Allow to store references and eventually delete them

package.json

@@ -61,6 +61,7 @@
   "devDependencies": {
     "@aureooms/js-compare": "2.0.0",
     "@aureooms/js-itertools": "5.1.0",
+    "@aureooms/js-pseudo-random": "^2.0.0",
     "@aureooms/js-random": "2.0.0",
     "@babel/core": "7.13.14",
     "@babel/preset-env": "7.13.12",
@@ -145,7 +146,7 @@
         ]
       },
       "cover": {
-        "sourceMaps": "inline",
+        "sourceMaps": "both",
         "presets": [
           "babel-preset-power-assert"
         ]

src/deletion/delete_case0.js

@@ -10,14 +10,15 @@ import delete_case1 from './delete_case1.js';
  *   - all other root-leaf paths have a black height of b
  *
  * @param {Node} n - The input node.
+ * @return {Node} The root of the modified subtree.
  */
 const delete_case0 = (n) => {
 	assert(n instanceof Node);
 	assert(n._color === BLACK);
 	// If n is the root, there is nothing to do:
 	//   - all paths go through n, and
 	//   - n is black.
-	if (n.parent !== null) delete_case1(n);
+	return n.parent === null ? n : delete_case1(n);
 };
 
 export default delete_case0;

src/deletion/delete_case1.js

@@ -17,6 +17,7 @@ import delete_case3 from './delete_case3.js';
  *   - n is not the root
  *
  * @param {Node} n - The input node.
+ * @return {Node} The root of the modified subtree.
  */
 const delete_case1 = (n) => {
 	assert(n instanceof Node);
@@ -28,25 +29,25 @@ const delete_case1 = (n) => {
 
 	if (s._color === BLACK) {
 		// If n's sibling is BLACK, go to case 2.
-		delete_case2(n);
-	} else {
-		/**
-		 * Otherwise, prepare for and go to case 3.
-		 *
-		 *           B                       B
-		 *         /   \                  /     \
-		 *      >B       R               R       B
-		 *      / \     / \     -->    /   \    / \
-		 *     -   -  B     B        >B     B  =   =
-		 *           / \   / \       / \   / \
-		 *          =   = =   =     -   - =   =
-		 */
-		n.parent._color = RED;
-		s._color = BLACK;
-		if (n === n.parent.left) rotate_left(n.parent);
-		else rotate_right(n.parent);
-		delete_case3(n);
+		return delete_case2(n);
 	}
+
+	/**
+	 * Otherwise, prepare for and go to case 3.
+	 *
+	 *           B                      *B
+	 *         /   \                  /     \
+	 *      >B       R               R       B
+	 *      / \     / \     -->    /   \    / \
+	 *     -   -  B     B        >B     B  =   =
+	 *           / \   / \       / \   / \
+	 *          =   = =   =     -   - =   =
+	 */
+	n.parent._color = RED;
+	s._color = BLACK;
+	if (n === n.parent.left) rotate_left(n.parent);
+	else rotate_right(n.parent);
+	return delete_case3(n).parent;
 };
 
 export default delete_case1;

src/deletion/delete_case2.js

@@ -16,6 +16,7 @@ import delete_case3 from './delete_case3.js';
  *   - n's sibling is black
  *
  * @param {Node} n - The input node.
+ * @return {Node} The root of the modified subtree.
  */
 const delete_case2 = (n) => {
 	assert(n instanceof Node);
@@ -44,11 +45,11 @@ const delete_case2 = (n) => {
 		(s.right === null || s.right._color === BLACK)
 	) {
 		s._color = RED;
-		delete_case0(n.parent);
+		return delete_case0(n.parent);
 	}
 
 	// Otherwise, go to case 3.
-	else delete_case3(n);
+	return delete_case3(n);
 };
 
 export default delete_case2;

src/deletion/delete_case3.js

@@ -16,6 +16,7 @@ import delete_case4 from './delete_case4.js';
  *   - n's parent and n's sibling's children cannot all be black
  *
  * @param {Node} n - The input node.
+ * @return {Node} The root of the modified subtree.
  */
 const delete_case3 = (n) => {
 	assert(n instanceof Node);
@@ -52,10 +53,11 @@ const delete_case3 = (n) => {
 	) {
 		s._color = RED;
 		n.parent._color = BLACK;
+		return n.parent;
 	}
 
 	// Otherwise, go to case 4.
-	else delete_case4(n);
+	return delete_case4(n);
 };
 
 export default delete_case3;

src/deletion/delete_case4.js

@@ -18,6 +18,7 @@ import delete_case5 from './delete_case5.js';
  *   - at least one of n's sibling's children is red
  *
  * @param {Node} n - The input node.
+ * @return {Node} The root of the modified subtree.
  */
 const delete_case4 = (n) => {
 	assert(n instanceof Node);
@@ -32,18 +33,18 @@ const delete_case4 = (n) => {
 	// the left of the left of the parent, or right of the right, so case 5
 	// will rotate correctly.
 
-	/**
-	 *           ?                       ?
-	 *         /   \                  /     \
-	 *      >B       B              >B        B
-	 *      / \     / \     -->     / \      / \
-	 *     -   -  R     B          -   -   =     R
-	 *           / \   / \                      / \
-	 *          =   = -   -                    =   B
-	 *                                            / \
-	 *                                           -   -
-	 */
 	if (n === n.parent.left && (s.right === null || s.right._color === BLACK)) {
+		/**
+		 *           ?                       ?
+		 *         /   \                  /     \
+		 *      >B       B              >B        B
+		 *      / \     / \     -->     / \      / \
+		 *     -   -  R     B          -   -   =     R
+		 *           / \   / \                      / \
+		 *          =   = -   -                    =   B
+		 *                                            / \
+		 *                                           -   -
+		 */
 		s._color = RED;
 		s.left._color = BLACK;
 		rotate_right(s);
@@ -67,7 +68,9 @@ const delete_case4 = (n) => {
 		rotate_left(s);
 	}
 
-	delete_case5(n);
+	// TODO we could merge case 4 and 5 without too much trouble.
+	// It would allow to avoid checking n's direction twice.
+	return delete_case5(n);
 };
 
 export default delete_case4;

src/deletion/delete_case5.js

@@ -17,6 +17,7 @@ import sibling from '../family/sibling.js';
  *   - if n is a right child, the left child of n's sibling is red
  *
  * @param {Node} n - The input node.
+ * @return {Node} The root of the modified subtree.
  */
 const delete_case5 = (n) => {
 	assert(n instanceof Node);
@@ -28,8 +29,9 @@ const delete_case5 = (n) => {
 
 	/**
 	 * Increment the black height of all root-leaf paths going through n by
+	 * swapping the colors of n's parent and n's sibling and
 	 * rotating at n's parent. This decrements the black height of all
-	 * root-leaft paths going through n's sibling's right child.
+	 * root-leaf paths going through n's sibling's right child.
 	 * We can repaint n's sibling's right child in black to fix this.
 	 * We are done.
 	 *
@@ -44,21 +46,23 @@ const delete_case5 = (n) => {
 	 *                   -   -
 	 */
 
+	// Swap the color of the parent and the sibling.
 	s._color = n.parent._color;
 	n.parent._color = BLACK;
 
 	if (n === n.parent.left) {
 		assert(s.right._color === RED);
 		s.right._color = BLACK;
 		rotate_left(n.parent);
+		return s;
 	}
 
 	// Symmetric case
-	else {
-		assert(s.left._color === RED);
-		s.left._color = BLACK;
-		rotate_right(n.parent);
-	}
+
+	assert(s.left._color === RED);
+	s.left._color = BLACK;
+	rotate_right(n.parent);
+	return s;
 };
 
 export default delete_case5;

src/deletion/delete_no_child.js

@@ -16,6 +16,7 @@ import prune from './prune.js';
  *   - n is not the root
  *
  * @param {Node} n - The node to delete.
+ * @return {Node} The root of the modified subtree.
  */
 const delete_no_child = (n) => {
 	assert(n instanceof Node);
@@ -26,7 +27,7 @@ const delete_no_child = (n) => {
 	if (n._color !== BLACK) {
 		assert(n._color === RED);
 		prune(n);
-		return;
+		return n.parent;
 	}
 
 	// Mock leaf since there is no left child
@@ -39,10 +40,11 @@ const delete_no_child = (n) => {
 
 	// If n is black, deleting it reduces the black-height of every path going
 	// through it by 1. The leaf is black, so there are more things to fix.
-	delete_case1(leaf);
+	const subtree = delete_case1(leaf);
 
 	// Delete mocked leaf
 	prune(leaf);
+	return subtree;
 };
 
 export default delete_no_child;

src/deletion/replace_node.js

@@ -10,7 +10,7 @@ import Node from '../types/Node.js';
 const replace_node = (A, B) => {
 	assert(A instanceof Node);
 	assert(B instanceof Node);
-	// We never apply delete_one_child or delete_no_child on the root
+	// We never apply replace_node on the root
 	assert(A.parent !== null);
 
 	if (A === A.parent.left) A.parent.left = B;

src/index.js

@@ -26,6 +26,9 @@ export {default as insert_case4} from './insertion/insert_case4.js';
 export {default as rotate_left} from './rotate/rotate_left.js';
 export {default as rotate_right} from './rotate/rotate_right.js';
 export {default as search} from './search/search.js';
+export {default as swap_color} from './swap/swap_color.js';
+export {default as swap_left} from './swap/swap_left.js';
+export {default as swap_non_adjacent} from './swap/swap_non_adjacent.js';
 export {default as inordertraversal} from './traversal/inordertraversal.js';
 export {default as rangetraversal} from './traversal/rangetraversal.js';
 export {default as Node} from './types/Node.js';

src/insertion/insert_case0.js

@@ -10,6 +10,7 @@ import insert_case1 from './insert_case1.js';
  *   - n's children are BLACK
  *
  * @param {Node} n - The input node.
+ * @return {Node} The root of the modified subtree.
  */
 const insert_case0 = (n) => {
 	assert(n instanceof Node);
@@ -23,8 +24,12 @@ const insert_case0 = (n) => {
 	 *      / \
 	 *     -   -
 	 */
-	if (n.parent === null) n._color = BLACK;
-	else insert_case1(n);
+	if (n.parent === null) {
+		n._color = BLACK;
+		return n;
+	}
+
+	return insert_case1(n);
 };
 
 export default insert_case0;

src/insertion/insert_case1.js

@@ -11,6 +11,7 @@ import insert_case2 from './insert_case2.js';
  *   - n is not the root of the tree.
  *
  * @param {Node} n - The input node.
+ * @return {Node} The root of the modified subtree.
  */
 const insert_case1 = (n) => {
 	assert(n instanceof Node);
@@ -28,9 +29,7 @@ const insert_case1 = (n) => {
 	 *      / \
 	 *     -   -
 	 */
-	if (n.parent._color === BLACK) return;
-
-	insert_case2(n);
+	return n.parent._color === BLACK ? n : insert_case2(n);
 };
 
 export default insert_case1;

src/insertion/insert_case2.js

@@ -15,6 +15,7 @@ import insert_case3 from './insert_case3.js';
  *   - n's parent is red.
  *
  * @param {Node} n - The input node.
+ * @return {Node} The root of the modified subtree.
  */
 const insert_case2 = (n) => {
 	assert(n instanceof Node);
@@ -45,8 +46,10 @@ const insert_case2 = (n) => {
 		u._color = BLACK;
 		const g = grandparent(n);
 		g._color = RED;
-		insert_case0(g);
-	} else insert_case3(n);
+		return insert_case0(g);
+	}
+
+	return insert_case3(n);
 };
 
 export default insert_case2;