)| a[i].clone()).collect()
}

#[cfg(test)]

mod tests {

    use super::*;

    #[test]

    fn test_dp() {
        let s = "axyb".chars().collect::<Vec<_>>();

        let t = "abyxb".chars().collect::<Vec<_>>();

        let lcs = dp(&s, &t);

        let ans = vec![
            [0, 0, 0, 0, 0, 0],
            [0, 1, 1, 1, 1, 1],
            [0, 1, 1, 1, 2, 2],
            [0, 1, 1, 2, 2, 2],
            [0, 1, 2, 2, 2, 3],
        ];

        assert_eq!(lcs, ans);
    }

    #[test]

    fn test_len() {
        let s = "axyb".chars().collect::<Vec<_>>();

        let t = "abyxb".chars().collect::<Vec<_>>();

        assert_eq!(len(&s, &t), 3);
    }

    #[test]

    fn test_len_lowmem() {
        let s = "axyb".chars().collect::<Vec<_>>();

        let t = "abyxb".chars().collect::<Vec<_>>();

        assert_eq!(len_lowmem(&s, &t), 3);
    }

    #[test]

    fn test_restore() {
        let s = "axyb".chars().collect::<Vec<_>>();

        let t = "abyxb".chars().collect::<Vec<_>>();

        let indices = restore(&dp(&s, &t));

        assert_eq!(indices, vec![(0, 0), (2, 2), (3, 4)]);
        // ayb
    }

    #[test]

    fn test_struct_one() {
        let s = "axyb".chars().collect::<Vec<_>>();

        let t = "abyxb".chars().collect::<Vec<_>>();

        assert_eq!(struct_one(&s, &t), vec!['a', 'y', 'b']);
    }
}