# Trie

> Mathematical theory and implementation details for Trie

## Mathematical Theory

**Mathematical Foundation**:

- **Tree Structure**: Each node represents a character
- **Path from Root**: Represents a string
- **Child Nodes**: Represent possible next characters
- **Terminal Nodes**: Mark end of valid strings

**Key Properties**:

- **Height**: Maximum string length
- **Branching Factor**: Size of character set (typically 26 for lowercase letters)
- **Space Complexity**: $O(\text{total characters})$ in worst case

## Implementation

For implementation details and usage examples, see the source code in the `src/` directory.

## API Reference

```typescript
// Import the algorithm
import { Trie } from '@entropy-tamer/reynard-algorithms';
```

## Performance

See the [Performance Analysis](../performance/) section for detailed benchmarks and optimization strategies.