Unit 1: Recursion

Write a recursive method that counts ways to move right or down through a grid while avoiding blocked cells and stopping cleanly at boundaries.

Generate all strings with n pairs of matched symbols, using counts of opened and closed symbols to prevent invalid prefixes.

Given a set of valid words, decide whether a string can be split into valid pieces and explain where repeated subproblems appear.

Given an array of positive integers, recursively choose or skip each value and collect subsets whose sum equals a target.

For a sorted array, trace the low, high, and mid values for binary search and explain the base case for a missing target.

Check whether a phrase is a palindrome after ignoring spaces and case, without creating a full reversed copy.

Use recursion to count connected land regions in a small grid, marking cells safely so the same cell is not counted twice.

Return one path through a maze from start to finish, using a visited grid to prevent cycles.

Given digits mapped to letters, recursively generate all possible letter strings and explain the branching factor.

Given a simplified nested-list object, compute its maximum depth and describe the result for an empty nested list.

Reverse a singly linked list using recursion and explain which reference becomes the new head.

Traverse a binary tree recursively and append values to a list in preorder while preserving the original tree.

Generate all length-k increasing sequences from 1 to n and prune choices that cannot complete the sequence.

Given a grid of nonnegative costs, recursively compute the cheapest path to the bottom-right using only right and down moves.

Count ways to reach step n using steps of size 1, 2, or 3, and identify why a plain recursive solution repeats work.

Compress consecutive characters into character-count groups using recursion over the current index and run length.

Determine whether an array can be split into two groups with equal sum by recursively assigning each value to one side.

Compare two strings recursively and return the first index where they differ, including behavior when one string ends first.

Generate all permutations of distinct values using in-place swaps, then restore the array after each recursive call.

Modify permutation generation so duplicate input values do not produce duplicate output arrangements.

Given a binary expression tree, recursively evaluate operators and operands while rejecting malformed operator nodes.

Split an array into halves, find a candidate in each half, and verify which candidate appears most often.

Given a DAG, recursively count paths from a start node to an end node and explain why memoization is safe.

Expand a small pattern such as repeated grouped text by recursively processing bracketed sections.

Generate lexicographic strings over a small alphabet, but skip whole branches when their size is smaller than k.

Recolor a connected region in a matrix and explain the four checks needed before each recursive call.

Assign students to limited project teams recursively while respecting capacity and prerequisite constraints.

Given a recursive method that returns a value after two calls, draw the call tree and compute the final return value.

Rewrite a recursive depth-first traversal using an explicit stack and compare the order of processing.

Create a multi-part assignment that asks students to trace, implement, test, and analyze one recursive problem.