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use ndarray::*;
use ndarray::{Array1, Array2};

use num_traits::Float;

#[cfg(test)]
mod test;

fn initial_table<T: Float + std::convert::From<i32>>(
    objective: &Array1<T>,
    constraints: &Array2<T>,
    requirements: &Array1<T>,
) -> Array2<T> {
    let n_variables = objective.len();
    // Margen izquierdo, valor de cada variable en la restriccion, columna de requerimientos, variables artificiales
    let dimension_j = 1 + n_variables + 1 + constraints.len_of(Axis(0));
    // Cada restriccion y el renglon z
    let dimension_i = constraints.len_of(Axis(0)) + 1;
    let mut table = Array2::<T>::zeros((dimension_i, dimension_j));
    // Renglon Z
    table[[0, 0]] = 1i32.into();
    for j in 0..objective.len() {
        table[[0, j + 1]] = objective[j];
        table[[0, j + 1]] = table[[0, j + 1]] * (-1).into();
    }
    // Restricciones
    for i in 0..constraints.len_of(Axis(0)) {
        for j in 0..constraints.len_of(Axis(1)) {
            table[[i + 1, j + 1]] = constraints[[i, j]];
        }
    }
    // Requerimientos
    for i in 0..requirements.len() {
        table[[i + 1, dimension_j - 1]] = requirements[i];
    }
    table
}

fn pivot_point<T: Float + std::convert::From<i32>>(table: &Array2<T>) -> Option<[usize; 2]> {
    let mut out_var = None;
    let mut out_var_max = 0.into();
    let mut in_var = None;
    let mut in_var_min = None;

    for j in 1..(table.len_of(Axis(1)) - 1) {
        if table[[0, j]] > out_var_max {
            out_var_max = table[[0, j]];
            out_var = Some(j);
        }
    }

    if let Some(j) = out_var {
        let req = table.len_of(Axis(1)) - 1;
        for i in 1..table.len_of(Axis(0)) {
            if let Some(m) = in_var_min {
                if table[[i, req]] / table[[i, j]] < m && table[[i, req]] / table[[i, j]] > 0.into()
                {
                    in_var_min = Some(table[[i, req]] / table[[i, j]]);
                    in_var = Some(i);
                }
            } else {
                in_var_min = Some(table[[i, req]] / table[[i, j]]);
                in_var = Some(i);
            }
        }
    }
    match (out_var, in_var) {
        (Some(j), Some(i)) => Some([i, j]),
        _ => None,
    }
}

fn gauss<T>(pivot: [usize; 2], table: &mut Array2<T>)
where
    T: Float
        + std::fmt::Debug
        + std::ops::MulAssign
        + std::ops::AddAssign
        + std::ops::DivAssign
        + ndarray::ScalarOperand,
{
    for i in 0..table.len_of(Axis(0)) {
        if i != pivot[0] {
            // Aplicar GAUSS a la fila
            let pivot_n = table[pivot];
            let make_zero = table[[i, pivot[1]]];
            {
                let mut row_pivot = table.row_mut(pivot[0]);
                row_pivot /= pivot_n;
            }
            // Multiplicar la fila de make_zero por pivot_n
            let mut row_pivot = table.row(pivot[0]).to_owned();
            let mut row_make_zero = table.row_mut(i);
            row_make_zero *= pivot_n;
            row_pivot *= -make_zero;
            row_make_zero += &row_pivot;
        }
    }
    let pivot_n = table[[0, 0]];
    let mut row_pivot = table.row_mut(0);
    row_pivot /= pivot_n;
}

// Comprobar si existe solucion, soluciones degeneradas

#[allow(dead_code)]
fn check_optimus() {}

pub fn simplex<T>(
    objective: Array1<T>,
    constraints: Array2<T>,
    requirements: Array1<T>,
) -> Array2<T>
where
    T: Float
        + std::convert::From<i32>
        + std::fmt::Debug
        + std::ops::MulAssign
        + std::ops::AddAssign
        + std::ops::DivAssign
        + ndarray::ScalarOperand,
{
    let mut table = initial_table(&objective, &constraints, &requirements);
    while let Some(pivot) = pivot_point(&table) {
        gauss(pivot, &mut table);
    }
    table
}