feat(rbt): implement red-black tree

Signed-off-by: Matej Focko <mfocko@redhat.com>

comparator.html

@@ -148,6 +148,18 @@
             <label class="btn btn-outline-primary" for="lRavlTreeBtn"
               >rAVL</label
             >
+
+            <input
+              type="radio"
+              class="btn-check"
+              name="leftTreeSelection"
+              id="lRbTreeBtn"
+              autocomplete="off"
+              onclick="switchTree(RBTree, 'left')"
+            />
+            <label class="btn btn-outline-primary" for="lRbTreeBtn"
+              >Red-Black</label
+            >
           </div>
         </div>
       </div>
@@ -190,6 +202,18 @@
             <label class="btn btn-outline-primary" for="rRavlTreeBtn"
               >rAVL</label
             >
+
+            <input
+              type="radio"
+              class="btn-check"
+              name="rightTreeSelection"
+              id="rRbTreeBtn"
+              autocomplete="off"
+              onclick="switchTree(RBTree, 'right')"
+            />
+            <label class="btn btn-outline-primary" for="rRbTreeBtn"
+              >Red-Black</label
+            >
           </div>
         </div>
       </div>
@@ -211,6 +235,7 @@
   <script src="avl.js"></script>
   <script src="wavl.js"></script>
   <script src="ravl.js"></script>
+  <script src="rbt.js"></script>
 
   <script src="recorder.js"></script>
 

index.html

@@ -115,6 +115,18 @@
             <label class="btn btn-outline-primary" for="ravlTreeBtn"
               >rAVL</label
             >
+
+            <input
+              type="radio"
+              class="btn-check"
+              name="treeSelection"
+              id="rbTreeBtn"
+              autocomplete="off"
+              onclick="switchTree(RBTree)"
+            />
+            <label class="btn btn-outline-primary" for="rbTreeBtn"
+              >Red-Black</label
+            >
           </div>
         </div>
       </div>
@@ -186,6 +198,7 @@
   <script src="avl.js"></script>
   <script src="wavl.js"></script>
   <script src="ravl.js"></script>
+  <script src="rbt.js"></script>
 
   <script src="recorder.js"></script>
 

rbt.js

@@ -0,0 +1,161 @@
+const RED = 0;
+const BLACK = 1;
+
+function isDoubleBlack(x) {
+    return x && nodeDifferences(x).indexOf(2) != -1;
+}
+
+class RBTree extends RankedTree {
+    isCorrectNode(node, recursive) {
+        if (!node) {
+            return true;
+        }
+
+        let [left, right] = nodeDifferences(node);
+        if ([RED, BLACK].indexOf(left) == -1) {
+            // left subtree has invalid difference
+            return false;
+        } else if ([RED, BLACK].indexOf(right) == -1) {
+            // right subtree has invalid difference
+            return false;
+        }
+
+        if (nodeDifference(node) == RED && (left == RED || right == RED)) {
+            // two consecutive red nodes
+            return false;
+        }
+
+        recursive = recursive ?? true;
+        return (
+            !recursive ||
+            (this.isCorrectNode(node.left) && this.isCorrectNode(node.right))
+        );
+    }
+
+    insertRebalanceStep(z, y, rightChild, rotateLeft, rotateRight) {
+        let [p, pp] = [z.parent, z.parent.parent];
+
+        if (y && nodeDifference(y) == RED) {
+            // Case 1
+            // ======
+            // z’s uncle y is red
+            pp.rank++;
+            this.record("Insertion case #1: recoloring uncle", pp);
+            z = pp;
+        } else if (z === rightChild) {
+            // Case 2
+            // ======
+            // z’s uncle y is black and z is a right child
+            z = p;
+            rotateLeft(p, this);
+            this.record("Insertion case #2: rotating by parent");
+        } else {
+            // Case 3
+            // ======
+            // z’s uncle y is black and z is a left child
+            rotateRight(pp, this);
+            this.record("Insertion case #3: rotating by grandparent");
+        }
+
+        return z;
+    }
+
+    insertRebalance(z) {
+        while (z.parent && nodeDifference(z.parent) == RED) {
+            let [p, pp] = [z.parent, z.parent.parent];
+
+            if (p === pp.left) {
+                z = this.insertRebalanceStep(
+                    z,
+                    pp.right,
+                    p.right,
+                    rotateLeft,
+                    rotateRight
+                );
+            } else {
+                z = this.insertRebalanceStep(
+                    z,
+                    pp.left,
+                    p.left,
+                    rotateRight,
+                    rotateLeft
+                );
+            }
+        }
+    }
+
+    deleteRebalanceStep(x, w, parent, right, rotateLeft, rotateRight) {
+        if (nodeDifference(w) == RED) {
+            // Case 1
+            // ======
+            // x’s sibling w is red
+            rotateLeft(parent, this);
+            this.record("Deletion case #1: rotating by parent", parent);
+            w = right(parent);
+        }
+
+        if (nodeDifferences(w).equals([BLACK, BLACK])) {
+            // Case 2
+            // ======
+            // x’s sibling w is black, and both of w’s children are black
+            parent.rank--;
+            this.record("Deletion case #2: recoloring sibling", w);
+            x = parent;
+        } else {
+            // Case 3
+            // ======
+            // x’s sibling w is black,
+            // w’s left child is red, and w’s right child is black
+            if (nodeDifference(right(w), w) == BLACK) {
+                rotateRight(w, this);
+                this.record("Deletion case #3: rotating by w", w);
+                w = right(parent);
+            }
+
+            // Case 4
+            // ======
+            // x’s sibling w is black, and w’s right child is red
+            parent.rank--;
+            this.record(
+                "Deletion case #4: moving double black to parent",
+                parent
+            );
+            w.rank++;
+            this.record("Deletion case #4: coloring w's child", w);
+            rotateLeft(parent, this);
+            this.record("Deletion case #4: rotating by parent", parent);
+
+            x = this.root;
+        }
+
+        return [x, x ? x.parent : null];
+    }
+
+    deleteRebalance(node, parent) {
+        if (!node && !parent) {
+            return;
+        }
+
+        while (node !== this.root && isDoubleBlack(parent)) {
+            if (node === parent.left) {
+                [node, parent] = this.deleteRebalanceStep(
+                    node,
+                    parent.right,
+                    parent,
+                    (x) => x.right,
+                    rotateLeft,
+                    rotateRight
+                );
+            } else {
+                [node, parent] = this.deleteRebalanceStep(
+                    node,
+                    parent.left,
+                    parent,
+                    (x) => x.left,
+                    rotateRight,
+                    rotateLeft
+                );
+            }
+        }
+    }
+}