Data Structures and Algorithms in Java
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  • Preface
    • Syllabus
    • Schedule
  • 0. Getting Started
    • 0.1. Environment Setup
    • 0.2. Quiz
  • 1. Java Essentials
    • 1.1. Abstraction
    • 1.2. Implementation
    • 1.3. Unit Testing
    • 1.4. Quiz
  • 2. Priority Queues
    • 2.1. Simple Priority Queues
    • 2.2. Binary Heap
    • 2.3. Unit Testing
    • 2.4. Benchmarking
    • 2.5. Quiz
  • 3. Sorting Algorithms
    • 3.1. Abstraction
    • 3.2. Comparison-based Sort
    • 3.3. Divide & Conquer Sort
    • 3.4. Distribution-based Sort
    • 3.5. Quiz
    • 3.6. Homework
  • 4. Binary Search Trees
    • 4.1. Binary Search Trees
    • 4.2. Balanced BST
    • 4.2. AVL Trees
    • 4.3. Red-Black Trees
    • 4.4. Quiz
  • 5. Tries
    • 5.1. Concept
    • 5.2. Implementation
    • 5.3. Quiz
    • 5.4. Homework
  • 6. Disjoint Sets
    • 6.1. Concept
    • 6.2. Implementation
    • 6.3. Quiz
  • 7. Graphs
    • 7.1. Implementation
    • 7.2. Cycle Detection
    • 7.3. Topological Sorting
    • 7.4. Quiz
  • 8. Minimum Spanning Trees
    • 8.1. Abstraction
    • 8.2. Prim's Algorithm
    • 8.3. Kruskal’s Algorithm
    • 8.4. Edmonds' Algorithm
    • 8.5. Quiz
    • 8.6. Homework
  • 9. Network Flow
    • 9.1. Flow Network
    • 9.2. Ford-Fulkerson Algorithm
    • 9.3. Simplex Algorithm
    • 9.3. Quiz
  • 10. Dynamic Programming
    • 10.1. Fibonacci Sequence
    • 10.2. Tower of Hanoi
    • 10.3. Longest Common Subsequence
    • 10.4. Quiz
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  1. 5. Tries

5.1. Concept

This section gives an overview of tries.

Previous5. TriesNext5.2. Implementation

Last updated 4 years ago

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Overview

A trie is a tree where each node has:

  • 0-to-many children,

  • A key whose type is character,

  • A value that can be any type of object, and

  • An end-state that indicates if the node and its ancestors together represent the end of a certain word.

Let us consider the following list of strings:

["she", "shell", "see", "shore", "selling", "sell"]

Given the strings as keys, a binary search tree can be constructed as follows using a balancing algorithm:

How many character comparisons does it need to make to search a string in a balanced BST?

With the same list of strings, a trie can be constructed as follows:

  • 1st cell: key (a character).

  • 2nd cell: value (the index of the string that the node represents).

  • 3rd cell: end-state (T for true, F for false).

What is the worst-case complexity of searching a string in a trie?