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  • CS201: Elementary Data Structures
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    Course Introduction
    Course Syllabus
    Course Terms of Use
    Unit 1: Abstract Data Types and Arrays in C++
    1.1: Abstract Data Types
    Data Abstraction
    Sort Template with Callback
    Abstract Data Types
    Abstract Data Types in C++
    Standard Template Library
    1.2: Contiguous Implementation
    Arrays
    1.3: Non-Contiguous Implementation
    Memory Allocation in C++
    1.4: Introduction to Memory Pointers
    Pointers in C++
    1.5: Linked Lists
    Singly and Doubly-Linked Lists
    Examples of Linked Lists
    Linked List Programming Exercises
    1.6: Arrays
    Arrays in C
    Additional Features of Arrays
    Representations of Arrays
    Array Programming Exercises
    Unit 1 Assessment
    Unit 1 Assessment
    Unit 2: Introduction to Stacks and Queues
    2.1: Introduction to Lists
    Lists
    2.2: Implementing Lists with Arrays
    Array-Based Lists
    2.3: Overview of Stacks and Queues
    Stacks and Queues
    2.3.1: Introduction to Stacks
    Stacks
    More on Stacks
    Data Structures of Stacks
    The Stack Data Structure
    2.3.2: Introduction to Queues
    Queues
    More on Queues
    Data Structures of Queues
    Unit 2 Assessment
    Unit 2 Assessment
    Unit 3: Pointers and References in C++
    3.1: Review of C-Native Variables
    C Data Types
    Words in Computer Architecture
    3.2: Review of Pointers
    Backtracking Pseudocode
    3.3: Pointing to Memory
    Pointers
    3.4: Pointers for Scalars, Vectors, and Functions
    Everything You Need to Know about Pointers in C
    3.5: Pointers for Arrays
    Memory Allocation
    3.6: Pointer Arithmetic
    C Syntax – Pointers
    3.7: Working with Pointers
    Pointers
    Unit 3 Assessment
    Unit 3 Assessment
    Unit 4: Dynamic Memory Allocation
    4.1: C++ Memory Allocation
    Memory Management
    Dynamic Memory
    4.2: C Memory Allocation
    C Data Structures
    C Pointers and Dynamic Memory Allocation
    4.3: Memory Fragmentation
    Stacks and Heaps
    Allocations and Deallocations
    4.4: C/C++ Based on "Unsafe" Types
    Unsafe Languages
    Unit 4 Assessment
    Unit 4 Assessment
    Unit 5: Linked Stacks, Queues, and Lists
    5.1: Linked Lists
    Linked Lists
    Introduction to Linked Lists
    Other Ways to Use Linked Lists
    Doubly-Linked Lists
    5.2: Linked Stacks
    Linked Stacks
    Implement a Stack using a Linked List
    5.3: Linked Queues
    Linked Queues
    q Module
    Unit 5 Assessment
    Unit 5 Assessment
    Unit 6: Algorithm Efficiency
    6.1: The Importance of Algorithm Efficiency
    Algorithm Efficiency
    Introduction to Efficiency
    6.2: Big-O Analysis
    Big-O
    6.3: Discussions on Algorithm Efficiency
    Algorithm Analysis
    6.4: Measuring Algorithm Efficiency
    Introduction to Algorithms
    6.5: Space-Time Tradeoff
    Space-Time Tradeoff
    Unit 6 Assessment
    Unit 6 Assessment
    Unit 7: Searching and Sorting Algorithms
    7.1: Peak Finding via Vector Search
    Algorithmic Thinking and Peak Finding
    7.2: Models of Computation and Document Distance
    Models of Computation and Document Distance
    7.3: Why Sort? Insertion Sort and Merge Sort
    Insertion Sort and Merge Sort
    Divide and Conquer Methods, Merge Sort, and Exceptions
    7.3.1: Big-O Analysis of Merge and Insertion Sort
    Insertion Sort
    Merge Sort
    7.3.2: Merge and Insertion Sort in C/C++
    Examples of Insertion and Merge Sorts in C++
    7.4: Linear Search
    Linear Search
    7.5: Fibonacci Search
    Fibonacci Search
    7.6: Binary Search, Bubble Sort, and Selection Sorts
    Binary Search, Bubble Sort, and Selection Sort
    Binary Search, Bubble Sort, and Selection Sort in C++
    7.7: Quicksort
    Quicksort and Randomized Algorithms
    Recursive Quicksort in C++
    Non-Recursive Quicksort in C++
    Unit 7 Assessment
    Unit 7 Assessment
    Unit 8: Hash Tables, Graphs, and Trees
    8.1: Hash Tables
    Hashing with Chaining
    Table Doubling and Karp-Rabin
    Open Addressing and Cryptographic Hashing
    Hashing
    8.2: Graphs
    Graphs
    Graphs and Network Flows
    Finding Non-Cyclical Paths between Arbitrary Pairs of Nodes
    8.2.1: Graph Searches
    C Program for Depth-First Search in a Graph
    Breadth-First Search
    8.2.2: Finding Lowest-Cost Paths
    Dijkstra's Algorithm
    Bellman's Algorithm
    8.2.3: Finding a Minimum Spanning Tree
    Minimum Spanning Trees – Kruskal's Algorithm
    Minimum Spanning Trees – Prim's Algorithm
    8.3: Trees
    Trees
    Binary Trees
    Non-Binary Trees
    Unit 8 Assessment
    Unit 8 Assessment
    Study Guide
    CS201 Study Guide
    Course Feedback Survey
    Course Feedback Survey
    Certificate Final Exam
    CS201: Certificate Final Exam
    Proctor-Verified Final Exam
    Archived Materials
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  1. CS201: Elementary Data Structures
  2. Unit 8: Hash Tables, Graphs, and Trees
  3. 8.3: Trees
  4. Binary Trees

Binary Trees

Completion requirements

Most discussion about trees concerns binary trees, whose nodes have no more than two branches. Read this chapter, which offers background and practical applications for binary trees.

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Saylor Academy © 2010-2025 except as otherwise noted. Excluding course final exams, content authored by Saylor Academy is available under a Creative Commons Attribution 3.0 Unported license. Third-party materials are the copyright of their respective owners and shared under various licenses. See detailed licensing information. Saylor Academy®, Saylor.org®, and Harnessing Technology to Make Education Free® are trade names of the Constitution Foundation, a 501(c)(3) organization through which our educational activities are conducted.