algorithms(avl): add changes

Signed-off-by: Matej Focko <me@mfocko.xyz>

static/files/algorithms/rb-trees/avl/src/AVL.cs

@@ -1,6 +1,6 @@
 using System.Collections;
 
-namespace avl;
+namespace AVL;
 
 class AVL<T>(IComparer<T> comparator) : IEnumerable<T> {
     private Node<T>? _root = null;
@@ -10,11 +10,87 @@ class AVL<T>(IComparer<T> comparator) : IEnumerable<T> {
     public int Count { get; private set; } = 0;
     public IComparer<T> Comparator { get; } = comparator;
 
+    #region AVLSpecific
+
+    private static (bool correct, int depth) Check(Node<T>? node, int depth) {
+        if (node == null) {
+            return (true, depth);
+        }
+
+        var (leftCorrect, leftDepth) = Check(node.Left, 1 + depth);
+        if (!leftCorrect) {
+            return (false, leftDepth);
+        }
+
+        var (rightCorrect, rightDepth) = Check(node.Right, 1 + depth);
+
+        var foundDepth = Math.Max(leftDepth, rightDepth);
+        return (rightCorrect && Math.Abs(leftDepth - rightDepth) <= 1, foundDepth);
+    }
+
+    public bool IsCorrect() {
+        var (correct, _) = Check(_root, 0);
+        return correct;
+    }
+
+    private void InsertRebalance(List<Node<T>> nodes) {
+        // TODO
+    }
+
+    private void DeleteRebalance(List<Node<T>> nodes) {
+        // TODO
+    }
+
+    #endregion
+
     public bool Add(T item) {
-        throw new NotImplementedException();
+        int cmp;
+
+        // insert the node
+        var path = new List<Node<T>>();
+        var node = _root;
+        while (node != null) {
+            path.Add(node);
+            cmp = Comparator.Compare(node.Value, item);
+
+            if (cmp < 0) {
+                node = node.Right;
+            } else if (cmp == 0) {
+                return false;
+            } else {
+                node = node.Left;
+            }
+        }
+
+        var newItem = new Node<T>(item);
+        ++Count;
+
+        // adding root
+        if (path.Count == 0) {
+            _root = newItem;
+            return true;
+        }
+
+        var lastIdx = path.Count - 1;
+        cmp = Comparator.Compare(path[lastIdx].Value, item);
+
+        if (cmp < 0) {
+            path[lastIdx].Right = newItem;
+        } else {
+            path[lastIdx].Left = newItem;
+        }
+        path.Add(newItem);
+
+        // rebalance
+        InsertRebalance(path);
+        return true;
     }
 
     public bool Remove(T item) {
+        // delete the node
+
+        // rebalance
+
         throw new NotImplementedException();
     }
 

static/files/algorithms/rb-trees/avl/src/Node.cs

@@ -1,10 +1,16 @@
-namespace avl;
+namespace AVL;
+
+enum NodeType {
+    Minus,
+    Zero,
+    Plus,
+}
 
 class Node<T> {
     public T Value { get; init; }
 
-    public readonly Node<T>? Parent;
-    public readonly Node<T>? Left, Right;
+    public Node<T>? Left = null, Right = null;
+    public NodeType Type = NodeType.Zero;
 
     public Node(T value) {
         Value = value;

static/files/algorithms/rb-trees/avl/test/AVL.cs

@@ -1,4 +1,4 @@
-namespace avl.test;
+namespace AVL.Test;
 
 public class AVL {
     [Fact]
@@ -8,8 +8,10 @@ public class AVL {
         Assert.Equal(0, t.Count);
 
         for (int i = 0; i < 10; ++i) {
-            Assert.False(t.Contains(i));
+            Assert.False(t.Contains(i), $"Empty tree should not contain {i}");
         }
+
+        Assert.True(t.IsCorrect(), "AVL invariants hold for an empty tree");
     }
 
     [Fact]
@@ -19,6 +21,66 @@ public class AVL {
         };
 
         Assert.Equal(1, t.Count);
-        Assert.True(t.Contains(1));
+        Assert.True(t.Contains(123), "Tree contains the added element 123");
+
+        Assert.True(t.IsCorrect(), "AVL invariants hold");
+    }
+
+    [Fact]
+    public void TwoNodes() {
+        var t = new AVL<int> {
+            1, 2
+        };
+
+        Assert.Equal(2, t.Count);
+        Assert.True(t.Contains(1), "Tree contains the added element 1");
+        Assert.True(t.Contains(2), "Tree contains the added element 2");
+
+        Assert.True(t.IsCorrect(), "AVL invariants hold");
+    }
+
+    [Fact]
+    public void TwoNodesReversed() {
+        var t = new AVL<int> {
+            2, 1
+        };
+
+        Assert.Equal(2, t.Count);
+        Assert.True(t.Contains(1), "Tree contains the added element 1");
+        Assert.True(t.Contains(2), "Tree contains the added element 2");
+
+        Assert.True(t.IsCorrect(), "AVL invariants hold");
+    }
+
+    [Fact]
+    public void ThreeNodes() {
+        var t = new AVL<int> {
+            1, 2, 3
+        };
+
+        Assert.Equal(3, t.Count);
+        Assert.True(t.Contains(1), "Tree contains the added element 1");
+        Assert.True(t.Contains(2), "Tree contains the added element 2");
+        Assert.True(t.Contains(3), "Tree contains the added element 3");
+
+        Assert.True(t.IsCorrect(), "AVL invariants hold");
+    }
+
+
+    [Fact]
+    public void BiggerTree() {
+        var t = new AVL<int>();
+
+        for (int i = -10; i <= 10; ++i) {
+            t.Add(i);
+        }
+
+        Assert.Equal(21, t.Count);
+
+        for (int i = -100; i <= 100; ++i) {
+            Assert.Equal(-10 <= i && i <= 10, t.Contains(i));
+        }
+
+        Assert.True(t.IsCorrect(), "AVL invariants hold");
     }
 }

static/files/algorithms/rb-trees/avl/test/Node.cs

@@ -1,8 +0,0 @@
-namespace avl.test;
-
-public class Node {
-    [Fact]
-    public void Test1() {
-
-    }
-}