use super::{Axis, Key, Measure, Tag};
use std::sync::OnceLock;

/// One OEIS entry the tree cites, with the design sequence it names when it names one.
#[derive(Clone, Copy, Debug, PartialEq, Eq)]
pub struct Record {
    /// The OEIS id.
    pub id: &'static str,
    /// The entry's name.
    pub name: &'static str,
    /// The index of the first listed term.
    pub offset: i32,
    /// The record's index less the ledger's, where a key names the sequence.
    pub shift: i32,
    /// The first terms, as text.
    pub terms: &'static str,
    /// The status of the identification.
    pub status: Tag,
    /// The design sequence the entry names, when it names one.
    pub key: Option<Key>,
    /// The formula, or none.
    pub formula: &'static str,
    /// The generator or page that witnesses the entry.
    pub witness: &'static str,
}

const fn record(
    id: &'static str,
    name: &'static str,
    offset: i32,
    terms: &'static str,
    status: Tag,
    formula: &'static str,
    witness: &'static str,
) -> Record {
    Record {
        id,
        name,
        offset,
        shift: 0,
        terms,
        status,
        key: None,
        formula,
        witness,
    }
}

impl Record {
    const fn keyed(
        self,
        code: u128,
        dimension: usize,
        measure: Measure,
        axis: Axis,
        shift: i32,
    ) -> Record {
        Record {
            shift,
            key: Some(Key::new(code, dimension, 2, measure, axis)),
            ..self
        }
    }
}

const FILLS: &str = "mrlymath::formulas::fill";
const SIDES: &str = "mrlylab::ledger::terms, the odd-side law";
const EXPOSURE: &str = "mrlymath::formulas::exposure";

/// Every OEIS entry the tree cites, by id.
pub static RECORDS: &[Record] = &[
    record("A000029", "Number of necklaces with n beads of 2 colors, allowing turning over (bracelets)", 0, "1, 2, 3, 4, 6, 8, 13, 18, 30, 46, 78, 126", Tag::Verified, "none", "mrlymath::bang::baseq::bracelets, the base line at dim 1"),
    record("A000070", "a(n) = Sum_{k=0..n} p(k) where p(k) = number of partitions of k", 0, "1, 2, 4, 7, 12, 19, 30, 45, 67, 97, 139, 195", Tag::Verified, "none", "REFS.md"),
    record("A000244", "Powers of 3: a(n) = 3^n", 0, "1, 3, 9, 27, 81, 243, 729, 2187, 6561, 19683, 59049, 177147", Tag::Proved, "3^level", "mrlymath::three::diagonal, every admissible cut of bang dim 3, code 126 at side 2"),
    record("A000290", "The squares: a(n) = n^2", 0, "0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121", Tag::Proved, "k^2", SIDES).keyed(1, 2, Measure::Fills, Axis::Side, 0),
    record("A000351", "Powers of 5: a(n) = 5^n", 0, "1, 5, 25, 125, 625, 3125, 15625, 78125, 390625, 1953125, 9765625, 48828125", Tag::Proved, "5^level", FILLS).keyed(9, 2, Measure::Fills, Axis::Level, 0),
    record("A000370", "Number of NPN-equivalence classes of Boolean functions of n or fewer variables", 0, "1, 2, 4, 14, 222, 616126, 200253952527184", Tag::Verified, "none", "bijection.md, the NPN sibling at dim 1..4"),
    record("A000384", "Hexagonal numbers: a(n) = n*(2*n-1)", 0, "0, 1, 6, 15, 28, 45, 66, 91, 120, 153, 190, 231", Tag::Proved, "k(2k - 1)", SIDES).keyed(3, 2, Measure::Fills, Axis::Side, 0),
    record("A000420", "Powers of 7: a(n) = 7^n", 0, "1, 7, 49, 343, 2401, 16807, 117649, 823543, 5764801, 40353607, 282475249, 1977326743", Tag::Proved, "7^level", FILLS).keyed(11, 2, Measure::Fills, Axis::Level, 0),
    record("A000567", "Octagonal numbers: n*(3*n-2)", 0, "0, 1, 8, 21, 40, 65, 96, 133, 176, 225, 280, 341", Tag::Proved, "k(3k - 2)", SIDES).keyed(7, 2, Measure::Fills, Axis::Side, 0),
    record("A000578", "The cubes: a(n) = n^3", 0, "0, 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000, 1331", Tag::Proved, "k^3", SIDES).keyed(1, 3, Measure::Fills, Axis::Side, 0),
    record("A000616", "a(-1)=1 by convention; for n >= 0, a(n) = number of irreducible Boolean functions of n variables", -1, "1, 2, 3, 6, 22, 402, 1228158, 400507806843728", Tag::Proved, "none", "mrlymath::bang::counting::sequence, bijection.md"),
    record("A001018", "Powers of 8: a(n) = 8^n", 0, "1, 8, 64, 512, 4096, 32768, 262144, 2097152, 16777216, 134217728, 1073741824, 8589934592", Tag::Proved, "8^level", FILLS).keyed(7, 2, Measure::Fills, Axis::Level, 0),
    record("A001024", "Powers of 15: a(n) = 15^n", 0, "1, 15, 225, 3375, 50625, 759375, 11390625, 170859375, 2562890625, 38443359375", Tag::Verified, "15^n", "REFS.md"),
    record("A001316", "Gould's sequence: number of odd entries in row n of Pascal's triangle", 0, "1, 2, 2, 4, 2, 4, 4, 8, 2, 4, 4, 8", Tag::Verified, "2^wt(n)", "REFS.md"),
    record("A001481", "Numbers that are the sum of 2 squares", 1, "0, 1, 2, 4, 5, 8, 9, 10, 13, 16, 17, 18", Tag::Verified, "none", "spin.md, the ring radii of a spun square lattice"),
    record("A001844", "Centered square numbers: a(n) = 2*n*(n+1)+1", 0, "1, 5, 13, 25, 41, 61, 85, 113, 145, 181, 221, 265", Tag::Proved, "2k^2 - 2k + 1", SIDES).keyed(9, 2, Measure::Fills, Axis::Side, -1),
    record("A002407", "Cuban primes: primes which are the difference of two consecutive cubes", 1, "7, 19, 37, 61, 127, 271, 331, 397, 547, 631, 919, 1657", Tag::Verified, "none", "mrlymath::formulas::six theorems, slices.md"),
    record("A003136", "Loeschian numbers: numbers of the form x^2 + xy + y^2", 1, "0, 1, 3, 4, 7, 9, 12, 13, 16, 19, 21, 25", Tag::Verified, "none", "spin.md, the ring radii of a spun hexagonal lattice"),
    record("A003180", "Number of equivalence classes of Boolean functions of n variables under action of symmetric group", 0, "2, 4, 12, 80, 3984, 37333248, 25626412338274304", Tag::Verified, "none", "bijection.md, the axis-permutation orbits at a one-term shift"),
    record("A003215", "Hex (or centered hexagonal) numbers: 3*n*(n+1)+1", 0, "1, 7, 19, 37, 61, 91, 127, 169, 217, 271, 331, 397", Tag::Proved, "3k^2 - 3k + 1", SIDES).keyed(11, 2, Measure::Fills, Axis::Side, -1),
    record("A003463", "a(n) = (5^n - 1)/4", 0, "0, 1, 6, 31, 156, 781, 3906, 19531, 97656, 488281, 2441406, 12207031", Tag::Verified, "(5^n - 1)/4", "REFS.md"),
    record("A004016", "Theta series of planar hexagonal lattice A_2", 0, "1, 6, 0, 6, 6, 0, 0, 12, 0, 6, 0, 0", Tag::Verified, "none", "mrlydemo::ring_weights, spin.md"),
    record("A004018", "Theta series of square lattice: number of ways of writing n as a sum of 2 squares", 0, "1, 4, 4, 0, 4, 8, 0, 0, 4, 4, 8, 0", Tag::Verified, "4(d_1(n) - d_3(n))", "mrlydemo::ring_weights, spin.md"),
    record("A004662", "Powers of 3 written in base 8", 0, "1, 3, 11, 33, 121, 363, 1331, 4213, 14641, 46343, 163251, 531773", Tag::Verified, "none", "this page, a near miss of A396934 - 1"),
    record("A005418", "Number of (n-1)-bead black-white reversible strings", 1, "1, 2, 3, 6, 10, 20, 36, 72, 136, 272, 528, 1056", Tag::Verified, "none", "REFS.md"),
    record("A005728", "Number of fractions in Farey series of order n", 0, "1, 2, 3, 5, 7, 11, 13, 19, 23, 29, 33, 43", Tag::Verified, "1 + sum of phi(k) for k <= n", "mrlynum::lattice::farey, the lit nodes of the stack in farey.md"),
    record("A005898", "Centered cube numbers: n^3 + (n+1)^3", 0, "1, 9, 35, 91, 189, 341, 559, 855, 1241, 1729, 2331, 3059", Tag::Proved, "k^3 + (k - 1)^3", SIDES).keyed(129, 3, Measure::Fills, Axis::Side, -1),
    record("A009964", "Powers of 20", 0, "1, 20, 400, 8000, 160000, 3200000, 64000000, 1280000000, 25600000000, 512000000000", Tag::Proved, "20^level", FILLS).keyed(23, 3, Measure::Fills, Axis::Level, 0),
    record("A009971", "Powers of 27", 0, "1, 27, 729, 19683, 531441, 14348907, 387420489, 10460353203, 282429536481, 7625597484987", Tag::Proved, "27^level", FILLS).keyed(255, 3, Measure::Fills, Axis::Level, 0),
    record("A011934", "a(n) = abs(1^3 - 2^3 + 3^3 - 4^3 + ... + (-1)^(n+1)*n^3)", 0, "0, 1, 7, 20, 44, 81, 135, 208, 304, 425, 575, 756", Tag::Verified, "none", "this page, the parent of the bisections A103532 and A395241"),
    record("A016185", "a(n) = 9^n - 8^n", 0, "0, 1, 17, 217, 2465, 26281, 269297, 2685817, 26269505, 253202761, 2413042577, 22791125017", Tag::Proved, "9^level - 8^level", "mrlymath::formulas::void").keyed(7, 2, Measure::Voids, Axis::Level, 0),
    record("A016754", "Odd squares: a(n) = (2n+1)^2, also centered octagonal numbers", 0, "1, 9, 25, 49, 81, 121, 169, 225, 289, 361, 441, 529", Tag::Proved, "(2k - 1)^2", SIDES).keyed(15, 2, Measure::Fills, Axis::Side, -1),
    record("A016755", "Odd cubes: a(n) = (2*n + 1)^3", 0, "1, 27, 125, 343, 729, 1331, 2197, 3375, 4913, 6859, 9261, 12167", Tag::Proved, "(2k - 1)^3", SIDES).keyed(255, 3, Measure::Fills, Axis::Side, -1),
    record("A018413", "Divisors of 363", 1, "1, 3, 11, 33, 121, 363", Tag::Verified, "none", "this page, a near miss of A396934 - 1"),
    record("A034474", "a(n) = 5^n + 1", 0, "2, 6, 26, 126, 626, 3126, 15626, 78126, 390626, 1953126, 9765626, 48828126", Tag::Verified, "5^n + 1", "REFS.md"),
    record("A047999", "Sierpinski's triangle (or gasket): Pascal's triangle read by rows mod 2", 0, "1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0", Tag::Verified, "none", "coprime.md, the points i AND j = 0"),
    record("A048883", "a(n) = 3^wt(n), where wt(n) = A000120(n)", 0, "1, 3, 3, 9, 3, 9, 9, 27, 3, 9, 9, 27", Tag::Verified, "3^wt(n)", "REFS.md"),
    record("A054247", "Number of n X n binary matrices under action of dihedral group of the square D_4", 0, "1, 2, 6, 102, 8548, 4211744, 8590557312, 70368882591744, 2305843028004192256", Tag::Verified, "none", "README.md, the rigid hypercube census at dim 2"),
    record("A065473", "Decimal expansion of the strongly carefree constant: Product_{p prime} (1 - (3*p-2)/(p^3))", 0, "2, 8, 6, 7, 4, 7, 4, 2, 8, 4, 3, 4", Tag::Verified, "none", "coprime.md"),
    record("A069403", "a(n) = 2*Fibonacci(2*n+1) - 1", 0, "1, 3, 9, 25, 67, 177, 465, 1219, 3193, 8361, 21891, 57313", Tag::Verified, "2 F(2n + 1) - 1", "REFS.md"),
    record("A103532", "Number of divisors of 240^n", 0, "1, 20, 81, 208, 425, 756, 1225, 1856, 2673, 3700, 4961, 6480", Tag::Proved, "(4k - 3)k^2", SIDES).keyed(23, 3, Measure::Fills, Axis::Side, -1),
    record("A125833", "Numbers whose base-5 representation is 333333.......3", 0, "0, 3, 18, 93, 468, 2343, 11718, 58593, 292968, 1464843, 7324218, 36621093", Tag::Verified, "3(5^n - 1)/4", "REFS.md"),
    record("A128625", "Expansion of (1+3*x)/(1-5*x)", 0, "1, 8, 40, 200, 1000, 5000, 25000, 125000, 625000, 3125000, 15625000, 78125000", Tag::Verified, "8 5^(n-1) for n >= 1", "REFS.md"),
    record("A129824", "a(n) = Product_{k=0..n} (1 + binomial(n,k))", 0, "2, 4, 12, 64, 700, 17424, 1053696, 160579584, 62856336636, 63812936890000, 168895157342195152, 1169048914836855865344", Tag::Proved, "Prod_{k=0}^{n} (1 + C(n,k))", "lab/rs/design-census, the fill classes of base 2"),
    record("A141148", "Number of aperiodic ternary necklaces with n beads of each color and no adjacent beads of the same color", 1, "2, 3, 14, 65, 346, 1929, 11442, 70310, 445928, 2896239, 19186738, 129184583", Tag::Verified, "none", "REFS.md"),
    record("A154105", "a(n) = 12*n^2 + 18*n + 7", 0, "7, 37, 91, 169, 271, 397, 547, 721, 919, 1141, 1387, 1657", Tag::Verified, "12n^2 + 18n + 7", "slices.md, the centered hexagonal vertices at n = k - 1"),
    record("A192908", "Constant term in the reduction by (x^2 -> x + 1) of a polynomial family; a(n) = 2*Fibonacci(2n-2) + 1", 0, "1, 1, 3, 7, 17, 43, 111, 289, 755, 1975, 5169, 13531", Tag::Verified, "2 F(2n - 2) + 1", "REFS.md"),
    record("A229896", "Sizes of logical groups of the same integer in A229895", 1, "1, 1, 4, 1, 5, 27, 1, 7, 37, 256, 1, 9, 61, 369, 3125, 1, 11, 91, 671, 4651, 46656, 1, 13, 127, 1105, 9031, 70993, 823543, 1, 15, 169, 1695, 15961, 144495, 1273609, 16777216, 1, 17, 217, 2465, 26281, 269297, 2685817, 26269505, 387420489", Tag::Verified, "none", "this page, an interior window holding the carpet voids"),
    record("A255016", "Number of toroidal n X n binary arrays, allowing rotation and/or reflection of rows and/or columns as well as matrix transposition", 0, "1, 2, 6, 26, 805, 172112, 239123150, 1436120190288, 36028817512382026", Tag::Verified, "none", "mrlymath::bang::baseq::sequence at dim 2, bijection.md"),
    record("A268240", "Pascal's tetrahedron of trinomial coefficients read mod 2", 0, "1, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1", Tag::Verified, "none", "REFS.md"),
    record("A299916", "a(n) = A299914(2n+1); the six-pointed-star holes of the Menger slice, by a comment", 0, "1, 6, 42, 306, 2250, 16578, 122202, 900882, 6641514, 48963042, 360969210, 2661166386", Tag::Verified, "a(n) = 9a(n-1) - 12a(n-2)", "mrlymath::formulas::cut_fills, slices.md").keyed(23, 3, Measure::Triangles, Axis::Level, 1),
    record("A332705", "Number of unit square faces (or surface area) of a stage-n Menger sponge", 0, "6, 72, 1056, 18048, 336384, 6531072, 129048576, 2568388608, 51267108864, 1024536870912", Tag::Proved, "2*20^level + 4*8^level", EXPOSURE).keyed(23, 3, Measure::Surface, Axis::Level, 0),
    record("A347825", "Number of ways to cut a 2 X n rectangle into rectangles with integer sides up to symmetries of the rectangle", 0, "1, 2, 6, 17, 61, 220, 883, 3597, 15232, 65130, 282294, 1229729", Tag::Verified, "none", "this page, a near miss of A396934/2"),
    record("A361870", "Array read by downward antidiagonals: nonequivalent 2-colorings of the cells of an n-dimensional hypercube with edges k cells long", 0, "2, 2, 1, 2, 2, 1, 2, 3, 2, 1, 2, 6", Tag::Verified, "none", "README.md, the rigid hypercube census"),
    record("A381517", "Perimeter of the Sierpinski carpet at iteration n", 0, "4, 16, 80, 496, 3536, 26992, 212048, 1684720, 13442768, 107437168, 859182416, 6872514544", Tag::Proved, "(4*8^level + 16*3^level)/5", EXPOSURE).keyed(7, 2, Measure::Surface, Axis::Level, 0),
    record("A395134", "Decimal expansion of the probability that the line that passes through two points selected independently and uniformly at random in a half-disk intersects the arc at two points.", 0, "4, 5, 9, 6, 2, 0, 3, 5, 3, 9, 0, 7", Tag::Verified, "1 - 16/(3 Pi^2)", "coprime.md, the complement of the A396934 density"),
    record("A395241", "a(n) = n^2*(4*n + 3)", 0, "0, 7, 44, 135, 304, 575, 972, 1519, 2240, 3159, 4300, 5687", Tag::Verified, "a(n) = n^2*(4*n + 3)", "lab/rs/oeis-terms, the b-file to n = 10000").keyed(23, 3, Measure::Voids, Axis::Side, -1),
    record("A396922", "E.g.f. A(x) satisfies A( x / A(log(A(log(A(log(A(x))))))) ) = exp(x)", 0, "1, 1, 3, 40, 1421, 87896, 7921207, 951512332, 144407735033, 26715045346048", Tag::Verified, "none", "REFS.md"),
    record("A396934", "Number of pairs (i,j) with 0 <= i,j < 2^n, i AND j = 0, and gcd(i,j) = 1", 0, "0, 2, 4, 12, 34, 122, 362, 1130, 3406, 10506, 31550, 95260", Tag::Verified, "none", "lab/rs/oeis-terms, the b-file to n = 20"),
    record("A398348", "Number of toroidal n X n X n binary arrays, allowing rotation and/or reflection of the layers along each axis as well as all permutations of the axes", 1, "2, 22, 111618, 6005363762644688, 7089215977519836239803174210135872, 10157435539019790383692007859901914095646506996125324171134976", Tag::Verified, "none", "lab/rs/oeis-terms, the b-file to n = 14"),
];

/// Finds a record by id.
pub fn record_by_id(id: &str) -> Option<&'static Record> {
    RECORDS.iter().find(|record| record.id == id)
}

fn parsed() -> &'static [Vec<i128>] {
    static PARSED: OnceLock<Vec<Vec<i128>>> = OnceLock::new();
    PARSED.get_or_init(|| {
        RECORDS
            .iter()
            .map(|record| {
                record
                    .terms
                    .split(',')
                    .map_while(|term| term.trim().parse().ok())
                    .collect()
            })
            .collect()
    })
}

impl Record {
    /// Returns the listed terms that fit an i128, in order.
    pub fn parsed(&self) -> &'static [i128] {
        let at = RECORDS
            .iter()
            .position(|record| record.id == self.id)
            .expect("every record is listed");
        &parsed()[at]
    }
}

/// Finds every record holding the terms as a window, with the record's index of the first term.
///
/// ```
/// let found = mrlylab::ledger::identify(&[6, 42, 306, 2250]);
/// assert_eq!(found.iter().map(|(r, s)| (r.id, *s)).collect::<Vec<_>>(), [("A299916", 1)]);
/// ```
pub fn identify(terms: &[i128]) -> Vec<(&'static Record, i32)> {
    if terms.is_empty() {
        return Vec::new();
    }
    let mut found: Vec<(&'static Record, i32)> = RECORDS
        .iter()
        .zip(parsed())
        .filter_map(|(record, known)| {
            known
                .windows(terms.len())
                .position(|window| window == terms)
                .map(|at| (record, record.offset + at as i32))
        })
        .collect();
    found.sort_by_key(|(record, shift)| (record.key.is_none(), shift.abs(), record.id));
    found
}

#[cfg(test)]
mod tests {
    use super::super::{terms, BUDGET, TERMS};
    use super::*;

    #[test]
    fn the_records_are_sorted_distinct_and_parse() {
        for pair in RECORDS.windows(2) {
            assert!(
                pair[0].id < pair[1].id,
                "{} before {}",
                pair[0].id,
                pair[1].id
            );
        }
        for record in RECORDS {
            assert!(record.parsed().len() >= 5, "{}", record.id);
            assert!(!record.name.contains('|'), "{}", record.id);
        }
        assert_eq!(RECORDS.len(), 60);
        assert_eq!(record_by_id("A398348").unwrap().parsed().len(), 5);
    }

    #[test]
    fn every_keyed_record_reads_its_generator_at_its_shift() {
        let mut keyed = 0;
        for record in RECORDS.iter().filter(|record| record.key.is_some()) {
            let key = record.key.unwrap();
            let (got, _) = terms(&key, TERMS, BUDGET).unwrap();
            let known = record.parsed();
            let mut compared = 0;
            for (index, &term) in got.iter().enumerate() {
                let at = key.axis.start() + index as i32 + record.shift - record.offset;
                if let Some(&expected) = usize::try_from(at).ok().and_then(|at| known.get(at)) {
                    assert_eq!(term, expected, "{} at {index}", record.id);
                    compared += 1;
                }
            }
            assert!(compared >= 3, "{} compared {compared}", record.id);
            keyed += 1;
        }
        assert_eq!(keyed, 20);
    }

    #[test]
    fn identify_returns_the_shift() {
        let ids = |terms: &[i128]| -> Vec<(&str, i32)> {
            identify(terms).iter().map(|(r, s)| (r.id, *s)).collect()
        };
        assert_eq!(ids(&[8, 21, 40, 65]), [("A000567", 2)]);
        assert_eq!(ids(&[6, 15, 28]), [("A000384", 2)]);
        assert_eq!(ids(&[72, 1056, 18048]), [("A332705", 1)]);
        assert_eq!(ids(&[1, 17, 217]), [("A016185", 1), ("A229896", 37)]);
        assert_eq!(ids(&[3, 6, 22, 402]), [("A000616", 1)]);
        assert_eq!(ids(&[4, 12, 80, 3984]), [("A003180", 1)]);
        assert_eq!(ids(&[5, 7, 11, 13]), [("A005728", 3)]);
        assert!(ids(&[5, 7, 11, 14]).is_empty());
        assert!(ids(&[]).is_empty());
    }
}