Unit Plan - Recursion and 2D Arrays

Unit: Recursion and 2D Arrays

Objective: To provide students with a deep understanding of recursion and the manipulation of 2D arrays, enabling them to solve complex problems efficiently.

Duration: 2 weeks (8 class sessions of 1.5 hours each)

Key Topics:

1. Introduction to Recursion:

   • Definition and basic principles
   • Recursive vs. iterative solutions
   • Base cases and recursive cases

2. Understanding 2D Arrays:

   • Declaration and initialization
   • Accessing and modifying elements
   • Iterating through 2D arrays

3. Recursion in 2D Arrays:

   • Traversing 2D arrays using recursion
   • Solving problems like searching, sorting, and matrix manipulation

4. Recursion and Divide and Conquer:

   • Master theorem
   • Applications in 2D arrays (e.g., matrix multiplication, finding maximum subarray sum)

5. Dynamic Programming on 2D Arrays:

   • Memoization and tabulation
   • Solving problems like 0/1 Knapsack, Longest Increasing Subsequence

6. Space and Time Complexity Analysis:

   • Big O notation for recursive functions
   • Analyzing space complexity of 2D arrays

7. Advanced Recursion Techniques:

   • Backtracking
   • Recursion with multiple parameters

8. Practical Applications:

   • Image processing using 2D arrays
   • Game development with recursion and 2D arrays

Learning Outcomes:

• Students will understand the concept of recursion and be able to write recursive functions.
• Students will be able to implement and analyze 2D array manipulations.
• Students will apply recursion to solve problems in 2D arrays.
• Students will understand the divide and conquer strategy and its application in 2D arrays.
• Students will be able to use dynamic programming to optimize solutions for 2D array problems.
• Students will be able to analyze the space and time complexity of recursive functions and 2D array operations.
• Students will apply advanced recursion techniques to solve complex problems.
• Students will explore practical applications of recursion and 2D arrays in real-world scenarios.

Assessment:

• Assignments: Weekly programming assignments that involve implementing recursive functions and manipulating 2D arrays.
• Projects: A mid-unit project where students apply recursion and 2D arrays to solve a complex problem (e.g., a game or an image processing task).

Session Plan:

1. Session 1: Introduction to Recursion

   • Lecture and interactive examples
   • Hands-on exercises to write simple recursive functions

2. Session 2: Understanding 2D Arrays

   • Lecture on declaration, initialization, and accessing elements
   • Lab session for practicing 2D array operations

3. Session 3: Recursion in 2D Arrays

   • Lecture on recursive traversal and matrix manipulation
   • Lab session for implementing recursive solutions for 2D array problems

4. Session 4: Recursion and Divide and Conquer

   • Lecture on the master theorem and its application
   • Lab session for solving divide and conquer problems using recursion

5. Session 5: Dynamic Programming on 2D Arrays

   • Lecture on memoization and tabulation
   • Lab session for implementing dynamic programming solutions for 2D array problems

6. Session 6: Space and Time Complexity Analysis

   • Lecture on analyzing the complexity of recursive functions and 2D array operations
   • Lab session for complexity analysis exercises

7. Session 7: Advanced Recursion Techniques

   • Lecture on backtracking and recursion with multiple parameters
   • Lab session for solving problems using advanced recursion techniques

8. Session 8: Practical Applications

   • Guest lecture or workshop on real-world applications
   • Discussion and planning for the final project