Episode 7 — DSA with JavaScript / 7.17 — Binary Search Tree

7.17 — Quick Revision: BST

<< Overview

Key concepts

BST property

Left subtree < Root < Right subtree (for every node)

Operations

OpBalancedSkewed
SearchO(log n)O(n)
InsertO(log n)O(n)
DeleteO(log n)O(n)

Delete cases

  1. Leaf → remove
  2. One child → replace with child
  3. Two children → replace with inorder successor

Key algorithms

  • Validate: pass min/max bounds
  • Kth smallest: inorder count to k
  • LCA: both < root → left, both > root → right
  • Sorted array to BST: pick middle, recurse

Self-check drill

SC-001

  • Q: BST property?
  • A: Left < root < right for all nodes

SC-002

  • Q: BST search time?
  • A: O(log n) balanced, O(n) skewed

SC-003

  • Q: BST inorder gives?
  • A: Sorted ascending order

SC-004

  • Q: Delete node with 2 children?
  • A: Replace with inorder successor

SC-005

  • Q: Validate BST?
  • A: Pass min/max bounds recursively

SC-006

  • Q: Kth smallest?
  • A: Inorder traversal, count to k

SC-007

  • Q: Sorted array to BST?
  • A: Pick middle as root, recurse

SC-008

  • Q: BST vs Hash Map?
  • A: BST: sorted order + range queries

SC-009

  • Q: Balanced BST?
  • A: AVL or Red-Black tree

SC-010

  • Q: BST floor/ceiling?
  • A: Track closest while searching

SC-011

  • Q: BST property?
  • A: Left < root < right for all nodes

SC-012

  • Q: BST search time?
  • A: O(log n) balanced, O(n) skewed

SC-013

  • Q: BST inorder gives?
  • A: Sorted ascending order

SC-014

  • Q: Delete node with 2 children?
  • A: Replace with inorder successor

SC-015

  • Q: Validate BST?
  • A: Pass min/max bounds recursively

SC-016

  • Q: Kth smallest?
  • A: Inorder traversal, count to k

SC-017

  • Q: Sorted array to BST?
  • A: Pick middle as root, recurse

SC-018

  • Q: BST vs Hash Map?
  • A: BST: sorted order + range queries

SC-019

  • Q: Balanced BST?
  • A: AVL or Red-Black tree

SC-020

  • Q: BST floor/ceiling?
  • A: Track closest while searching

SC-021

  • Q: BST property?
  • A: Left < root < right for all nodes

SC-022

  • Q: BST search time?
  • A: O(log n) balanced, O(n) skewed

SC-023

  • Q: BST inorder gives?
  • A: Sorted ascending order

SC-024

  • Q: Delete node with 2 children?
  • A: Replace with inorder successor

SC-025

  • Q: Validate BST?
  • A: Pass min/max bounds recursively

SC-026

  • Q: Kth smallest?
  • A: Inorder traversal, count to k

SC-027

  • Q: Sorted array to BST?
  • A: Pick middle as root, recurse

SC-028

  • Q: BST vs Hash Map?
  • A: BST: sorted order + range queries

SC-029

  • Q: Balanced BST?
  • A: AVL or Red-Black tree

SC-030

  • Q: BST floor/ceiling?
  • A: Track closest while searching

SC-031

  • Q: BST property?
  • A: Left < root < right for all nodes

SC-032

  • Q: BST search time?
  • A: O(log n) balanced, O(n) skewed

SC-033

  • Q: BST inorder gives?
  • A: Sorted ascending order

SC-034

  • Q: Delete node with 2 children?
  • A: Replace with inorder successor

SC-035

  • Q: Validate BST?
  • A: Pass min/max bounds recursively

SC-036

  • Q: Kth smallest?
  • A: Inorder traversal, count to k

SC-037

  • Q: Sorted array to BST?
  • A: Pick middle as root, recurse

SC-038

  • Q: BST vs Hash Map?
  • A: BST: sorted order + range queries

SC-039

  • Q: Balanced BST?
  • A: AVL or Red-Black tree

SC-040

  • Q: BST floor/ceiling?
  • A: Track closest while searching

SC-041

  • Q: BST property?
  • A: Left < root < right for all nodes

SC-042

  • Q: BST search time?
  • A: O(log n) balanced, O(n) skewed

SC-043

  • Q: BST inorder gives?
  • A: Sorted ascending order

SC-044

  • Q: Delete node with 2 children?
  • A: Replace with inorder successor

SC-045

  • Q: Validate BST?
  • A: Pass min/max bounds recursively

SC-046

  • Q: Kth smallest?
  • A: Inorder traversal, count to k

SC-047

  • Q: Sorted array to BST?
  • A: Pick middle as root, recurse

SC-048

  • Q: BST vs Hash Map?
  • A: BST: sorted order + range queries

SC-049

  • Q: Balanced BST?
  • A: AVL or Red-Black tree

SC-050

  • Q: BST floor/ceiling?
  • A: Track closest while searching

SC-051

  • Q: BST property?
  • A: Left < root < right for all nodes

SC-052

  • Q: BST search time?
  • A: O(log n) balanced, O(n) skewed

SC-053

  • Q: BST inorder gives?
  • A: Sorted ascending order

SC-054

  • Q: Delete node with 2 children?
  • A: Replace with inorder successor

SC-055

  • Q: Validate BST?
  • A: Pass min/max bounds recursively

SC-056

  • Q: Kth smallest?
  • A: Inorder traversal, count to k

SC-057

  • Q: Sorted array to BST?
  • A: Pick middle as root, recurse

SC-058

  • Q: BST vs Hash Map?
  • A: BST: sorted order + range queries

SC-059

  • Q: Balanced BST?
  • A: AVL or Red-Black tree

SC-060

  • Q: BST floor/ceiling?
  • A: Track closest while searching

SC-061

  • Q: BST property?
  • A: Left < root < right for all nodes

SC-062

  • Q: BST search time?
  • A: O(log n) balanced, O(n) skewed

SC-063

  • Q: BST inorder gives?
  • A: Sorted ascending order

SC-064

  • Q: Delete node with 2 children?
  • A: Replace with inorder successor

SC-065

  • Q: Validate BST?
  • A: Pass min/max bounds recursively

SC-066

  • Q: Kth smallest?
  • A: Inorder traversal, count to k

SC-067

  • Q: Sorted array to BST?
  • A: Pick middle as root, recurse

SC-068

  • Q: BST vs Hash Map?
  • A: BST: sorted order + range queries

SC-069

  • Q: Balanced BST?
  • A: AVL or Red-Black tree

SC-070

  • Q: BST floor/ceiling?
  • A: Track closest while searching

SC-071

  • Q: BST property?
  • A: Left < root < right for all nodes

SC-072

  • Q: BST search time?
  • A: O(log n) balanced, O(n) skewed

SC-073

  • Q: BST inorder gives?
  • A: Sorted ascending order

SC-074

  • Q: Delete node with 2 children?
  • A: Replace with inorder successor

SC-075

  • Q: Validate BST?
  • A: Pass min/max bounds recursively

SC-076

  • Q: Kth smallest?
  • A: Inorder traversal, count to k

SC-077

  • Q: Sorted array to BST?
  • A: Pick middle as root, recurse

SC-078

  • Q: BST vs Hash Map?
  • A: BST: sorted order + range queries

SC-079

  • Q: Balanced BST?
  • A: AVL or Red-Black tree

SC-080

  • Q: BST floor/ceiling?
  • A: Track closest while searching

SC-081

  • Q: BST property?
  • A: Left < root < right for all nodes

SC-082

  • Q: BST search time?
  • A: O(log n) balanced, O(n) skewed

SC-083

  • Q: BST inorder gives?
  • A: Sorted ascending order

SC-084

  • Q: Delete node with 2 children?
  • A: Replace with inorder successor

SC-085

  • Q: Validate BST?
  • A: Pass min/max bounds recursively

SC-086

  • Q: Kth smallest?
  • A: Inorder traversal, count to k

SC-087

  • Q: Sorted array to BST?
  • A: Pick middle as root, recurse

SC-088

  • Q: BST vs Hash Map?
  • A: BST: sorted order + range queries

SC-089

  • Q: Balanced BST?
  • A: AVL or Red-Black tree

SC-090

  • Q: BST floor/ceiling?
  • A: Track closest while searching

SC-091

  • Q: BST property?
  • A: Left < root < right for all nodes

SC-092

  • Q: BST search time?
  • A: O(log n) balanced, O(n) skewed

SC-093

  • Q: BST inorder gives?
  • A: Sorted ascending order

SC-094

  • Q: Delete node with 2 children?
  • A: Replace with inorder successor

SC-095

  • Q: Validate BST?
  • A: Pass min/max bounds recursively

SC-096

  • Q: Kth smallest?
  • A: Inorder traversal, count to k

SC-097

  • Q: Sorted array to BST?
  • A: Pick middle as root, recurse

SC-098

  • Q: BST vs Hash Map?
  • A: BST: sorted order + range queries

SC-099

  • Q: Balanced BST?
  • A: AVL or Red-Black tree

SC-100

  • Q: BST floor/ceiling?
  • A: Track closest while searching

SC-101

  • Q: BST property?
  • A: Left < root < right for all nodes

SC-102

  • Q: BST search time?
  • A: O(log n) balanced, O(n) skewed

SC-103

  • Q: BST inorder gives?
  • A: Sorted ascending order

SC-104

  • Q: Delete node with 2 children?
  • A: Replace with inorder successor

SC-105

  • Q: Validate BST?
  • A: Pass min/max bounds recursively

SC-106

  • Q: Kth smallest?
  • A: Inorder traversal, count to k

SC-107

  • Q: Sorted array to BST?
  • A: Pick middle as root, recurse

SC-108

  • Q: BST vs Hash Map?
  • A: BST: sorted order + range queries

SC-109

  • Q: Balanced BST?
  • A: AVL or Red-Black tree

SC-110

  • Q: BST floor/ceiling?
  • A: Track closest while searching

SC-111

  • Q: BST property?
  • A: Left < root < right for all nodes

SC-112

  • Q: BST search time?
  • A: O(log n) balanced, O(n) skewed

SC-113

  • Q: BST inorder gives?
  • A: Sorted ascending order

SC-114

  • Q: Delete node with 2 children?
  • A: Replace with inorder successor

SC-115

  • Q: Validate BST?
  • A: Pass min/max bounds recursively

SC-116

  • Q: Kth smallest?
  • A: Inorder traversal, count to k

SC-117

  • Q: Sorted array to BST?
  • A: Pick middle as root, recurse

SC-118

  • Q: BST vs Hash Map?
  • A: BST: sorted order + range queries

SC-119

  • Q: Balanced BST?
  • A: AVL or Red-Black tree

SC-120

  • Q: BST floor/ceiling?
  • A: Track closest while searching

SC-121

  • Q: BST property?
  • A: Left < root < right for all nodes

SC-122

  • Q: BST search time?
  • A: O(log n) balanced, O(n) skewed

SC-123

  • Q: BST inorder gives?
  • A: Sorted ascending order

SC-124

  • Q: Delete node with 2 children?
  • A: Replace with inorder successor

SC-125

  • Q: Validate BST?
  • A: Pass min/max bounds recursively

SC-126

  • Q: Kth smallest?
  • A: Inorder traversal, count to k

SC-127

  • Q: Sorted array to BST?
  • A: Pick middle as root, recurse

SC-128

  • Q: BST vs Hash Map?
  • A: BST: sorted order + range queries

SC-129

  • Q: Balanced BST?
  • A: AVL or Red-Black tree

SC-130

  • Q: BST floor/ceiling?
  • A: Track closest while searching

SC-131

  • Q: BST property?
  • A: Left < root < right for all nodes

SC-132

  • Q: BST search time?
  • A: O(log n) balanced, O(n) skewed

SC-133

  • Q: BST inorder gives?
  • A: Sorted ascending order

SC-134

  • Q: Delete node with 2 children?
  • A: Replace with inorder successor

SC-135

  • Q: Validate BST?
  • A: Pass min/max bounds recursively

SC-136

  • Q: Kth smallest?
  • A: Inorder traversal, count to k

SC-137

  • Q: Sorted array to BST?
  • A: Pick middle as root, recurse

SC-138

  • Q: BST vs Hash Map?
  • A: BST: sorted order + range queries

SC-139

  • Q: Balanced BST?
  • A: AVL or Red-Black tree

SC-140

  • Q: BST floor/ceiling?
  • A: Track closest while searching

SC-141

  • Q: BST property?
  • A: Left < root < right for all nodes

SC-142

  • Q: BST search time?
  • A: O(log n) balanced, O(n) skewed

SC-143

  • Q: BST inorder gives?
  • A: Sorted ascending order

SC-144

  • Q: Delete node with 2 children?
  • A: Replace with inorder successor

SC-145

  • Q: Validate BST?
  • A: Pass min/max bounds recursively

SC-146

  • Q: Kth smallest?
  • A: Inorder traversal, count to k

SC-147

  • Q: Sorted array to BST?
  • A: Pick middle as root, recurse

SC-148

  • Q: BST vs Hash Map?
  • A: BST: sorted order + range queries

SC-149

  • Q: Balanced BST?
  • A: AVL or Red-Black tree

SC-150

  • Q: BST floor/ceiling?
  • A: Track closest while searching

SC-151

  • Q: BST property?
  • A: Left < root < right for all nodes

SC-152

  • Q: BST search time?
  • A: O(log n) balanced, O(n) skewed

SC-153

  • Q: BST inorder gives?
  • A: Sorted ascending order

SC-154

  • Q: Delete node with 2 children?
  • A: Replace with inorder successor

SC-155

  • Q: Validate BST?
  • A: Pass min/max bounds recursively

SC-156

  • Q: Kth smallest?
  • A: Inorder traversal, count to k

SC-157

  • Q: Sorted array to BST?
  • A: Pick middle as root, recurse

SC-158

  • Q: BST vs Hash Map?
  • A: BST: sorted order + range queries

SC-159

  • Q: Balanced BST?
  • A: AVL or Red-Black tree

SC-160

  • Q: BST floor/ceiling?
  • A: Track closest while searching

SC-161

  • Q: BST property?
  • A: Left < root < right for all nodes

SC-162

  • Q: BST search time?
  • A: O(log n) balanced, O(n) skewed

SC-163

  • Q: BST inorder gives?
  • A: Sorted ascending order

SC-164

  • Q: Delete node with 2 children?
  • A: Replace with inorder successor

SC-165

  • Q: Validate BST?
  • A: Pass min/max bounds recursively

SC-166

  • Q: Kth smallest?
  • A: Inorder traversal, count to k

SC-167

  • Q: Sorted array to BST?
  • A: Pick middle as root, recurse

SC-168

  • Q: BST vs Hash Map?
  • A: BST: sorted order + range queries

SC-169

  • Q: Balanced BST?
  • A: AVL or Red-Black tree

SC-170

  • Q: BST floor/ceiling?
  • A: Track closest while searching

SC-171

  • Q: BST property?
  • A: Left < root < right for all nodes

SC-172

  • Q: BST search time?
  • A: O(log n) balanced, O(n) skewed

SC-173

  • Q: BST inorder gives?
  • A: Sorted ascending order

SC-174

  • Q: Delete node with 2 children?
  • A: Replace with inorder successor

SC-175

  • Q: Validate BST?
  • A: Pass min/max bounds recursively

SC-176

  • Q: Kth smallest?
  • A: Inorder traversal, count to k

SC-177

  • Q: Sorted array to BST?
  • A: Pick middle as root, recurse

SC-178

  • Q: BST vs Hash Map?
  • A: BST: sorted order + range queries

SC-179

  • Q: Balanced BST?
  • A: AVL or Red-Black tree

SC-180

  • Q: BST floor/ceiling?
  • A: Track closest while searching

SC-181

  • Q: BST property?
  • A: Left < root < right for all nodes

SC-182

  • Q: BST search time?
  • A: O(log n) balanced, O(n) skewed

SC-183

  • Q: BST inorder gives?
  • A: Sorted ascending order

SC-184

  • Q: Delete node with 2 children?
  • A: Replace with inorder successor

SC-185

  • Q: Validate BST?
  • A: Pass min/max bounds recursively

SC-186

  • Q: Kth smallest?
  • A: Inorder traversal, count to k

SC-187

  • Q: Sorted array to BST?
  • A: Pick middle as root, recurse

SC-188

  • Q: BST vs Hash Map?
  • A: BST: sorted order + range queries

SC-189

  • Q: Balanced BST?
  • A: AVL or Red-Black tree

SC-190

  • Q: BST floor/ceiling?
  • A: Track closest while searching

SC-191

  • Q: BST property?
  • A: Left < root < right for all nodes

SC-192

  • Q: BST search time?
  • A: O(log n) balanced, O(n) skewed

SC-193

  • Q: BST inorder gives?
  • A: Sorted ascending order

SC-194

  • Q: Delete node with 2 children?
  • A: Replace with inorder successor

SC-195

  • Q: Validate BST?
  • A: Pass min/max bounds recursively

SC-196

  • Q: Kth smallest?
  • A: Inorder traversal, count to k

SC-197

  • Q: Sorted array to BST?
  • A: Pick middle as root, recurse

SC-198

  • Q: BST vs Hash Map?
  • A: BST: sorted order + range queries

SC-199

  • Q: Balanced BST?
  • A: AVL or Red-Black tree

SC-200

  • Q: BST floor/ceiling?
  • A: Track closest while searching