Model the problem as a directed graph where each character is a node and edges represent the relative order derived from adjacent word pairs. Then perform a topological sort to find a valid character ordering, detecting cycles to handle invalid inputs.
Pro tip: Clarify edge cases upfront, such as when a shorter word appears after a longer word with the same prefix (invalid), and mention that the graph can be built in O(N*L) time where N is the number of words and L is the maximum word length.
Iterate through adjacent word pairs and find the first differing character to establish a directed edge from the earlier character to the later one. Also, check for invalid cases like a longer word preceding a shorter word with the same prefix.
Use a set or list to collect all unique characters from the words, and maintain an adjacency list and in-degree count for each character.
Perform a topological sort using either Kahn's algorithm (BFS with in-degree) or DFS with cycle detection to produce a linear ordering of characters.
If a cycle is detected (e.g., not all characters are processed in Kahn's algorithm), return an empty string or indicate no valid ordering. Otherwise, return the sorted character sequence.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Use dynamic programming with a bottom-up approach, starting from the princess's cell and moving backwards to compute the minimum health needed at each cell. At each cell, calculate the health required to survive the current cell and proceed to the next optimal cell (right or down), ensuring health is at least 1.
Pro tip: Emphasize that the problem requires working backwards because the initial health depends on future requirements, and mention that you can optimize space to O(n) by using a 1D DP array.
Restate the problem: find the minimum initial health to reach the bottom-right cell, ensuring health > 0 at all times. Discuss edge cases like 1x1 grid and large grids.
Define dp[i][j] as the minimum health needed at cell (i,j) to reach the end. Recurrence: dp[i][j] = max(1, min(dp[i+1][j], dp[i][j+1]) - dungeon[i][j]).
Initialize dp for the bottom-right cell: dp[m-1][n-1] = max(1, 1 - dungeon[m-1][n-1]). Set boundary conditions for last row and last column.
Iterate from bottom-right to top-left, filling the DP table. Optionally optimize space to O(n) by using a 1D array.
State time complexity O(m*n) and space complexity O(m*n) or O(n). Walk through a small example to verify correctness.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Clarify the problem and constraints, then explain the prefix sum technique: precompute cumulative sums to answer range sum queries in O(1) time. Walk through a small example, write clean code, and analyze time/space complexity.
Pro tip: Mention that prefix sums can be extended to 2D or used with hashing for subarray sum problems, showing you understand the pattern beyond this specific question.
Ask about input size, query frequency, and whether updates are needed. Confirm the expected output format and any constraints.
Describe how to build a prefix sum array where prefix[i] = sum of elements from index 0 to i-1. Then each range sum [l, r] is prefix[r+1] - prefix[l].
Use a small array like [1, 2, 3, 4] to show how the prefix array is built and how a query is answered in O(1).
Implement the solution in your preferred language, handling edge cases like empty arrays or out-of-bounds indices.
State that preprocessing takes O(n) time and O(n) space, and each query takes O(1) time. Discuss trade-offs if updates are required.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Depends on whether they want the naive sort approach or something fancier like quickselect.
Start by clarifying the problem: ask about input size, data type, whether the array is sorted, and if duplicates are allowed. Then present multiple solutions, from the simple sort-based approach to the optimal Quickselect algorithm, discussing trade-offs in time and space complexity. Finally, walk through the chosen algorithm with a concrete example and handle edge cases like even-length arrays and empty input.
Pro tip: Mention that for even-length arrays, the median is typically the average of the two middle elements, and confirm this with the interviewer to avoid ambiguity. Also, highlight that Quickselect has an average O(n) time but worst-case O(n^2), and discuss how randomized pivot selection mitigates this.
Ask about input size, data type, sortedness, duplicates, and definition of median for even-length arrays. This ensures you solve the correct problem and shows attention to detail.
Outline naive sorting (O(n log n)), heap-based (O(n log k)), and Quickselect (average O(n)). Compare their trade-offs in time, space, and simplicity.
Explain Quickselect: partition the array around a pivot, recursively search the side containing the median index. Include how to handle even-length arrays by finding two middle elements.
Trace the algorithm on a small array (e.g., [3,1,4,1,5]) to demonstrate correctness and clarify the partitioning logic.
State average O(n) time and O(1) space for Quickselect, worst-case O(n^2). Discuss edge cases: empty array, single element, all duplicates, and large input.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.