add exercise with tree

- add descendants of a node
- add distance to leaf
- add max width of a tree

src/main/kotlin/it/norangeb/algorithms/exam/DescendentsTree.kt

@@ -0,0 +1,99 @@
+/*
+ * 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)
+    }
+}

src/main/kotlin/it/norangeb/algorithms/exam/DistanceToLeafTree.kt

@@ -0,0 +1,114 @@
+/*
+ * 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
+import it.norangeb.algorithms.datastructures.queue.Queue
+import it.norangeb.algorithms.datastructures.queue.ResizingArrayQueue
+import kotlin.math.abs
+
+class DistanceToLeafTree<K : Comparable<K>, V> {
+
+    private var root: Option<Node<K, V>> = None
+
+    operator fun set(key: K, value: V) {
+        root = set(key, value, root)
+    }
+
+    private fun set(
+        key: K,
+        value: V,
+        node: Option<Node<K, 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(key, value, it.right))
+                else -> it.clone(left = set(key, value, it.left))
+            }
+        }).toOption()
+
+    operator fun get(key: K): Option<V> = get(key, root).map { it.value }
+
+    private fun get(
+        key: K,
+        node: Option<Node<K, V>>
+    ): Option<Node<K, V>> = node.flatMap {
+        when {
+            key == it.key -> node
+            key > it.key -> get(key, it.right)
+            else -> get(key, it.left)
+        }
+    }
+
+    fun distanceToLeaf(key: K): Option<Int> = get(key, root).map {
+        if (it.isLeaf())
+            0
+        else
+            distanceToLeaf(it)
+    }
+
+    private fun distanceToLeaf(node: Node<K, V>): Int {
+        val toExplore: Queue<Pair<Node<K, V>, Int>> = ResizingArrayQueue()
+        node.left.map { toExplore.enqueue(Pair(it, 1)) }
+        node.right.map { toExplore.enqueue(Pair(it, 1)) }
+
+        while (!toExplore.isEmpty()) {
+            toExplore.dequeue().map { elem ->
+                if (elem.first.isLeaf())
+                    return elem.second
+
+                elem.first.left.map {
+                    toExplore.enqueue(Pair(it, elem.second + 1))
+                }
+                elem.first.right.map {
+                    toExplore.enqueue(Pair(it, elem.second + 1))
+                }
+            }
+        }
+
+        return -1
+    }
+
+    private 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(key, value, left, right)
+
+        fun isLeaf() = left == None && right == None
+    }
+}

src/main/kotlin/it/norangeb/algorithms/exam/MaxWidthTree.kt

@@ -0,0 +1,111 @@
+/*
+ * 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
+import kotlin.math.abs
+
+class MaxWidthTree<K : Comparable<K>, V> {
+
+    private var root: Option<Node<K, V>> = None
+
+    operator fun set(key: K, value: V) {
+        root = set(key, value, root)
+    }
+
+    private fun set(
+        key: K,
+        value: V,
+        node: Option<Node<K, 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(key, value, it.right))
+                else -> it.clone(left = set(key, value, it.left))
+            }
+        }).toOption()
+
+    operator fun get(key: K): Option<V> = get(key, root).map { it.value }
+
+    private fun get(
+        key: K,
+        node: Option<Node<K, V>>
+    ): Option<Node<K, V>> = node.flatMap {
+        when {
+            key == it.key -> node
+            key > it.key -> get(key, it.right)
+            else -> get(key, it.left)
+        }
+    }
+
+    fun getMaxWidth(): Int {
+        val count = Array(100) { 0 }
+        val level = 0
+        computeWidth(root, count, level)
+
+        return count[getMax(count)]
+    }
+
+    private fun computeWidth(
+        node: Option<Node<K, V>>,
+        count: Array<Int>,
+        level: Int
+    ) {
+       node.map {
+           count[level]++
+           computeWidth(it.left, count, level + 1)
+           computeWidth(it.right, count, level + 1)
+       }
+    }
+
+    private fun getMax(count: Array<Int>): Int {
+        var maxIndex = 0
+        count.forEachIndexed { index, i ->
+            if (i > count[maxIndex])
+                maxIndex = index
+        }
+
+        return maxIndex
+    }
+
+    private 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(key, value, left, right)
+    }
+}

src/test/kotlin/it/norangeb/algorithms/exam/DescendentsTest.kt

@@ -0,0 +1,124 @@
+/*
+ * 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.Some
+import org.amshove.kluent.`should equal`
+import org.spekframework.spek2.Spek
+import org.spekframework.spek2.style.gherkin.Feature
+
+object DescendentsTest : Spek({
+    Feature("descendents") {
+        Scenario("get and set") {
+            val tree by memoized { DescendentsTree<Int, Int>() }
+
+            When("add couple 15-15, 13-13, 23-23, 5-5") {
+                tree[15] = 15
+                tree[13] = 13
+                tree[23] = 24
+                tree[5] = 5
+            }
+
+            Then("tree of 23 should equal 24") {
+                tree[23] `should equal` Some(24)
+            }
+
+            Then("tree of 25 should equal None") {
+                tree[25] `should equal` None
+            }
+
+            Then("tree of 5 should equal 5") {
+                tree[5] `should equal` Some(5)
+            }
+
+            When("add couple 1-1, 17-17, 25-25, 23-23") {
+                tree[1] = 1
+                tree[17] = 17
+                tree[25] = 25
+                tree[23] = 23
+            }
+
+            Then("tree of 23 should equal 23") {
+                tree[23] `should equal` Some(23)
+            }
+
+            Then("tree of 25 should equal 25") {
+                tree[25] `should equal` Some(25)
+            }
+        }
+
+        Scenario("descendents") {
+            val tree by memoized { DescendentsTree<Int, Int>() }
+
+            Given("tree 15, 23, 7, 18, 25, 21, 22, 20") {
+                tree[15] = 15
+                tree[23] = 23
+                tree[7] = 7
+                tree[18] = 18
+                tree[25] = 25
+                tree[21] = 21
+                tree[22] = 22
+                tree[20] = 20
+            }
+
+            lateinit var result: Option<Int>
+
+            When("compute descendents of 21") {
+                result = tree.descendents(21)
+            }
+
+            Then("result should equal 2") {
+                result `should equal` Some(2)
+            }
+
+            When("compute descendents of 7") {
+                result = tree.descendents(7)
+            }
+
+            Then("result should equal 0") {
+                result `should equal` Some(0)
+            }
+
+            When("compute descendents of 23") {
+                result = tree.descendents(23)
+            }
+
+            Then("result should equal 5") {
+                result `should equal` Some(5)
+            }
+
+            When("compute descendents of 8") {
+                result = tree.descendents(8)
+            }
+
+            Then("result should equal None") {
+                result `should equal` None
+            }
+        }
+    }
+})

src/test/kotlin/it/norangeb/algorithms/exam/DistanceToLeafTest.kt

@@ -0,0 +1,108 @@
+/*
+ * 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.Some
+import org.amshove.kluent.`should equal`
+import org.spekframework.spek2.Spek
+import org.spekframework.spek2.style.gherkin.Feature
+
+object DistanceToLeafTest : Spek({
+    Feature("distance to leaf") {
+        Scenario("get and set") {
+            val tree by memoized { DistanceToLeafTree<Int, Int>() }
+
+            When("add couple 15-15, 13-13, 23-23, 5-5") {
+                tree[15] = 15
+                tree[13] = 13
+                tree[23] = 24
+                tree[5] = 5
+            }
+
+            Then("tree of 23 should equal 24") {
+                tree[23] `should equal` Some(24)
+            }
+
+            Then("tree of 25 should equal None") {
+                tree[25] `should equal` None
+            }
+
+            Then("tree of 5 should equal 5") {
+                tree[5] `should equal` Some(5)
+            }
+
+            When("add couple 1-1, 17-17, 25-25, 23-23") {
+                tree[1] = 1
+                tree[17] = 17
+                tree[25] = 25
+                tree[23] = 23
+            }
+
+            Then("tree of 23 should equal 23") {
+                tree[23] `should equal` Some(23)
+            }
+
+            Then("tree of 25 should equal 25") {
+                tree[25] `should equal` Some(25)
+            }
+        }
+
+        Scenario("distance to leaf") {
+            val tree by memoized { DistanceToLeafTree<Int, Int>() }
+
+            Given("") {
+                tree[18] = 18
+                tree[15] = 15
+                tree[23] = 23
+                tree[7] = 7
+                tree[17] = 17
+                tree[3] = 3
+                tree[10] = 10
+                tree[1] = 1
+                tree[4] = 4
+                tree[12] = 12
+                tree[14] = 14
+            }
+
+            Then("distance to leaf of 25 should equal None") {
+                tree.distanceToLeaf(25) `should equal` None
+            }
+
+            Then("distance to leaf of 15 should equal 1") {
+                tree.distanceToLeaf(15) `should equal` Some(1)
+            }
+
+            Then("distance to leaf of 7 should equal 2") {
+                tree.distanceToLeaf(7) `should equal` Some(2)
+            }
+
+            Then("distance to leaf of 4 should equal 0") {
+                tree.distanceToLeaf(4) `should equal` Some(0)
+            }
+        }
+    }
+})

src/test/kotlin/it/norangeb/algorithms/exam/MaxWidthTreeTest.kt

@@ -0,0 +1,112 @@
+/*
+ * 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.Some
+import org.amshove.kluent.`should be equal to`
+import org.amshove.kluent.`should equal`
+import org.spekframework.spek2.Spek
+import org.spekframework.spek2.style.gherkin.Feature
+
+object MaxWidthTreeTest : Spek({
+    Feature("width") {
+        Scenario("get and set") {
+            val tree by memoized { MaxWidthTree<Int, Int>() }
+
+            When("add couple 15-15, 13-13, 23-23, 5-5") {
+                tree[15] = 15
+                tree[13] = 13
+                tree[23] = 24
+                tree[5] = 5
+            }
+
+            Then("tree of 23 should equal 24") {
+                tree[23] `should equal` Some(24)
+            }
+
+            Then("tree of 25 should equal None") {
+                tree[25] `should equal` None
+            }
+
+            Then("tree of 5 should equal 5") {
+                tree[5] `should equal` Some(5)
+            }
+
+            When("add couple 1-1, 17-17, 25-25, 23-23") {
+                tree[1] = 1
+                tree[17] = 17
+                tree[25] = 25
+                tree[23] = 23
+            }
+
+            Then("tree of 23 should equal 23") {
+                tree[23] `should equal` Some(23)
+            }
+
+            Then("tree of 25 should equal 25") {
+                tree[25] `should equal` Some(25)
+            }
+        }
+
+        Scenario("width") {
+            val tree by memoized { MaxWidthTree<Int, Int>() }
+
+            var width = -1
+
+            Then("width should equal 0") {
+                tree.getMaxWidth() `should be equal to` 0
+            }
+
+            Given("tree 15, 23, 7, 18, 25, 21, 22, 20") {
+                tree[15] = 15
+                tree[23] = 23
+                tree[7] = 7
+                tree[18] = 18
+                tree[25] = 25
+                tree[21] = 21
+                tree[22] = 22
+                tree[20] = 20
+                tree[10] = 10
+            }
+
+            Then("width should equal 3") {
+                tree.getMaxWidth() `should be equal to` 3
+            }
+
+            When("add 27, 26, 28") {
+                tree[27] = 27
+                tree[26] = 26
+                tree[28] = 28
+            }
+
+            Then("width should equal 4") {
+                tree.getMaxWidth() `should be equal to` 4
+            }
+        }
+    }
+})