/*
 * MIT License
 *
 * Copyright (c) 2019 norangebit
 *
 * Permission is hereby granted, free of charge, to any person obtaining a copy
 * of this software and associated documentation files (the "Software"), to deal
 * in the Software without restriction, including without limitation the rights
 * to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
 * copies of the Software, and to permit persons to whom the Software is
 * furnished to do so, subject to the following conditions:
 *
 * The above copyright notice and this permission notice shall be included in all
 * copies or substantial portions of the Software.
 *
 * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
 * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
 * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
 * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
 * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
 * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
 * SOFTWARE.
 *
 */

package it.norangeb.algorithms.exam

import arrow.core.None
import arrow.core.Option
import arrow.core.toOption

class DescendentsTree<K : Comparable<K>, V> {

    private var root: Option<Node<K, V>> = None

    operator fun get(key: K): Option<V> = get(root, key).map { it.value }

    private fun get(
        node: Option<Node<K, V>>,
        key: K
    ): Option<Node<K, V>> = node.flatMap {
        when {
            key == it.key -> node
            key > it.key -> get(it.right, key)
            else -> get(it.left, key)
        }
    }

    operator fun set(key: K, value: V) {
        root = set(root, key, value)
    }

    private fun set(
        node: Option<Node<K, V>>,
        key: K,
        value: V
    ): Option<Node<K, V>> = node.fold(
        { Node(key, value) },
        {
            when {
                key == it.key -> it.clone(value = value)
                key > it.key -> it.clone(right = set(it.right, key, value))
                else -> it.clone(left = set(it.left, key, value))
            }
        }
    ).toOption()

    fun descendents(key: K): Option<Int> {
        val parent = get(root, key)
        var descendents = 0

        return parent.map {
            inOrder(parent) { descendents++ }
            descendents - 1
        }
    }

    private fun <R> inOrder(node: Option<Node<K, V>>, action: (V) -> R) {
        node.map {
            inOrder(it.left, action)
            action(it.value)
            inOrder(it.right, action)
        }
    }

    data class Node<K, V>(
        val key: K,
        val value: V,
        val left: Option<Node<K, V>> = None,
        val right: Option<Node<K, V>> = None
    ) {
        fun clone(
            key: K = this.key,
            value: V = this.value,
            left: Option<Node<K, V>> = this.left,
            right: Option<Node<K, V>> = this.right
        ): Node<K, V> = Node(key, value, left, right)
    }
}