Recursive Runtime Analysis - CSC Data Structures/Algorithms Tutorial Gen Z Visual Edition 1/2

In this CSC 225 Algorithms & Data Structures lecture, we're introducing recursion, recurrence relations, and runtime analysis! Topics covered: Recursion: How recursive algorithms work, including recursive calls, base cases, and inductive steps. Recursive Algorithms: Walking through recursiveMax() to understand how recursive functions execute and return values. Runtime Analysis: Counting primitive operations in recursive algorithms to determine their running time, (T(n)). Recurrence Relations: Expressing an algorithm's runtime using its base case and recursive step. Repeated Substitution: Solving recurrence relations by expanding them step by step. General Form vs. Closed Form: Identifying patterns after (i) substitutions and eliminating recursive terms. Linear Recurrences: Deriving the closed-form solution (T(n)=7n-4) from (T(n)=T(n-1)+7), with (T(1)=3). By the end, you'll understand how to go from recursive pseudocode → recurrence relation → repeated substitution → general form → closed-form solution. Perfect for CSC 225 students reviewing Lecture 7 or preparing for their Algorithms & Data Structures midterm!