Tree AlgorithmsIntermediate

Trie (Prefix Tree)

Tree-based data structure that stores strings efficiently by sharing common prefixes. Each path from root to leaf represents a word or key. Excels at autocomplete, spell checking, IP routing tables, and dictionary implementations with O(m) operations where m is key length.

#tree#string-algorithms#prefix-matching#autocomplete

Complexity Analysis

Time (Average)

O(m)

Expected case performance

Space

O(ALPHABET_SIZE × N × M)

Memory requirements

Time (Best)

O(m)

Best case performance

Time (Worst)

O(m)

Worst case performance

Words to Insert (comma-separated)

Word to Search

Example Sets:

How it works

• Each character is a node in the tree
• Words share common prefixes
• End-of-word markers for complete words
• O(m) insert and search time
• Perfect for autocomplete systems

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Animation Speed500ms

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Real-time Statistics

Algorithm Performance Metrics

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Comparisons

Swaps

Array Accesses

Steps

1/ 0

Algorithm Visualization

Step 1 of 0

Initialize array to begin

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Comparing

Swapped

Sorted

Code Execution

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Implementation

Related Algorithms

View all in Tree Algorithms

Lowest Common Ancestor (LCA)

Intermediate

Finds the deepest node that is an ancestor of two given nodes in a tree. Fundamental operation in tree queries with applications in computational biology (species evolution), network routing, and version control systems. Various algorithms offer different time-space tradeoffs.

AVL Tree

Advanced

First self-balancing binary search tree invented in 1962 by Adelson-Velsky and Landis. Maintains height balance through rotations, guaranteeing O(log n) operations. Stricter balancing than red-black trees makes it ideal for lookup-heavy applications like databases and file systems.

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