#include "binary_tree.h"

#include <stddef.h>
#include <stdio.h>

int size(const struct binary_tree *tree)
{
    if (tree == NULL)
        return 0;

    return 1 + size(tree->left) + size(tree->right);
}

static int max(int a, int b)
{
    if (a > b)
        return a;
    return b;
}

int height(const struct binary_tree *tree)
{
    if (tree == NULL)
    {
        return -1;
    }

    return 1 + max(height(tree->left), height(tree->right));
}

int is_perfect(const struct binary_tree *tree)
{
    if (tree == NULL)
        return 1;
    return height(tree->left) == height(tree->right) && is_perfect(tree->right)
        && is_perfect(tree->right);
}

int is_complete(const struct binary_tree *tree)
{
    if (tree == NULL)
    {
        return 1;
    }

    int hg = height(tree->left);
    int hd = height(tree->right);

    if (hg - hd != 0 && hg - hd != 1)
    {
        return 0;
    }

    return is_complete(tree->left) && is_complete(tree->right);
}

int is_degenerate(const struct binary_tree *tree)
{
    if (tree == NULL)
    {
        return 1;
    }

    if (tree->left && tree->right)
    {
        return 0;
    }
    return is_degenerate(tree->left) && is_degenerate(tree->right);
}

int is_full(const struct binary_tree *tree)
{
    if (tree == NULL)
        return 1;
    if ((tree->left && !tree->right) || (!tree->left && tree->right))
        return 0;
    return is_full(tree->right) && is_full(tree->left);
}

static int is_bzt(const struct binary_tree *tree, int min, int max)
{
    if (tree == NULL)
        return 1;
    if (tree->data > max || tree->data <= min)
        return 0;
    return is_bzt(tree->left, min, tree->data)
        && is_bzt(tree->right, tree->data, max);
}

int is_bst(const struct binary_tree *tree)
{
    if (tree == NULL)
        return 1;
    return is_bzt(tree, -2147483647, 2147483647);
}