🌳 Binary Search Tree

Insert

Tree shape

nodes (n)5

height3

ideal ⌈log₂(n+1)⌉3

worst case5

Search cost = height. Balanced height ≈ log₂ n → O(log n).

Insert Pseudocode

1insert(node, v):
2  if node is null: return Node(v)
3  if v < node.value:
4    node.left = insert(node.left, v)
5  else:
6    node.right = insert(node.right, v)

Speed: 55%

Binary Search Tree Visualizer: Insert, Search, Balanced vs Skewed

This binary search tree simulator animates the one rule that defines a BST: smaller values go left, larger go right. Insert a value and watch it walk from the root to its slot; search a value and follow the highlighted path to a match or a dead end. The lab makes balance tangible with a tree-shape card comparing the current height against the ideal log-base-2 height and the worst case, and a one-tap Skewed preset that inserts already-sorted values so the tree collapses into a linked-list chain of height n. The signature interaction: Predict mode pauses each search and asks you to call left, right, or found at every node before it moves, with instant feedback and a score, turning passive watching into active recall of the comparison rule.

What you can do in this simulation

Insert values and watch each one animate down the tree comparing at every node until it finds an empty slot
Search for a value and follow the highlighted path to a match (green) or a dead end (red)
Predict mode: call left / here / right at each node of a search before it moves, with instant feedback and a running score
Balanced vs Skewed presets show how insertion order alone turns O(log n) into O(n) — the tree-shape card compares height to the ideal
Adjust speed, load presets, or clear the tree, with a pseudocode panel synced to the insert and search recurrences

Concepts covered

binary search tree · BST insert and search · tree height and balance · O(log n) vs O(n) · in-order traversal · self-balancing trees · degenerate tree

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Binary Search Tree Visualizer: Insert, Search, Balanced vs Skewed

What you can do in this simulation

Insert values and watch each one animate down the tree comparing at every node until it finds an empty slot

Search for a value and follow the highlighted path to a match (green) or a dead end (red)

Predict mode: call left / here / right at each node of a search before it moves, with instant feedback and a running score

Balanced vs Skewed presets show how insertion order alone turns O(log n) into O(n) — the tree-shape card compares height to the ideal

Adjust speed, load presets, or clear the tree, with a pseudocode panel synced to the insert and search recurrences