From 95c2f8c02a68163619ffadbb9bfeecaa6097d39e Mon Sep 17 00:00:00 2001
From: norangebit <git@norangeb.it>
Date: Wed, 17 Apr 2019 22:49:09 +0200
Subject: [PATCH] add basic implementation of BST

---
 .../datastructures/dictionary/Dictionaries.kt |   4 +
 .../datastructures/dictionary/ImmutableBST.kt | 200 ++++++++++++++++++
 .../dictionary/ImmutableBSTTest.kt            | 180 ++++++++++++++++
 3 files changed, 384 insertions(+)
 create mode 100644 src/main/kotlin/it/norangeb/algorithms/datastructures/dictionary/ImmutableBST.kt
 create mode 100644 src/test/kotlin/it/norangeb/algorithms/datastructures/dictionary/ImmutableBSTTest.kt

diff --git a/src/main/kotlin/it/norangeb/algorithms/datastructures/dictionary/Dictionaries.kt b/src/main/kotlin/it/norangeb/algorithms/datastructures/dictionary/Dictionaries.kt
index e36e98a..3a3674a 100644
--- a/src/main/kotlin/it/norangeb/algorithms/datastructures/dictionary/Dictionaries.kt
+++ b/src/main/kotlin/it/norangeb/algorithms/datastructures/dictionary/Dictionaries.kt
@@ -41,4 +41,8 @@ interface OrderedDictionary<K : Comparable<K>, V> : Dictionary<K, V> {
     fun min(): Option<K>
     fun floor(key: K): Option<K>
     fun ceiling(key: K): Option<K>
+    fun select(pos: Int): Option<K>
+    fun <R> preOrder(transform: (K) -> R)
+    fun <R> inOrder(transform: (K) -> R)
+    fun <R> postOrder(transform: (K) -> R)
 }
diff --git a/src/main/kotlin/it/norangeb/algorithms/datastructures/dictionary/ImmutableBST.kt b/src/main/kotlin/it/norangeb/algorithms/datastructures/dictionary/ImmutableBST.kt
new file mode 100644
index 0000000..269e696
--- /dev/null
+++ b/src/main/kotlin/it/norangeb/algorithms/datastructures/dictionary/ImmutableBST.kt
@@ -0,0 +1,200 @@
+/*
+ * 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.datastructures.dictionary
+
+import arrow.core.None
+import arrow.core.Option
+import arrow.core.Some
+import arrow.core.toOption
+
+class ImmutableBST<K : Comparable<K>, V> : OrderedDictionary<K, V> {
+    private var root: Option<Node<K, V>> = None
+
+    override 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 {
+                it.key == key -> it.toOption()
+                key > it.key -> get(it.right, key)
+                else -> get(it.left, key)
+            }
+        }
+
+    override 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()
+
+    override fun delete(key: K) {
+        root = delete(root, key)
+    }
+
+    private fun delete(
+        node: Option<Node<K, V>>,
+        key: K
+    ): Option<Node<K, V>> = node.flatMap { deleteNode(it, key) }
+
+    private fun deleteNode(
+        node: Node<K, V>,
+        key: K
+    ): Option<Node<K, V>> = when {
+        node.key == key -> when {
+            node.left is None && node.right is None -> None
+            node.left is None -> node.right
+            node.right is None -> node.left
+            else -> node.right.map { deleteNodeWithTwoChild(node, it) }
+        }
+
+        key > node.key -> node.clone(
+            right = delete(node.right, key)
+        ).toOption()
+
+        else -> node.clone(left = delete(node.left, key)).toOption()
+    }
+
+    private fun deleteNodeWithTwoChild(
+        father: Node<K, V>,
+        rightChild: Node<K, V>
+    ): Node<K, V> {
+        val replacement = down(rightChild) { left }
+        return replacement
+            .clone(
+                left = father.left,
+                right = delete(rightChild.toOption(), replacement.key)
+            )
+    }
+
+    override fun contains(key: K): Boolean = get(root, key) is Some
+
+    override fun isEmpty(): Boolean = root is None
+
+    override fun size(): Int = size(root)
+
+    private fun size(node: Option<Node<K, V>>) = node.fold(
+        { 0 },
+        { it.child + 1 }
+    )
+
+    override fun max(): Option<K> = root.map {
+        down(it) { right }.key
+    }
+
+    override fun min(): Option<K> = root.map {
+        down(it) { left }.key
+    }
+
+    private fun down(
+        node: Node<K, V>,
+        side: Node<K, V>.() -> Option<Node<K, V>>
+    ): Node<K, V> = side(node)
+        .fold({ node }, { down(it, side) })
+
+    override fun select(pos: Int): Option<K> = select(root, pos)
+
+    private fun select(
+        node: Option<Node<K, V>>,
+        pos: Int
+    ): Option<K> =
+        node.flatMap {
+            val leftChild = size(it.left)
+            when {
+                leftChild > pos -> select(it.left, pos)
+                leftChild < pos -> select(it.right, pos - leftChild - 1)
+                else -> it.key.toOption()
+            }
+        }
+
+    override fun floor(key: K): Option<K> {
+        TODO("not implemented") //To change body of created functions use File | Settings | File Templates.
+    }
+
+    override fun ceiling(key: K): Option<K> {
+        TODO("not implemented") //To change body of created functions use File | Settings | File Templates.
+    }
+
+    override fun <R> inOrder(transform: (K) -> R) = inOrder(root, transform)
+
+    private fun <R> inOrder(node: Option<Node<K, V>>, action: (K) -> R) {
+        node.map {
+            inOrder(it.left, action)
+            action(it.key)
+            inOrder(it.right, action)
+        }
+    }
+
+    override fun <R> postOrder(transform: (K) -> R) = postOrder(root, transform)
+
+    private fun <R> postOrder(node: Option<Node<K, V>>, action: (K) -> R) {
+        node.map {
+            postOrder(it.left, action)
+            postOrder(it.right, action)
+            action(it.key)
+        }
+    }
+
+    override fun <R> preOrder(transform: (K) -> R) = preOrder(root, transform)
+
+    private fun <R> preOrder(node: Option<Node<K, V>>, action: (K) -> R) {
+        node.map {
+            action(it.key)
+            preOrder(it.left, action)
+            preOrder(it.right, action)
+        }
+    }
+
+    data class Node<K : Comparable<K>, V>(
+        val key: K,
+        val value: V,
+        val left: Option<Node<K, V>> = None,
+        val right: Option<Node<K, V>> = None,
+        val child: Int = 0
+    ) {
+        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> {
+            val leftChild = left.fold({ 0 }, { it.child + 1 })
+            val rightChild = right.fold({ 0 }, { it.child + 1 })
+            return Node(key, value, left, right, leftChild + rightChild)
+        }
+    }
+}
\ No newline at end of file
diff --git a/src/test/kotlin/it/norangeb/algorithms/datastructures/dictionary/ImmutableBSTTest.kt b/src/test/kotlin/it/norangeb/algorithms/datastructures/dictionary/ImmutableBSTTest.kt
new file mode 100644
index 0000000..1634d3f
--- /dev/null
+++ b/src/test/kotlin/it/norangeb/algorithms/datastructures/dictionary/ImmutableBSTTest.kt
@@ -0,0 +1,180 @@
+/*
+ * 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.datastructures.dictionary
+
+import arrow.core.None
+import arrow.core.Some
+import org.amshove.kluent.`should be equal to`
+import org.amshove.kluent.`should be`
+import org.amshove.kluent.should
+import org.amshove.kluent.shouldEqual
+import org.junit.jupiter.api.Test
+
+
+class ImmutableBSTTest {
+
+    @Test
+    fun test() {
+        val orderedMap: OrderedDictionary<String, Int> = ImmutableBST()
+        orderedMap.isEmpty() `should be` true
+        orderedMap.size() `should be equal to` 0
+        orderedMap.contains("UNO") `should be` false
+        orderedMap.max() `should be` None
+        orderedMap.min() `should be` None
+
+        orderedMap["QUATTRO"] = 4
+        orderedMap["UNO"] = 0
+
+        orderedMap.contains("UNO") `should be` true
+
+        orderedMap["TRE"] = 3
+        orderedMap["UNO"] = 1
+
+        orderedMap.size() `should be equal to` 3
+        orderedMap["UNO"] should { this == Some(1) }
+
+        orderedMap["DUE"] = 2
+
+        orderedMap["DUE"] should { this == Some(2) }
+        orderedMap.max() should { this == Some("UNO") }
+        orderedMap.min() should { this == Some("DUE") }
+    }
+
+    @Test
+    fun testDelete() {
+        val orderedMap: OrderedDictionary<Int, String> = ImmutableBST()
+
+        orderedMap[7] = "sette"
+        orderedMap[2] = "due"
+        orderedMap[3] = "tre"
+        orderedMap[10] = "dieci"
+        orderedMap[1] = "uno"
+        orderedMap[8] = "otto"
+        orderedMap[13] = "tredici"
+        orderedMap[5] = "cinque"
+        orderedMap[11] = "undici"
+
+        orderedMap.size() `should be equal to` 9
+
+        // delete absent key
+        orderedMap.delete(0)
+
+        orderedMap.size() `should be equal to` 9
+
+        //delete node with no child
+        orderedMap.delete(1)
+
+        orderedMap.size() `should be equal to` 8
+        orderedMap.min() should { this == Some(2) }
+
+        //delete node with only right child
+        orderedMap.delete(2)
+
+        orderedMap.size() `should be equal to` 7
+        orderedMap.min() should { this == Some(3) }
+
+        //delete node with two child
+        orderedMap.delete(10)
+
+        orderedMap.size() `should be equal to` 6
+
+        orderedMap.delete(13)
+        //delete node with only left child
+        orderedMap.delete(11)
+
+        orderedMap.size() `should be equal to` 4
+        orderedMap.max() should { this == Some(8) }
+    }
+
+    @Test
+    fun testOrderedOperation() {
+        val orderedMap: OrderedDictionary<Int, Int> = ImmutableBST()
+
+        orderedMap.select(0) `should be` None
+
+        orderedMap[9] = 9
+        orderedMap[4] = 4
+        orderedMap[14] = 14
+
+        orderedMap.select(0) should { this == Some(4) }
+        orderedMap.select(1) should { this == Some(9) }
+        orderedMap.select(2) should { this == Some(14) }
+        orderedMap.select(3) `should be` None
+
+        orderedMap[13] = 13
+        orderedMap[15] = 15
+        orderedMap[3] = 3
+        orderedMap[5] = 5
+        orderedMap[2] = 2
+        orderedMap[6] = 6
+        orderedMap[12] = 12
+        orderedMap[16] = 16
+        orderedMap[1] = 1
+
+        orderedMap.select(0) shouldEqual orderedMap.min()
+        orderedMap.select(11) shouldEqual orderedMap.max()
+
+        orderedMap[0] = 0
+        orderedMap[11] = 11
+        orderedMap[10] = 10
+        orderedMap[17] = 17
+        orderedMap[18] = 18
+        orderedMap[7] = 7
+        orderedMap[8] = 8
+
+        orderedMap.select(-1) `should be` None
+        orderedMap.select(0) should { this == Some(0) }
+        orderedMap.select(1) should { this == Some(1) }
+        orderedMap.select(5) should { this == Some(5) }
+        orderedMap.select(8) should { this == Some(8) }
+        orderedMap.select(9) should { this == Some(9) }
+        orderedMap.select(10) should { this == Some(10) }
+        orderedMap.select(14) should { this == Some(14) }
+        orderedMap.select(17) should { this == Some(17) }
+        orderedMap.select(18) should { this == Some(18) }
+        orderedMap.select(19) `should be` None
+
+        println(orderedMap.select(19))
+
+        val orderList = ArrayList<Int>()
+        orderedMap.inOrder { orderList.add(it) }
+
+        orderList shouldEqual listOf(0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12,
+            13, 14, 15, 16, 17, 18)
+
+        val postOrderList = ArrayList<Int>()
+        orderedMap.postOrder { postOrderList.add(it) }
+
+        postOrderList shouldEqual listOf(0, 1, 2, 3, 8, 7, 6, 5, 4, 10, 11, 12, 13, 18, 17, 16, 15,
+            14, 9)
+
+        val preOrderList = ArrayList<Int>()
+        orderedMap.preOrder { preOrderList.add(it) }
+
+        preOrderList shouldEqual listOf(9, 4, 3, 2, 1, 0, 5, 6, 7, 8, 14, 13, 12, 11, 10, 15, 16,
+            17, 18)
+    }
+}
\ No newline at end of file