lowerBound & upperBound

CHANGELOG.md

@@ -5,6 +5,13 @@ The format is based on [Keep a Changelog](https://keepachangelog.com/en/1.0.0/),
 and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0.html).
 
 ## [Unreleased]
+
+## [4.1.0] - 2021-04-21
+
+### Added
+- `.lowerBound(k)` to find the node with biggest key less or equal a value k.
+- `.upperBound(k)` to find the node with smallest key bigger than a value k.
+
 ## [4.0.1] - 2021-04-15
 ### Fixed
 - exported AvlTreeNode path.

README.md

@@ -32,6 +32,8 @@ Binary Search Tree & AVL Tree (Self Balancing Tree) implementation in javascript
   * [.find(key)](#findkey)
   * [.min()](#min)
   * [.max()](#max)
+  * [.lowerBound(k)](#lowerboundk)
+  * [.upperBound(k)](#upperboundk)
   * [.root()](#root)
   * [.count()](#count)
   * [.traverseInOrder(cb)](#traverseinordercb)
@@ -202,6 +204,49 @@ const max = bst.max();
 console.log(max.getKey()); // 90
 console.log(max.getValue()); // v4
 ```
+
+### .lowerBound(k)
+finds the node with the biggest key less or equal a given value k.
+
+<table>
+  <tr>
+    <th align="center">params</th>
+    <th align="center">return</th>
+    <th align="center">runtime</th>
+  </tr>
+  <tr>
+    <td>k: number | string</td>
+    <td align="center"><a href="#binarysearchtreenode">BinarySearchTreeNode</a> | <a href="#avltreenode">AvlTreeNode</a></td>
+    <td align="center">O(log(n))</td>
+  </tr>
+</table>
+
+```js
+console.log(bst.lowerBound(60).getKey()); // 50
+console.log(bst.lowerBound(10)); // null
+```
+
+### .upperBound(k)
+finds the node with the smallest key bigger than a given value k.
+
+<table>
+  <tr>
+    <th align="center">params</th>
+    <th align="center">return</th>
+    <th align="center">runtime</th>
+  </tr>
+  <tr>
+    <td>k: number | string</td>
+    <td align="center"><a href="#binarysearchtreenode">BinarySearchTreeNode</a> | <a href="#avltreenode">AvlTreeNode</a></td>
+    <td align="center">O(log(n))</td>
+  </tr>
+</table>
+
+```js
+console.log(bst.upperBound(75).getKey()); // 80
+console.log(bst.upperBound(110)); // null
+```
+
 ### .root()
 returns the root node of the tree.
 

package.json

@@ -1,6 +1,6 @@
 {
   "name": "@datastructures-js/binary-search-tree",
-  "version": "4.0.1",
+  "version": "4.1.0",
   "description": "binary search tree & avl tree (self balancing tree) implementation in javascript",
   "main": "index.js",
   "scripts": {

src/binarySearchTree.js

@@ -142,6 +142,54 @@ class BinarySearchTree {
     return current;
   }
 
+  /**
+   * Returns the node with the biggest key less or equal to k
+   * @public
+   * @param {number|string} k
+   * @return {BinarySearchTreeNode|null}
+   */
+  lowerBound(k, current = this._root) {
+    if (current === null) {
+      return null;
+    }
+
+    if (current.getKey() === k) {
+      return current;
+    }
+
+    if (current.getKey() > k) {
+      return this.lowerBound(k, current.getLeft());
+    }
+
+    if (current.hasRight() && current.getRight().getKey() <= k) {
+      return this.lowerBound(k, current.getRight());
+    }
+
+    return current;
+  }
+
+  /**
+   * Returns the node with the smallest key bigger than k
+   * @public
+   * @param {number|string} k
+   * @return {BinarySearchTreeNode|null}
+   */
+  upperBound(k, current = this._root) {
+    if (current === null) {
+      return null;
+    }
+
+    if (current.getKey() <= k) {
+      return this.upperBound(k, current.getRight());
+    }
+
+    if (current.hasLeft() && current.getLeft().getKey() > k) {
+      return this.upperBound(k, current.getLeft());
+    }
+
+    return current;
+  }
+
   /**
    * Returns the root node
    * @public

test/binarySearchTree.test.js

@@ -80,6 +80,26 @@ describe('BinarySearchTree tests', () => {
     });
   });
 
+  describe('.lowerBound(k)', () => {
+    it('gets the node with biggest key less or equal k', () => {
+      expect(bst.lowerBound(60).getKey()).to.equal(50);
+    });
+
+    it('returns null when k is less than all tree keys', () => {
+      expect(bst.lowerBound(10)).to.equal(null);
+    });
+  });
+
+  describe('.upperBound(k)', () => {
+    it('gets the node with smallest key bigger than k', () => {
+      expect(bst.upperBound(75).getKey()).to.equal(80);
+    });
+
+    it('returns null when k is bigger than all tree keys', () => {
+      expect(bst.upperBound(110)).to.equal(null);
+    });
+  });
+
   describe('.traverseInOrder(cb)', () => {
     it('traverse the tree in-order', () => {
       const keys = [];