use crate::Graph;

pub fn theorem3_1(g: &Graph) -> bool {
    let claw = Graph {
        size: 4,
        matrix: vec![
            vec![0, 1, 1, 1],
            vec![1, 0, 0, 0],
            vec![1, 0, 0, 0],
            vec![1, 0, 0, 0],
        ],
    };

    let z1 = Graph {
        size: 4,
        matrix: vec![
            vec![0, 1, 0, 0],
            vec![1, 0, 1, 1],
            vec![0, 1, 0, 1],
            vec![0, 1, 1, 0],
        ],
    };

    let forbidden = vec![claw, z1];

    return g.is_2_connected() && g.is_free_of(&forbidden);
}

pub fn theorem3_2(g: &Graph) -> bool {
    let claw = Graph {
        size: 4,
        matrix: vec![
            vec![0, 1, 1, 1],
            vec![1, 0, 0, 0],
            vec![1, 0, 0, 0],
            vec![1, 0, 0, 0],
        ],
    };

    let forbidden = vec![claw];
    return g.size >= 3
        && g.is_connected()
        && g.is_locally_connected()
        && g.is_free_of(&forbidden);
}

pub fn corollary3_5(g: &Graph) -> bool {
    let claw = Graph {
        size: 4,
        matrix: vec![
            vec![0, 1, 1, 1],
            vec![1, 0, 0, 0],
            vec![1, 0, 0, 0],
            vec![1, 0, 0, 0],
        ],
    };

    let ig = Graph {
        size: 4,
        matrix: vec![
            vec![0, 1, 0, 0],
            vec![1, 0, 1, 0],
            vec![0, 1, 0, 1],
            vec![0, 0, 1, 0],
        ],
    };

    let ag = Graph {
        size: 5,
        matrix: vec![
            vec![0, 1, 1, 0, 0],
            vec![1, 0, 0, 1, 0],
            vec![1, 0, 0, 0, 1],
            vec![0, 1, 0, 0, 0],
            vec![0, 0, 1, 0, 0],
        ],
    };

    let is_2 = g.is_2_connected();
    let claw_free = g.is_free_of(&vec![claw]);
    return (is_2 && claw_free && g.is_free_of(&vec![ig]))
        || (is_2 && claw_free && g.is_free_of(&vec![ag]));
}

// 2003 Gould

pub fn theorem85(g: &Graph) -> bool {
    let claw = Graph {
        size: 4,
        matrix: vec![
            vec![0, 1, 1, 1],
            vec![1, 0, 0, 0],
            vec![1, 0, 0, 0],
            vec![1, 0, 0, 0],
        ],
    };

    let ng = Graph {
        size: 6,
        matrix: vec![
            vec![0, 1, 1, 1, 0, 0],
            vec![1, 0, 1, 0, 0, 1],
            vec![1, 1, 0, 0, 1, 0],
            vec![1, 0, 0, 0, 0, 0],
            vec![0, 0, 1, 0, 0, 0],
            vec![0, 1, 0, 0, 0, 0],
        ],
    };

    return g.is_2_connected() && g.is_free_of(&vec![claw, ng]);
}

pub fn theorem86(g: &Graph) -> bool {
    let claw = Graph {
        size: 4,
        matrix: vec![
            vec![0, 1, 1, 1],
            vec![1, 0, 0, 0],
            vec![1, 0, 0, 0],
            vec![1, 0, 0, 0],
        ],
    };

    let p6 = Graph {
        size: 6,
        matrix: vec![
            vec![0, 1, 0, 0, 0, 0],
            vec![1, 0, 1, 0, 0, 0],
            vec![0, 1, 0, 1, 0, 0],
            vec![0, 0, 1, 0, 1, 0],
            vec![0, 0, 0, 1, 0, 1],
            vec![0, 0, 0, 0, 1, 0],
        ],
    };

    return g.is_2_connected() && g.is_free_of(&vec![claw, p6]);
}

pub fn theorem87(g: &Graph) -> bool {
    let claw = Graph {
        size: 4,
        matrix: vec![
            vec![0, 1, 1, 1],
            vec![1, 0, 0, 0],
            vec![1, 0, 0, 0],
            vec![1, 0, 0, 0],
        ],
    };

    let z2 = Graph {
        size: 5,
        matrix: vec![
            vec![0, 1, 0, 0, 0],
            vec![1, 0, 1, 0, 0],
            vec![0, 1, 0, 1, 1],
            vec![0, 0, 1, 0, 1],
            vec![0, 0, 1, 1, 1],
        ],
    };

    return g.is_2_connected() && g.is_free_of(&vec![claw, z2]);
}

pub fn theorem88(g: &Graph) -> bool {
    let claw = Graph {
        size: 4,
        matrix: vec![
            vec![0, 1, 1, 1],
            vec![1, 0, 0, 0],
            vec![1, 0, 0, 0],
            vec![1, 0, 0, 0],
        ],
    };

    let wg = Graph {
        size: 6,
        matrix: vec![
            vec![0, 1, 1, 0, 0, 0],
            vec![1, 0, 1, 0, 1, 0],
            vec![1, 1, 0, 1, 0, 0],
            vec![0, 0, 1, 0, 0, 0],
            vec![0, 1, 0, 0, 0, 1],
            vec![0, 0, 0, 0, 1, 0],
        ],
    };

    return g.is_2_connected() && g.is_free_of(&vec![claw, wg]);
}

pub fn theorem96(g: &Graph) -> bool {
    let claw = Graph {
        size: 4,
        matrix: vec![
            vec![0, 1, 1, 1],
            vec![1, 0, 0, 0],
            vec![1, 0, 0, 0],
            vec![1, 0, 0, 0],
        ],
    };

    let ng = Graph {
        size: 6,
        matrix: vec![
            vec![0, 1, 1, 1, 0, 0],
            vec![1, 0, 1, 0, 0, 1],
            vec![1, 1, 0, 0, 1, 0],
            vec![1, 0, 0, 0, 0, 0],
            vec![0, 0, 1, 0, 0, 0],
            vec![0, 1, 0, 0, 0, 0],
        ],
    };

    return g.is_3_connected() && g.is_free_of(&vec![claw, ng]);
}

pub fn conjecture17(g: &Graph) -> bool {
    let claw = Graph {
        size: 4,
        matrix: vec![
            vec![0, 1, 1, 1],
            vec![1, 0, 0, 0],
            vec![1, 0, 0, 0],
            vec![1, 0, 0, 0],
        ],
    };

    return g.is_4_connected() && g.is_free_of(&vec![claw]);
}