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These 17 coding challenges exercise different kinds of problem-solving: breaking a task into parts, choosing between algorithms, tracking state, proving a shortcut is safe, and testing edge cases. They are useful practice for learners and interview preparation, but the list is not proof that solving these exact problems improves general critical-thinking ability. Use them to make your reasoning visible, not just to produce a passing answer.
How to practice so the challenge tests your reasoning
Before opening an editor, turn the prompt into a small specification. Then solve it in stages:
- Restate the task. Write down the input, the required output, and what counts as a valid answer. Note whether the input can be empty, contain duplicates, or be unusually large.
- List constraints and assumptions. Clarify such details as whether numbers are consecutive, whether a path must be shortest, and whether a cache operation must be constant-time. If the prompt does not say, identify the assumption your solution uses.
- Make a baseline. Describe the simplest correct approach in plain language, even if it is slow. A baseline gives you something to compare against and helps separate correctness from optimization.
- Choose tests before coding. Include an ordinary case, a boundary case, and an adversarial case. For example, test an empty or one-item input where allowed, repeated values, an already ordered input, and a case that forces the worst behavior you expect.
- Compare alternatives. State the time and extra-space costs of each approach. Explain what the faster method stores or assumes in exchange for its improvement.
- Explain why it works. Identify an invariant, a state transition, or a proof of the greedy choice. Then trace one example by hand and only then implement.
- Review failures as evidence. When a test fails, find the smallest input that reproduces it. Ask whether the mistake is in the model, the invariant, a boundary condition, or the code.
Keep a short record for each problem: baseline, improved idea, complexity, key correctness argument, and the test that caught your hardest bug. This turns a collection of solved prompts into reusable patterns.
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1. Find the missing number in an array
Given a range of consecutive integers with one value absent, find the missing value. First establish the exact range and whether there is exactly one omission. Compare summing the expected range and subtracting the observed sum with an XOR-based approach. The sum method highlights a numerical invariant; XOR cancels matching values and avoids ordinary addition overflow concerns in fixed-width integer contexts. Test the smallest permitted range and omissions at both ends. Do not apply either method if duplicates or multiple missing values are allowed without revisiting the specification.
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2. Two Sum
Find two values whose sum equals a target. The direct approach checks pairs and takes O(n²) time with O(1) extra space. A hash map can reduce expected lookup work to O(n) time using O(n) space. Think carefully about whether to store a value before or after checking its complement: checking first avoids pairing an item with itself unless the input contains a second matching item. Test duplicates, negative values, no solution, and a target requiring the same value twice.
3. Valid parentheses
Determine whether opening and closing brackets are correctly matched and nested. A stack records unmatched opening symbols; each closing symbol must match the stack top, and the stack must be empty at the end. The reasoning is about nested state, not just counting characters: a string can have equal numbers of each bracket and still be invalid. Test a premature close, a missing close, an empty string if allowed, and mixed bracket types.
4. Reverse a linked list
Reverse the links in a singly linked list without losing access to the rest of the list. The iterative method maintains previous, current, and next references, saving next before redirecting the current link. The key invariant is that the processed prefix is already reversed and the unprocessed suffix remains reachable. Compare this with recursion: recursive reasoning can be concise, but uses call-stack space and may encounter depth limits on long lists. Test empty, one-node, and multi-node lists; verify both the new head and termination of the final link.
Pattern building: windows, centers, and two pointers
5. Palindromic substrings
Count or find palindromic substrings, making sure the prompt distinguishes substrings from distinct palindrome values. Expanding around each center checks outward while characters match; there are odd-length centers at characters and even-length centers between characters. This approach is commonly O(n²) time and O(1) extra space, aside from output. Dynamic programming records whether smaller intervals are palindromes and reuses that result, typically trading O(n²) space for stored subproblems. Test repeated characters and even-length palindromes, which reveal missed centers.
6. Container With Most Water
Given vertical lines at positions, choose two that maximize width multiplied by the shorter height. A brute-force scan considers every pair. The two-pointer method starts at the ends and moves the pointer at the shorter line. Its justification matters: keeping the shorter boundary while reducing width cannot improve the area, so a better candidate must discard that limiting boundary. Test steadily increasing heights, equal heights, and a tall line paired with a very short one. Do not move a pointer arbitrarily; the movement rule is the heart of the algorithm.
7. Find all anagrams in a string
Find positions where a window in one string has the same character frequencies as a target string. A sliding window avoids recounting each candidate from scratch: add the incoming character and remove the outgoing one as the window advances. Frequency accounting must match the character model and alphabet assumed by the prompt. Test repeated letters, a target longer than the source, overlapping matches, and characters outside any assumed lowercase alphabet.
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8. Trapping Rain Water
Given bar heights, calculate how much water is trapped after rain. A boundary-based formulation says the water above a position depends on the shorter of the tallest boundary to its left and right, minus its own height, when positive. A two-pointer method can compute this while advancing the side whose maximum boundary is smaller, maintaining the relevant maxima. The exercise is to justify why the opposite boundary is sufficient at that step. Test flat terrain, monotonic heights, a single basin, and zero-height boundaries.
Graphs and search: shortest paths, dependencies, and backtracking
9. Word Ladder
Given a start word, an end word, and an allowed dictionary, find a shortest sequence in which adjacent words differ by one letter. Model each valid word as a graph node and each one-letter change as an edge. Breadth-first search finds a shortest path when all transitions have equal cost. The details that change answers include whether the end word must be in the dictionary and whether the sequence length counts words or transformations. Track visited words so cycles do not cause repeated work. Test an unreachable target and a case with multiple paths of the same length.
10. Course Schedule
Given courses and prerequisite relationships, decide whether all courses can be completed. Represent prerequisites as a directed graph; a cycle means a course ultimately depends on itself. Use depth-first cycle detection or a topological-ordering method such as repeatedly removing courses with no remaining prerequisites. Be explicit about edge direction, since reversing it can still look plausible while changing the interpretation. Test no prerequisites, a simple chain, a disconnected cycle, and duplicate relationships if the input permits them.
11. Word Search
Search for a word in a two-dimensional character grid by moving between adjacent cells, typically without reusing a cell in one path. Depth-first search explores candidate paths, and backtracking restores a cell’s availability when a branch fails. The state is the current grid position, the next character index, and the set of cells already used in that path. Test a one-character word, a word longer than the grid can support, repeated letters, and a path that would succeed only if a cell were incorrectly reused.
Data-structure design and divide-and-conquer
12. Least Recently Used cache
Design a cache with get and put operations that evicts the least recently used item at capacity. A hash map finds entries quickly; a doubly linked list orders them by recency, allowing a touched entry to move to the front and the least recent entry to be removed from the tail. The design targets O(1) get and put operations. Specify what a get miss returns, how updating an existing key affects recency, and what happens at zero capacity if that case is allowed. Test repeated access, overwrite, and eviction order.
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13. Merge k sorted lists
Merge several sorted lists into one sorted sequence. Pairwise merging is a useful baseline. A min-heap keeps the smallest current head among the lists available, producing a typical O(N log k) approach for N total elements and k lists, with heap size up to k. Another option is divide-and-conquer pairwise merging. Compare the costs and implementation complexity, and test empty lists, one list, duplicates, and lists of very different lengths.
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14. Count inversions
Count pairs of positions i < j where the value at i is greater than the value at j. A quadratic pair scan gives a clear baseline. A modified merge sort counts inversions while combining sorted halves: when a right-side value precedes remaining left-side values, it contributes multiple inversions at once. This is a divide-and-conquer improvement to O(n log n) time. Be precise about strict versus non-strict comparison; equal values are not inversions under the usual definition. Test sorted, reverse-sorted, and duplicate-heavy inputs.
15. Maximal Rectangle in a Binary Matrix
Find the largest all-one rectangle in a binary matrix. Treat each row as the base of a histogram: for every column, carry forward the height of consecutive ones ending at that row. Then solve the largest-rectangle-in-a-histogram problem with a monotonic stack. This combines matrix traversal with a stack invariant about increasing heights. Test all zeros, all ones, a single row, a single column, and a rectangle whose best area appears below the first row.
Constraint reasoning and careful validation
16. Sudoku validator
Check whether a Sudoku board violates row, column, or subgrid constraints. Traverse cells while tracking seen digits in each relevant row, column, and subgrid. A subgrid index can be derived from the row and column coordinates, but validate the board dimensions and symbols according to the prompt rather than assuming a complete standard puzzle. Distinguish a valid partial board from a board that has a unique solution: validation alone does not establish solvability or uniqueness. Test duplicates in each constraint type and empty cells.
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Find the smallest positive integer absent from an unsorted array. Sorting is an understandable baseline, generally O(n log n). The classic in-place indexing approach places each value x in the position associated with x when x is within the range 1 through n, then scans for the first mismatch. It can achieve O(n) time and O(1) extra space, but requires careful bounds checks and a swap loop that always makes progress. Ignore or safely handle values outside the useful range. Test negatives, zero, duplicates, an already complete prefix, and an array containing every value from 1 through its length.
Independent reader supportYour contribution helps us test, update, and keep practical guides available for everyone.A sensible order for working through the set
Difficulty depends on your experience and language, but this sequence builds reusable patterns rather than simply increasing code length:
- Foundations: missing number, Two Sum, valid parentheses, reverse a linked list.
- Pattern building: palindromic substrings, Container With Most Water, find all anagrams, Trapping Rain Water.
- Graphs and search: Word Ladder, Course Schedule, Word Search.
- Data-structure design: LRU cache, merge k sorted lists, maximal rectangle.
- Optimization and proof: count inversions, first missing positive, Sudoku validation.
Once you can solve a challenge, revisit it in another language or implement the alternative approach. A second implementation is especially useful when the first solution relies on a language-specific collection or hides an important invariant.
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Where to find more exercises
For short, practical exercises, EMKC organizes challenges by difficulty and describes support for 17 languages. Its examples include string reversal, frequency counting, Fibonacci, recursive sums, invalid JSON repair, and Roman-numeral conversion. Codewars offers community-created kata, browser test cases, peer solutions, ranks from beginner to expert, and support for 55+ languages. Those language and platform details can change, so check the current service pages before choosing based on a particular language or feature.
If you prefer a physical collection, Exercises for Programmers: 57 Challenges to Develop Your Coding Skills by PragProg is a larger challenge set. Confirm current availability and price with the seller; neither is fixed here. Seventeen exercises are a starting set, not a ceiling.
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Frequently Asked Questions
Do I need to solve every challenge in the same programming language?
No. Solving in a familiar language first can help isolate the algorithm; reimplementing later in another language can expose assumptions about collections, integer behavior, or recursion.
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Pick the symptom - the matching free tool is one click away.
Should I memorize these solutions for coding interviews?
Memorize the patterns and correctness arguments, not a fixed implementation. Interview prompts often alter constraints, and those changes can invalidate a memorized approach.
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