union-find

- implement quick find
- implement quick union
- implement quick union with optimization

src/main/kotlin/it/norangeb/algorithms/datastructures/unionfind/QuickFind.kt

@@ -0,0 +1,46 @@
+/*
+ * 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, tryMerge, 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.unionfind
+
+class QuickFind(private val capacity: Int) : UnionFind {
+    private val ids = IntArray(capacity) { it }
+
+    override fun find(element: Int): Int {
+        return ids[element]
+    }
+
+    override fun union(first: Int, second: Int) {
+        val firstId = find(first)
+        val secondId = find(second)
+
+        if (firstId == secondId)
+            return
+
+        for (i in 0 until capacity)
+            if (ids[i] == firstId)
+                ids[i] = secondId
+    }
+}

src/main/kotlin/it/norangeb/algorithms/datastructures/unionfind/QuickUnion.kt

@@ -0,0 +1,48 @@
+/*
+ * 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, tryMerge, 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.unionfind
+
+class QuickUnion(capacity: Int) : UnionFind {
+    private val ids = IntArray(capacity) { it }
+
+    override fun find(element: Int): Int {
+        var i = element
+        while (i != ids[i])
+            i = ids[i]
+
+        return i
+    }
+
+    override fun union(first: Int, second: Int) {
+        val firstId = find(first)
+        val secondId = find(second)
+
+        if (firstId == secondId)
+            return
+
+        ids[firstId] = secondId
+    }
+}

src/main/kotlin/it/norangeb/algorithms/datastructures/unionfind/QuickUnionCompressionPath.kt

@@ -0,0 +1,50 @@
+/*
+ * 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.unionfind
+
+class QuickUnionCompressionPath(capacity: Int) : UnionFind {
+    private val ids = IntArray(capacity) { it }
+
+    override fun find(element: Int): Int {
+        var i = element
+        while (i != ids[i]) {
+            ids[i] = ids[ids[i]]
+            i = ids[i]
+        }
+
+        return i
+    }
+
+    override fun union(first: Int, second: Int) {
+        val firstId = find(first)
+        val secondId = find(second)
+
+        if (firstId == secondId)
+            return
+
+        ids[firstId] = secondId
+    }
+}

src/main/kotlin/it/norangeb/algorithms/datastructures/unionfind/QuickUnionWithSize.kt

@@ -0,0 +1,58 @@
+/*
+ * 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.unionfind
+
+class QuickUnionWithSize(capacity: Int) : UnionFind {
+    private val ids = IntArray(capacity) { it }
+    private val size = IntArray(capacity) { 0 }
+
+    override fun find(element: Int): Int {
+        var i = element
+        while (i != ids[i])
+            i = ids[i]
+
+        return i
+    }
+
+    override fun union(first: Int, second: Int) {
+        val firstId = find(first)
+        val secondId = find(second)
+
+        if (firstId == secondId)
+            return
+
+        when {
+            size[first] < size[second] -> {
+                ids[firstId] = secondId
+                size[secondId] += size[firstId]
+            }
+            else -> {
+                ids[secondId] = firstId
+                size[firstId] += size[secondId]
+            }
+        }
+    }
+}

src/main/kotlin/it/norangeb/algorithms/datastructures/unionfind/UnionFind.kt

@@ -0,0 +1,32 @@
+/*
+ * 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, tryMerge, 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.unionfind
+
+interface UnionFind {
+    fun find(element: Int): Int
+    fun union(first: Int, second: Int)
+    fun connected(first: Int, second: Int): Boolean = find(first) == find(second)
+}

src/test/kotlin/it/norangeb/algorithms/datastructures/unionfind/QuickFindTest.kt

@@ -0,0 +1,54 @@
+/*
+ * 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, tryMerge, 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.unionfind
+
+import org.amshove.kluent.`should be equal to`
+import org.junit.Before
+import org.junit.jupiter.api.Test
+
+class QuickFindTest {
+    private var unionFind = QuickFind(10)
+
+    @Before
+    fun init() {
+        unionFind = QuickFind(10)
+    }
+
+    @Test
+    fun testUnion() {
+        unionFind.connected(1, 2) `should be equal to` false
+        unionFind.union(1, 2)
+        unionFind.connected(1, 2) `should be equal to` true
+    }
+
+    @Test
+    fun testTransitiveUnion() {
+        unionFind.connected(1, 3) `should be equal to` false
+        unionFind.union(1, 2)
+        unionFind.union(2, 3)
+        unionFind.connected(1, 3) `should be equal to` true
+    }
+}

src/test/kotlin/it/norangeb/algorithms/datastructures/unionfind/QuickUnionCompressionPathTest.kt

@@ -0,0 +1,54 @@
+/*
+ * 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.unionfind
+
+import org.amshove.kluent.`should be equal to`
+import org.junit.Before
+import org.junit.jupiter.api.Test
+
+class QuickUnionCompressionPathTest {
+    private var unionFind = QuickUnion(10)
+
+    @Before
+    fun init() {
+        unionFind = QuickUnion(10)
+    }
+
+    @Test
+    fun testUnion() {
+        unionFind.connected(1, 2) `should be equal to` false
+        unionFind.union(1, 2)
+        unionFind.connected(1, 2) `should be equal to` true
+    }
+
+    @Test
+    fun testTransitiveUnion() {
+        unionFind.connected(1, 3) `should be equal to` false
+        unionFind.union(1, 2)
+        unionFind.union(2, 3)
+        unionFind.connected(1, 3) `should be equal to` true
+    }
+}

src/test/kotlin/it/norangeb/algorithms/datastructures/unionfind/QuickUnionTest.kt

@@ -0,0 +1,54 @@
+/*
+ * 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, tryMerge, 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.unionfind
+
+import org.amshove.kluent.`should be equal to`
+import org.junit.Before
+import org.junit.jupiter.api.Test
+
+class QuickUnionTest {
+    private var unionFind = QuickUnion(10)
+
+    @Before
+    fun init() {
+        unionFind = QuickUnion(10)
+    }
+
+    @Test
+    fun testUnion() {
+        unionFind.connected(1, 2) `should be equal to` false
+        unionFind.union(1, 2)
+        unionFind.connected(1, 2) `should be equal to` true
+    }
+
+    @Test
+    fun testTransitiveUnion() {
+        unionFind.connected(1, 3) `should be equal to` false
+        unionFind.union(1, 2)
+        unionFind.union(2, 3)
+        unionFind.connected(1, 3) `should be equal to` true
+    }
+}

src/test/kotlin/it/norangeb/algorithms/datastructures/unionfind/QuickUnionWithSizeTest.kt

@@ -0,0 +1,54 @@
+/*
+ * 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.unionfind
+
+import org.amshove.kluent.`should be equal to`
+import org.junit.Before
+import org.junit.jupiter.api.Test
+
+class QuickUnionWithSizeTest {
+    private var unionFind = QuickUnionWithSize(10)
+
+    @Before
+    fun init() {
+        unionFind = QuickUnionWithSize(10)
+    }
+
+    @Test
+    fun testUnion() {
+        unionFind.connected(1, 2) `should be equal to` false
+        unionFind.union(1, 2)
+        unionFind.connected(1, 2) `should be equal to` true
+    }
+
+    @Test
+    fun testTransitiveUnion() {
+        unionFind.connected(1, 3) `should be equal to` false
+        unionFind.union(1, 2)
+        unionFind.union(2, 3)
+        unionFind.connected(1, 3) `should be equal to` true
+    }
+}