Recording-2025-03-05T21:35:29.076Z

Introduction to Static Global Variables

• A static global variable can be declared using the keyword static which allows the variable to maintain its value between function calls.

• The purpose of a static integer counter is to count the total number of lines of code executed.

Implementing a Counter

• The counter is incremented each time a specific line of code is executed in the function.

• Example: c++ is used to increment the counter.

• The counter can be accessed and updated in both the main function and other functions, such as max().

Code Execution and Analysis

• When the program runs, it calculates the maximum value based on the inputs provided.

• For instance, if an input of $1.99 is provided, the algorithm will find and return this as the maximum since no greater value is provided in the dataset.

• The program's performance is influenced when finding maximum values and how often comparisons are made.

Complexity Analysis

• The complexity of certain algorithms can be analyzed using Big O notation, which expresses how the runtime or space requirements grow as the input size increases.

• Basic complexity classifications could be:

  • O(n): Linear complexity

  • O(n²): Quadratic complexity

• Factors affecting complexity include the number of operations performed and their growth as input size increases.

Recursive Functions

• Recursive functions call themselves to solve a problem by breaking it down into smaller subproblems.

• The complexity of a recursive function can be analyzed by counting the number of times it is called or the number of statements executed.

Application of Limits in Complexity

• When analyzing algorithms, limits can be utilized to determine growth functions.

• Example computation would involve taking the limit as n approaches infinity to find a constant or a bound on growth.

• Important criterion: If the limit results in a constant (not infinite), it supports the function being classified within a certain Big O notation.

Examples of Growth Functions

• If a function f(n) is approximated as 3n² + 2n, the leading term dominates as n becomes large, determining the Big O classification as O(n²).

• Testing specific cases with fixed values allows students to identify patterns in execution and resource needs.

Homework Assignments

• Students are encouraged to practice by determining the complexity of provided code segments.

• Problems may involve analyzing execution counts and utilizing recursive relations to derive complexity classifications.

Conclusion

• Understanding static global variables, counters, recursive functions, and complexity analysis in algorithms is crucial.

• Students should practice by implementing and debugging various algorithms while analyzing their performance under different input sizes.