Intermediate Practice - Algorithms

Start with the partition step: choose a pivot, then move smaller elements left and larger ones right. Recurse on each side. Practice with a randomized or median pivot to avoid the O(n^2) worst case. Tracing small arrays first helps you get the index boundaries right before scaling up.

Begin by clearly stating the base case that stops recursion and the recursive case that shrinks the problem. Trace the call stack for small inputs on paper. Classic drills include factorial, Fibonacci, and tree traversals. Watching how calls unwind builds confidence and prevents infinite recursion or stack overflow errors.

Practice by asking what the problem needs. If it wants the shortest path in an unweighted graph or nearest neighbors, drill breadth-first search with a queue. If it wants to explore full paths, detect cycles, or order dependencies, drill depth-first search with recursion or a stack. Repetition makes the choice quick.

A plain binary search tree teaches the core insert, search, and traversal logic and shows how sorted input degrades it to O(n). Mastering that motivates why balancing matters. Once the basic operations feel automatic, the rotations of AVL and red-black trees at the advanced level are much easier to learn.

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