Tree height
Tree height is the number of edges on the longest downward path from a tree’s root to any node, typically a leaf.
Advanced Algorithms and Data Structures
Tree height is the number of edges on the longest path from a tree's root to a leaf.
- How it is used
- Measures the depth that governs tree-operation cost and supports practical comparisons between balanced and unbalanced structures.
- How deep it goes
- Defines height and connects it to runtime, then derives logarithmic growth for size-based merges without developing formal proofs.
- Examples
- Uses profiling charts, recursive findPartition, and balanced versus unbalanced disjoint-set merges as concrete examples.
- What you can do after
- Evaluate tree implementations by relating height to operation cost, worst-case behavior, and logarithmic performance.
Read how Advanced Algorithms and Data Structures explains tree height →
Grokking Data Structures
Tree height is the length of the longest path from a tree's root to any leaf, measured in edges or levels according to the chosen convention.
- How it is used
- Uses height to measure tree depth and estimate the cost of heap and binary-search-tree operations.
- How deep it goes
- Defines height with paths and levels, applies it to performance, and defers the mathematical derivation of logarithmic growth.
- Examples
- Uses a three-link path, a height-two subtree, heap levels, and sorted insertions that create skewed binary search trees.
- What you can do after
- Evaluate tree shape and estimate search, insertion, deletion, and related operation costs from the height.
Grokking Algorithms, Second Edition
Tree height is the maximum number of edges or steps on a downward path from the root to a leaf or other node.
- How it is used
- Uses tree height to compare search performance and motivate balancing binary search trees.
- How deep it goes
- Explains height through concrete trees and complexity, then connects it to AVL updates without detailing rotation mechanics.
- Examples
- Uses seven-node trees, a degenerate right-leaning tree, and AVL insertion with updated heights and balance factors.
- What you can do after
- Evaluate tree shape and search cost, and diagnose when AVL height imbalance requires rebalancing.
Read how Grokking Algorithms, Second Edition explains tree height →
Related concepts
- branching factorconfigured by · A branching factor is the number of successor nodes or choices available from a node, commonly represented by a maximum or average value.
- treemeasures · A tree is a connected, acyclic structure of nodes, commonly organized hierarchically through parent-child relationships and optionally around a designated root.
- treapused by · A treap is a randomized binary search tree whose nodes satisfy both binary-search-tree ordering by key and heap ordering by priority.
- heapmeasures · A binary heap is an almost complete binary tree in which each parent satisfies an ordering property relative to its children, enabling efficient access to a minimum or maximum element.
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