Solved it, but missed a space optimization that I only realized after the fact.
Clarify the problem constraints (e.g., grid size, word length, allowed moves) and then describe a DFS backtracking solution that explores all four directions from each cell, marking visited cells to avoid reuse. Analyze time and space complexity, and discuss potential optimizations like pruning or early termination.
Pro tip: Mention that you can optimize by checking character frequency or using a trie if multiple words are involved, and always discuss trade-offs between DFS and BFS for this problem.
Ask about grid dimensions, word length, allowed moves (4-directional or 8-directional), and whether cells can be revisited. Confirm if the word must be formed by a simple path.
Explain that you will iterate over each cell as a starting point and perform DFS to match the target word character by character. Use a visited set or modify the grid in-place to avoid revisiting cells.
Describe the recursive function: if the current character matches, mark the cell as visited, recurse in all four directions, then unmark. Base cases: if index equals word length, return true; if out of bounds or character mismatch, return false.
State that time complexity is O(N * 3^L) where N is number of cells and L is word length, as each step branches to at most 3 directions (excluding the one we came from). Space complexity is O(L) for recursion stack.
Mention pruning: if the first character doesn't match, skip; if word length exceeds grid cells, return false. Also discuss handling empty grid or empty word.
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Start by clarifying the problem: whether order matters (combinations vs permutations) and if coins can be reused (unbounded knapsack). Then propose a dynamic programming solution where dp[i] represents the number of ways to make amount i, iterating over coins in the outer loop to avoid counting permutations.
Pro tip: Mention that iterating coins in the outer loop and amounts in the inner loop ensures each combination is counted once, whereas the reverse order counts permutations. This subtlety often trips up candidates and showing awareness demonstrates deep understanding.
Ask if order matters (combinations vs permutations) and if coins can be reused unlimited times. Confirm that we need distinct combinations, not permutations.
Let dp[i] be the number of ways to make amount i using the given coin denominations. Initialize dp[0] = 1 (one way to make amount 0: use no coins).
Iterate over each coin in the outer loop, and for each coin, iterate over amounts from coin to target in the inner loop. This ensures combinations are counted once.
For each coin, update dp[amount] += dp[amount - coin]. This accumulates the number of ways to form each amount using the current coin and previously processed coins.
Time complexity is O(n * target) where n is number of coins, space O(target). Discuss edge cases: target=0, no coins, unreachable amounts, and large target requiring optimization.
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First, clarify the problem: given a target number of combinations, find a set of coin denominations that yields exactly that many combinations for some amount (or for all amounts up to a limit). Then, reason about the relationship between denominations and combination counts, and propose a constructive algorithm or reduction to a known problem.
Pro tip: This is an inverse problem, so start by identifying invariants or simple cases (e.g., using only 1s) and then show how adding a new denomination multiplies the number of combinations. Demonstrating that you can reduce the problem to a known NP-hard problem (like subset sum) or provide a constructive solution for special cases will impress the interviewer.
Ask whether the target number of combinations is for a specific amount or for all amounts up to a limit, and whether denominations must be positive integers. Confirm if the coin change problem is the standard one (order doesn't matter).
Start with trivial solutions: e.g., using only denomination 1 gives exactly 1 combination for any amount. Adding a denomination d increases combinations in a predictable way. Derive formulas for small sets.
Determine if the problem is always solvable. For arbitrary target counts, it may be NP-hard (related to subset sum or integer factorization). Discuss whether a constructive solution exists for all inputs or only special cases.
For special cases (e.g., target is a power of 2), give a constructive method. For general case, suggest a search/backtracking approach or reduction to known problems. Mention dynamic programming for verification.
Walk through an example: given target combinations = 4, find denominations. Show how your algorithm produces a valid set (e.g., {1,2} gives 3 combinations for amount 3? Actually need to compute). Verify by running the standard coin change DP.
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Start by clarifying the exact partitioning condition and constraints, then explain how prefix sums can reduce the time complexity from O(n^2) to O(n) or O(n log n). Walk through a concrete example and derive the recurrence or greedy strategy, emphasizing the role of prefix sums in enabling O(1) subarray sum queries.
Pro tip: After presenting the optimal solution, mention how you would handle edge cases like negative numbers or large inputs, and discuss potential follow-ups such as using a hash map to count valid partitions or extending to circular arrays.
Ask questions to confirm the partitioning condition (e.g., each subarray sum ≤ K, or equal sums) and constraints (array size, element range, negative numbers allowed).
Explain that prefix sums allow O(1) computation of any subarray sum: sum(i, j) = prefix[j] - prefix[i-1].
Use prefix sums to efficiently check the condition for each possible partition point, either greedily or with dynamic programming, and analyze time/space complexity.
Trace the algorithm on a small array to demonstrate correctness and show how prefix sums simplify the process.
Mention how to handle negative numbers, large inputs, and potential follow-ups like counting all valid partitions or minimizing the number of subarrays.
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Had my stories ready and structured as situation-action-result, so this was fine.
Use the STAR method to structure your behavioral answers, ensuring you highlight the situation, task, action, and result. For the hypothetical scenario, apply a similar framework by describing how you would approach the challenge step-by-step, emphasizing adaptability and stakeholder management. Tailor your responses to Google's values, such as innovation, collaboration, and user focus.
Pro tip: Demonstrate self-awareness by briefly reflecting on what you learned from past experiences and how you would apply those lessons to the hypothetical scenario. This shows growth and maturity.
Listen carefully to identify whether it's a past experience or hypothetical scenario. For past experiences, recall a specific example; for hypotheticals, outline a clear approach.
For behavioral questions, use STAR: describe the Situation, Task, Action, and Result. For hypotheticals, adapt to describe the Situation, Task, Approach, and expected Result.
Emphasize how you remained flexible, learned quickly, and managed relationships with stakeholders like product managers, designers, or clients.
Include measurable outcomes (e.g., reduced latency by 20%) and reflect on lessons learned or how you would improve next time.
Tie your answer to Google's culture, such as innovation, scalability, or user-centricity, showing alignment with the company's values.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.