Trie

lib/trees/binary_tree_adt.dart

@@ -38,21 +38,21 @@ abstract class BinaryTreeADT<N extends BinaryNodeADT, V extends Comparable>
   @override
   void nullify() => root = null;
 
-  @override
+  /// In Order Traversal.
   List<V> inOrder() {
     var result = <V>[];
     _inOrder(root, result);
     return result;
   }
 
-  @override
+  /// PostOrder Traversal.
   List<V> postOrder() {
     var result = <V>[];
     _postOrder(root, result);
     return result;
   }
 
-  @override
+  /// PreOrder Traversal.
   List<V> preOrder() {
     var result = <V>[];
     _preOrder(root, result);

lib/trees/tree_adt.dart

@@ -28,15 +28,6 @@ abstract class TreeADT<N extends NodeADT, V extends Comparable> {
   /// Deletes [value] from the tree and updates it's [root].
   void delete(V value);
 
-  /// In Order Traversal.
-  List<V> inOrder();
-
   /// Empty the tree.
   void nullify();
-
-  /// PostOrder Traversal.
-  List<V> postOrder();
-
-  /// PreOrder Traversal.
-  List<V> preOrder();
 }

lib/trie/trie.dart

@@ -0,0 +1,159 @@
+/// Trie is an ordered tree data structure used to store a dynamic set
+///  or associative array where the keys are usually strings.
+class Trie<V extends Comparable> {
+  /// Root of the trie.
+  TrieNode root;
+
+  /// Separates the value into it's components.
+  final Function splitter;
+
+  List _components;
+
+  /// Initialises trie with custom set of values.
+  Trie(Set components, this.splitter) {
+    _components = [...components];
+  }
+
+  /// Generates trie of lower-case alphabets.
+  Trie.ofAlphabets()
+      : this({...List.generate(26, (i) => String.fromCharCode(97 + i))},
+            (value) => value.split(''));
+
+  /// Returns the set of [components] that make up a value.
+  Set<V> get components => {..._components};
+
+  /// Tests if this trie is empty.
+  bool get isEmpty => root?.children == null ? true : false;
+
+  /// Adds a [value] to the trie.
+  void add(V value) {
+    var list = _split(value);
+    if (isEmpty) {
+      root ??= TrieNode({..._components});
+    }
+    _add(root, list);
+  }
+
+  /// Checks if [value] is contained in the trie.
+  bool contains(V value) {
+    var list = _split(value);
+    return isEmpty ? false : _contains(root, list);
+  }
+
+  /// Deletes [value] from the trie.
+  void delete(V value) {
+    var list = _split(value);
+    var returnValue = _delete(root, list);
+    returnValue ?? nullify();
+  }
+
+  /// Empty the trie.
+  void nullify() => root?.children = null;
+
+  /// Traverses the path following [value]
+  ///  and marks `node.isValue` to true at end.
+  void _add(TrieNode node, List<V> value) {
+    if (value.isEmpty) {
+      node.isValue = true;
+      return;
+    }
+    var path = _indexOf(value.first);
+    value = value.sublist(1);
+
+    if (node.children[path] == null) {
+      node.children[path] = TrieNode(components);
+    }
+
+    _add(node.children[path], value);
+  }
+
+  bool _contains(TrieNode node, List<V> value) {
+    if (value.isEmpty) {
+      return node.isValue;
+    }
+    var path = _indexOf(value.first);
+    value = value.sublist(1);
+
+    if (node.children[path] != null) {
+      return _contains(node.children[path], value);
+    } else {
+      return false;
+    }
+  }
+
+  /// Traverses the path following [value] and marks
+  ///  `node.isValue` to `false` at end. Deletes values eagerly i.e.
+  ///  cleans up any parent nodes that are no longer necessary.
+  TrieNode _delete(TrieNode node, List<V> value) {
+    if (value.isEmpty) {
+      // In case trie is empty and an empty value is passed.
+      if (node == null) return null;
+
+      node.isValue = false;
+
+      // Checks all the children. If null, then deletes the node.
+      var allNull = true;
+      for (var child in node.children) {
+        if (child != null) {
+          allNull = false;
+          break;
+        }
+      }
+      return allNull ? null : node;
+    }
+
+    // In case trie is empty and some value is passed.
+    if (node == null) return null;
+
+    var path = _indexOf(value.first);
+    value = value.sublist(1);
+
+    // Path to value doesn't exist.
+    if (node.children[path] == null) {
+      return node;
+    }
+
+    node.children[path] = _delete(node.children[path], value);
+
+    // Delete node if all children are null.
+    if (node.children[path] == null) {
+      var allNull = true;
+      for (var child in node.children) {
+        if (child != null) {
+          allNull = false;
+          break;
+        }
+      }
+      return allNull ? null : node;
+    }
+
+    return node;
+  }
+
+  /// Returns index, which represents the [component] in `node.children`.
+  int _indexOf(V component) => _components.indexOf(component);
+
+  List _split(V value) {
+    List<V> list = splitter(value);
+    for (var component in list) {
+      // TODO: Implement an error class instead.
+      if (!components.contains(component)) throw ('$component ∉ $components');
+    }
+    return list;
+  }
+}
+
+/// Node of the trie, has connection to the set of components as [children].
+class TrieNode<V extends Comparable> {
+  /// If this node represents a value in the trie.
+  bool isValue = false;
+
+  /// Connection to [children].
+  List<TrieNode> children;
+
+  /// Initializes the node to have as many [children]
+  ///  as there are components in the trie.
+  TrieNode(Set components) {
+    children = List<TrieNode>(components.length);
+  }
+}

test/trie/trie_test.dart

@@ -0,0 +1,63 @@
+import 'package:test/test.dart';
+import 'package:algorithms/trie/trie.dart';
+
+void main() {
+  Trie emptyTrie, trie, customTrie;
+
+  setUp(() {
+    emptyTrie = Trie.ofAlphabets();
+
+    trie = Trie.ofAlphabets();
+    trie.add('algorithms');
+
+    customTrie = Trie(
+        {'a', 'b', 'f', 'o', 'r', 'z'}, (value) => value.toString().split(''));
+    customTrie.add('foo');
+  });
+
+  test('Components', () {
+    expect(trie.components,
+        equals({...List.generate(26, (i) => String.fromCharCode(122 - i))}));
+
+    expect(customTrie.components, equals({'f', 'o', 'b', 'a', 'r', 'z'}));
+  });
+
+  test('Empty trie', () {
+    expect(emptyTrie.isEmpty, isTrue);
+    expect(trie.isEmpty, isFalse);
+  });
+
+  test('Add value', () {
+    trie.add('hi');
+    expect(trie.root.children[7].children[8].isValue, isTrue);
+
+    customTrie.add('bar');
+    expect(customTrie.root.children[1].children[0].children[4].isValue, isTrue);
+
+    customTrie.add('baz');
+    expect(customTrie.root.children[1].children[0].children[5].isValue, isTrue);
+  });
+
+  test('Contains value', () {
+    expect(emptyTrie.contains('test'), isFalse);
+
+    expect(trie.contains('algorithm'), isFalse);
+    expect(trie.contains('algorithms'), isTrue);
+
+    expect(customTrie.contains('boar'), isFalse);
+    expect(customTrie.contains('foo'), isTrue);
+  });
+
+  test('Delete value', () {
+    emptyTrie.delete('');
+    emptyTrie.delete('test');
+
+    expect(trie.contains('algorithms'), isTrue);
+    trie.delete('algorithms');
+    expect(trie.contains('algorithms'), isFalse);
+
+    expect(customTrie.contains('foo'), isTrue);
+    customTrie.delete('foo');
+    expect(customTrie.contains('foo'), isFalse);
+  });
+}