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//! Utils for tree traversal strategies

/// 2-torsion tree-traversal strategy
pub type Torsion2Strategy = Vec<usize>;

/// 3-torsion tree-traversal strategy
pub type Torsion3Strategy = Vec<usize>;

/// 2-torsion reference strategy for SIKEp434 (ref C.1.1.)
pub const P434_TWO_TORSION_STRATEGY: [usize; 107] = [
    48, 28, 16, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2,
    1, 1, 13, 7, 4, 2, 1, 1, 2, 1, 1, 3, 2, 1, 1, 1, 1, 5, 4, 2, 1, 1, 2, 1, 1, 2, 1, 1, 1, 21, 12,
    7, 4, 2, 1, 1, 2, 1, 1, 3, 2, 1, 1, 1, 1, 5, 3, 2, 1, 1, 1, 1, 2, 1, 1, 1, 9, 5, 3, 2, 1, 1, 1,
    1, 2, 1, 1, 1, 4, 2, 1, 1, 1, 2, 1, 1,
];

/// 3-torsion reference strategy for SIKEp434 (ref C.1.2.)
pub const P434_THREE_TORSION_STRATEGY: [usize; 136] = [
    66, 33, 17, 9, 5, 3, 2, 1, 1, 1, 1, 2, 1, 1, 1, 4, 2, 1, 1, 1, 2, 1, 1, 8, 4, 2, 1, 1, 1, 2, 1,
    1, 4, 2, 1, 1, 2, 1, 1, 16, 8, 4, 2, 1, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 8, 4, 2, 1, 1, 2,
    1, 1, 4, 2, 1, 1, 2, 1, 1, 32, 16, 8, 4, 3, 1, 1, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 8, 4, 2,
    1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 16, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 8, 4, 2,
    1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1,
];

/// 2-torsion reference strategy for SIKEp503 (ref C.2.1.)
pub const P503_TWO_TORSION_STRATEGY: [usize; 124] = [
    61, 32, 16, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2,
    1, 1, 16, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2,
    1, 1, 29, 16, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1,
    2, 1, 1, 13, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 5, 4, 2, 1, 1, 2, 1, 1, 2, 1, 1, 1,
];

/// 3-torsion reference strategy for SIKEp503 (ref C.2.2.)
pub const P503_THREE_TORSION_STRATEGY: [usize; 158] = [
    71, 38, 21, 13, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 5, 4, 2, 1, 1, 2, 1, 1, 2, 1, 1,
    1, 9, 5, 3, 2, 1, 1, 1, 1, 2, 1, 1, 1, 4, 2, 1, 1, 1, 2, 1, 1, 17, 9, 5, 3, 2, 1, 1, 1, 1, 2,
    1, 1, 1, 4, 2, 1, 1, 1, 2, 1, 1, 8, 4, 2, 1, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 33, 17, 9, 5,
    3, 2, 1, 1, 1, 1, 2, 1, 1, 1, 4, 2, 1, 1, 1, 2, 1, 1, 8, 4, 2, 1, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2,
    1, 1, 16, 8, 4, 2, 1, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1,
    2, 1, 1,
];

/// 2-torsion reference strategy for SIKEp610 (ref C.3.1.)
pub const P610_TWO_TORSION_STRATEGY: [usize; 151] = [
    67, 37, 21, 12, 7, 4, 2, 1, 1, 2, 1, 1, 3, 2, 1, 1, 1, 1, 5, 3, 2, 1, 1, 1, 1, 2, 1, 1, 1, 9,
    5, 3, 2, 1, 1, 1, 1, 2, 1, 1, 1, 4, 2, 1, 1, 1, 2, 1, 1, 16, 9, 5, 3, 2, 1, 1, 1, 1, 2, 1, 1,
    1, 4, 2, 1, 1, 1, 2, 1, 1, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 33, 16, 8, 5, 2, 1, 1,
    1, 2, 1, 1, 1, 4, 2, 1, 1, 2, 1, 1, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 16, 8, 4, 2,
    1, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1,
];

/// 3-torsion reference strategy for SIKEp610 (ref C.3.2.)
pub const P610_THREE_TORSION_STRATEGY: [usize; 191] = [
    86, 48, 27, 15, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 7, 4, 2, 1, 1, 2, 1, 1, 3, 2, 1,
    1, 1, 1, 12, 7, 4, 2, 1, 1, 2, 1, 1, 3, 2, 1, 1, 1, 1, 5, 3, 2, 1, 1, 1, 1, 2, 1, 1, 1, 21, 12,
    7, 4, 2, 1, 1, 2, 1, 1, 3, 2, 1, 1, 1, 1, 5, 3, 2, 1, 1, 1, 1, 2, 1, 1, 1, 9, 5, 3, 2, 1, 1, 1,
    1, 2, 1, 1, 1, 4, 2, 1, 1, 1, 2, 1, 1, 38, 21, 12, 7, 4, 2, 1, 1, 2, 1, 1, 3, 2, 1, 1, 1, 1, 5,
    3, 2, 1, 1, 1, 1, 2, 1, 1, 1, 9, 5, 3, 2, 1, 1, 1, 1, 2, 1, 1, 1, 4, 2, 1, 1, 1, 2, 1, 1, 17,
    9, 5, 3, 2, 1, 1, 1, 1, 2, 1, 1, 1, 4, 2, 1, 1, 1, 2, 1, 1, 8, 4, 2, 1, 1, 1, 2, 1, 1, 4, 2, 1,
    1, 2, 1, 1,
];

/// 2-torsion reference strategy for SIKEp751 (ref C.4.1.)
pub const P751_TWO_TORSION_STRATEGY: [usize; 185] = [
    80, 48, 27, 15, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 7, 4, 2, 1, 1, 2, 1, 1, 3, 2, 1,
    1, 1, 1, 12, 7, 4, 2, 1, 1, 2, 1, 1, 3, 2, 1, 1, 1, 1, 5, 3, 2, 1, 1, 1, 1, 2, 1, 1, 1, 21, 12,
    7, 4, 2, 1, 1, 2, 1, 1, 3, 2, 1, 1, 1, 1, 5, 3, 2, 1, 1, 1, 1, 2, 1, 1, 1, 9, 5, 3, 2, 1, 1, 1,
    1, 2, 1, 1, 1, 4, 2, 1, 1, 1, 2, 1, 1, 33, 20, 12, 7, 4, 2, 1, 1, 2, 1, 1, 3, 2, 1, 1, 1, 1, 5,
    3, 2, 1, 1, 1, 1, 2, 1, 1, 1, 8, 5, 3, 2, 1, 1, 1, 1, 2, 1, 1, 1, 4, 2, 1, 1, 2, 1, 1, 16, 8,
    4, 2, 1, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1,
];

/// 3-torsion reference strategy for SIKEp751 (ref C.4.2.)
pub const P751_THREE_TORSION_STRATEGY: [usize; 238] = [
    112, 63, 32, 16, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1,
    1, 2, 1, 1, 16, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1,
    1, 2, 1, 1, 31, 16, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2,
    1, 1, 2, 1, 1, 15, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 7, 4, 2, 1, 1, 2, 1, 1, 3, 2,
    1, 1, 1, 1, 49, 31, 16, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 8, 4, 2, 1, 1, 2, 1, 1, 4,
    2, 1, 1, 2, 1, 1, 15, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 7, 4, 2, 1, 1, 2, 1, 1, 3,
    2, 1, 1, 1, 1, 21, 12, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 5, 3, 2, 1, 1, 1, 1, 2, 1,
    1, 1, 9, 5, 3, 2, 1, 1, 1, 1, 2, 1, 1, 1, 4, 2, 1, 1, 1, 2, 1, 1,
];

/// Computing optimised strategy (ref `compute_strategy`, Algorithm 46 p. 75).
///   * Input: strategy size `n`, parameters `p`, `q`
///   * Output: optimal strategy of size `n`  
///
/// # Examples
/// ```rust
/// use rust_sike::compute_strategy;
/// let strat = compute_strategy(12, 13, 14);
/// println!("{:?}", strat);
/// ```
pub fn compute_strategy(n: usize, p: u64, q: u64) -> Result<Vec<usize>, &'static str> {
    // 1.
    let mut strategies = vec![vec![]];

    // 2.
    let mut cost = vec![0];

    let eval = |c: &Vec<u64>, i: u64, b: u64| {
        c[(i - b) as usize - 1] + c[b as usize - 1] + b * p + (i - b) * q
    };

    // 3.
    for i in 2..=(n as u64 + 1) {
        // 4.
        let mut min_val = eval(&cost, i, 1);
        let mut b = 1;
        for b_val in 2..i {
            let c_val = eval(&cost, i, b_val);
            if c_val < min_val {
                min_val = c_val;
                b = b_val;
            }
        }

        // 5.
        let mut new_strat = vec![b as usize];
        new_strat.extend(&strategies[(i - b - 1) as usize]);
        new_strat.extend(&strategies[b as usize - 1]);
        strategies.push(new_strat);

        // 6.
        cost.push(min_val);
    }

    // 7.
    match strategies.last() {
        Some(s) => Ok(s.to_vec()),
        None => Err("No valid strategy found"),
    }
}