The single-pass constraint is what makes this annoying.
Clarify the problem constraints and edge cases first, then propose a single-pass solution using a stack or running total with a pending operator. Walk through the algorithm with a concrete example, emphasizing how to handle operator precedence and integer division truncation toward zero.
Pro tip: Mention that you can avoid a stack by maintaining a running result and a 'last term' to handle precedence, which reduces space complexity to O(1). Also, explicitly state how you handle negative division truncation (e.g., -3/2 = -1) to show attention to detail.
Ask about input format (spaces, multi-digit numbers), division truncation, and potential overflow. Confirm that no parentheses are allowed and that operators are binary.
Decide between a stack-based approach or a running total with a 'last term' for O(1) space. Explain how to handle operator precedence by deferring addition/subtraction until after multiplication/division.
Describe parsing the string character by character, building numbers, and applying operators. Use a concrete example like '3+2*2' to illustrate the steps.
Explain how to implement integer division that truncates toward zero, especially for negative numbers, and mention potential pitfalls like integer overflow.
State time and space complexity (O(n) time, O(1) or O(n) space depending on approach). Suggest test cases including single number, multiple operators, and negative results.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Sort first, then for each pair (i, k) binary search or use a two-pointer to count valid j values.
Sort the array first, then for each pair (i, j) with i < j, use binary search to find the largest k such that a[i] + a[j] > a[k]. The number of valid triplets for this pair is k - j, and summing over all pairs gives the total count in O(n^2 log n), which can be optimized to O(n^2) with a two-pointer approach.
Pro tip: Mention that sorting is safe because triangle validity depends only on side lengths, not order. Also, emphasize that the two-pointer method avoids binary search overhead, achieving true O(n^2) time.
Sort the array in non-decreasing order. This allows us to use the triangle inequality efficiently and ensures that for any i < j < k, we only need to check a[i] + a[j] > a[k].
Iterate k from 2 to n-1, treating a[k] as the largest side of the triangle. For each k, find all pairs (i, j) with i < j < k such that a[i] + a[j] > a[k].
For each k, initialize i = 0 and j = k-1. While i < j, if a[i] + a[j] > a[k], then all pairs (i, j), (i+1, j), ..., (j-1, j) are valid, so add (j - i) to the count and decrement j. Otherwise, increment i.
Accumulate the counts for all k and return the total number of valid triplets. The overall time complexity is O(n^2) due to the nested loops with two pointers.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Start by clarifying the input format and edge cases, then propose sorting the intervals by start time and merging in a single pass. Explain the O(n log n) time and O(n) space complexity, and walk through a concrete example to demonstrate correctness.
Pro tip: Mention that sorting is essential for efficiency, but also note that if the input is already sorted or nearly sorted, you can optimize by using insertion sort or skipping the sort. This shows awareness of real-world data characteristics.
Ask about input format (list of pairs, sorted or unsorted), whether intervals are inclusive, and how to handle empty input or single interval. Confirm that merging should combine overlapping or touching intervals.
Propose sorting intervals by start time, then iterating through them while maintaining a current merged interval. If the next interval overlaps or touches the current one, extend the end; otherwise, add the current to the result and start a new one.
State that sorting takes O(n log n) time and the merge pass takes O(n), so overall O(n log n) time. Space is O(n) for the output (or O(1) extra if merging in-place, but typically O(n) for result).
Use a small example like [[1,3],[2,6],[8,10],[15,18]] to show how the algorithm merges [1,3] and [2,6] into [1,6], and produces [[1,6],[8,10],[15,18]]. This demonstrates understanding and catches off-by-one errors.
Mention handling of empty input, single interval, intervals that are already sorted, and intervals that share an endpoint (e.g., [1,4] and [4,5] should merge). Optionally, discuss in-place merging if the input can be modified.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Treat the grid as a graph and use DFS or BFS to explore each unvisited land cell, marking all connected land cells as visited. Each time you start a traversal from an unvisited land cell, increment the island count. Ensure you handle edge cases like empty grid or no land.
Pro tip: Clarify whether modifying the input grid is acceptable; if not, use a separate visited matrix. Also, discuss trade-offs between DFS (recursive, risk of stack overflow) and BFS (iterative, uses queue) especially for large grids.
Confirm that connectivity is 4-directional (up, down, left, right) and that clusters are maximal connected components of '1's. Ask about grid size limits and whether the grid can be modified.
Decide between DFS (recursive or iterative) and BFS. Consider space complexity and potential stack overflow for large grids; BFS with a queue is often safer.
Iterate through each cell; when you find an unvisited '1', increment count and start traversal to mark all connected '1's as visited (e.g., set to '0' or use a visited set).
Check for empty grid, grid with no land, or all land. Ensure boundary conditions are handled in neighbor checks.
State time complexity O(M*N) and space complexity O(M*N) in worst case (e.g., all land) due to recursion stack or queue.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
This one tripped me up more than I expected.
Use the array itself as a hash table by placing each number in its correct index (e.g., value x at index x-1) through cyclic swaps. Then scan the array to find the first index where the value is not index+1; that index+1 is the smallest missing positive. This achieves O(n) time and O(1) extra space.
Pro tip: Clarify upfront that the array is modifiable; if not, the O(1) space constraint is impossible. Also, mention that you handle edge cases like all numbers present (answer n+1) and ignore non-positive or out-of-range values.
Confirm that the array can be modified in-place and discuss edge cases such as empty array, all negatives, or all numbers 1..n present.
Describe how to iterate through the array and swap each positive integer x (where 1 <= x <= n) into its correct position at index x-1, ignoring values outside this range.
Walk through the swapping process, ensuring each number is placed correctly. Use a while loop to continue swapping until the current element is in the right place or out of range.
After rearrangement, iterate through the array and return the first index i where nums[i] != i+1; if all are correct, return n+1.
Conclude that the algorithm runs in O(n) time (each element swapped at most once) and O(1) extra space, and discuss why alternative approaches (sorting, hash set) fail the constraints.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Start by clarifying the problem constraints (e.g., array size, element types, whether indices are required) and then present Kadane's algorithm as the optimal O(n) solution. Explain the algorithm step-by-step, handle edge cases like all negative numbers, and if indices are needed, describe how to track the start and end positions.
Pro tip: Mention that Kadane's algorithm is a dynamic programming approach and discuss how it can be adapted for circular arrays or other variants, showing depth beyond the basic problem.
Ask about input size, possible values (negative, zero, positive), and whether returning indices is required. This ensures you address the exact problem and edge cases.
Briefly mention that checking all subarrays takes O(n^2) or O(n^3) time, which is inefficient for large inputs, motivating a better solution.
Describe the O(n) dynamic programming solution: maintain current_sum and max_sum, updating current_sum as max(arr[i], current_sum + arr[i]) and max_sum as max(max_sum, current_sum).
Explain how to track start and end indices by recording the start when current_sum resets and updating the end when max_sum changes.
Cover cases like all negative numbers (return the maximum single element), empty array (if allowed), and single element. Walk through a small example to verify.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Track the running minimum as you scan and update max profit at each step.
Clarify the problem constraints and edge cases, then propose an efficient one-pass solution that tracks the minimum price seen so far and the maximum profit. Explain the algorithm step-by-step, analyze its time and space complexity, and test it with examples including edge cases.
Pro tip: Demonstrate awareness of real-world constraints by mentioning that stock prices are typically positive and that the solution should handle large datasets efficiently. Also, proactively discuss potential follow-ups like multiple transactions or handling streaming data.
Ask about input size, data types, and whether prices can be zero or negative. Confirm that only one buy and one sell are allowed, and that the buy must occur before the sell.
Briefly mention that a naive O(n^2) solution checks all pairs of buy and sell days, but this is inefficient for large inputs.
Explain that you can iterate through the array once, keeping track of the minimum price seen so far and the maximum profit achievable. Update these variables at each step.
State that the time complexity is O(n) and space complexity is O(1). Walk through a few examples, including cases where no profit is possible (return 0).
Mention extensions like multiple transactions, transaction fees, or handling streaming data, showing depth of understanding.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Put everything in a hash set, then for each number that has no left neighbor (n-1 not in set), walk forward counting the streak.
Use a hash set to store all elements for O(1) lookups. For each number, check if it's the start of a sequence (i.e., num-1 not in set), then count consecutive numbers. This ensures each number is visited at most twice, achieving O(n) average time.
Pro tip: Mention that you only start counting from numbers that are sequence starts to avoid redundant work, and discuss handling duplicates and edge cases like empty arrays. This shows attention to efficiency and robustness.
Ask clarifying questions: Are there duplicates? Can the array be empty? What are the constraints on integer values? Confirm that the expected time complexity is O(n) average.
Explain that you'll insert all elements into a hash set for O(1) lookups. Then iterate through the array, and for each element, check if it's the start of a sequence by verifying if num-1 is not in the set.
For each sequence start, increment a counter while the next consecutive number exists in the set. Keep track of the maximum length found.
State that each element is visited at most twice (once in the initial loop, once during counting), so time is O(n) average. Space is O(n) for the set. Discuss edge cases: empty array, all duplicates, negative numbers.
Walk through a small example, e.g., [100, 4, 200, 1, 3, 2] to show the algorithm finds the longest sequence [1,2,3,4] of length 4. Also test with duplicates and negative numbers.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Topological sort via Kahn's algorithm (BFS with in-degree tracking).
Model the courses and prerequisites as a directed graph, then perform a topological sort using Kahn's algorithm (BFS) or DFS. If a cycle exists, return false; otherwise, return the topological order. Ensure the solution handles large inputs efficiently with O(V+E) time and space.
Pro tip: Mention that Kahn's algorithm naturally detects cycles by checking if the processed nodes count equals the total number of courses, and it avoids recursion depth issues for large graphs. Also, discuss how this approach scales to 100,000 nodes and edges with linear time complexity.
Clarify that the input is a number of courses and a list of prerequisite pairs, and the goal is to determine if all courses can be completed and return a valid order if possible. Recognize this as a topological sorting problem on a directed graph.
Select either Kahn's algorithm (BFS-based) or DFS-based topological sort. For large graphs, Kahn's algorithm is often preferred due to its iterative nature and explicit cycle detection.
Build the graph and compute in-degrees for each node. Use a queue to process nodes with zero in-degree, appending them to the order and reducing in-degrees of their neighbors. If the order contains all nodes, return it; otherwise, return an empty array or false.
State that the time complexity is O(V+E) and space complexity is O(V+E). Discuss edge cases such as no prerequisites, disconnected graphs, and cycles. Mention that the solution handles up to 100,000 nodes and edges efficiently.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.