This explains how to analyze algorithm time and space complexity using frequency counting. It demonstrates this on three examples: array summation (O(n) time, O(n) space), matrix addition (O(n²) time/space), and matrix multiplication (O(n³) time, O(n²) space). The method involves counting statement executions to determine the dominant term in the time function. This segment details a step-by-step methodology for calculating the time complexity of an algorithm using the frequency count method. It explains how to assign time units to individual statements, account for loop iterations, and determine the overall time function, focusing on a simple summation algorithm as an example. The explanation clarifies how to identify the dominant term in the time function to determine the algorithm's order. This segment provides a comprehensive analysis of the time and space complexity for a matrix multiplication algorithm. It builds upon the previous examples by analyzing a more complex algorithm with three nested loops. The presenter clearly explains how the nested loops affect the time complexity, leading to a cubic time complexity (O(n³)). The space complexity analysis is also presented, showing how it remains quadratic (O(n²)) despite the increased time complexity. This segment demonstrates the analysis of both time and space complexity for an algorithm that sums two matrices. It meticulously breaks down the algorithm's steps, calculating the frequency of each operation within nested loops to derive the time complexity. The analysis then extends to determining the space complexity by identifying and counting the variables used, highlighting the relationship between algorithm structure and resource usage.