Use binary search to find the peak element by comparing mid with its neighbors. If mid is less than the next element, the peak lies to the right; otherwise, it lies to the left. This achieves O(log n) time complexity.
Pro tip: Mention that this approach is optimal for large arrays and handles edge cases like single-element or strictly increasing/decreasing arrays. Also, clarify that the array is guaranteed to be a mountain array, so no need to check for invalid inputs.
Confirm that the array is a mountain array (strictly increasing then strictly decreasing) and that the maximum element is the peak. Ask if there are any constraints on array size or element values.
Explain that a linear scan would work but is O(n). Propose binary search for O(log n) efficiency, which is preferred for large arrays.
Set low = 0, high = n-1. While low < high, compute mid. If arr[mid] < arr[mid+1], the peak is to the right, so low = mid+1; else, the peak is at mid or to the left, so high = mid.
Discuss cases like array of size 1, peak at the beginning or end, and ensure the loop terminates correctly. Return arr[low] as the peak.
State that time complexity is O(log n) and space complexity is O(1). Compare with linear search O(n) to highlight efficiency.
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.
Clarify the problem constraints (e.g., numbers can be reused, order matters, target sum range) and then propose a dynamic programming solution that tracks the last used number to enforce the no-consecutive rule. Explain the state definition, recurrence relation, and how to optimize space if needed.
Pro tip: Mention that the DP state can be reduced to O(target) space by keeping only the previous step's counts, and discuss how the solution changes if the numbers are not distinct or if the target is very large.
Ask clarifying questions: Are the three numbers distinct? Can each number be used multiple times? Does order of addition matter? What is the range of the target sum?
Define dp[i][j] as the number of ways to reach sum i where the last used number is j (or a state indicating no last number). Initialize dp[0][none] = 1.
For each sum i from 1 to target, and for each number j, if j != last, add dp[i-j][last] to dp[i][j]. Handle base cases and avoid double-counting.
Iterate through sums and numbers in increasing order, then sum dp[target][j] over all j to get the total number of valid sequences.
State time complexity O(target * 3) and space O(target * 3). Discuss reducing space to O(target) by keeping only the previous sum's states.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Clarify the problem constraints and edge cases, then propose a dynamic programming solution that tracks the length of the longest common substring ending at each position, along with the number of mismatches and the class of the mismatched character. Optimize space to O(n) and discuss time complexity O(m*n).
Pro tip: Demonstrate awareness of trade-offs: mention that while DP is straightforward, a suffix automaton or rolling hash with binary search could be more efficient for large inputs, but DP is acceptable for an interview setting.
Ask about input size, character set, definition of vowels/consonants, and whether the mismatch can be at any position. Confirm that the substring must be contiguous.
Define dp[i][j] as the length of the longest common substring ending at s1[i] and s2[j] with at most one allowed mismatch. Track the mismatch class (vowel/consonant) to enforce the condition.
Fill the DP table row by row, using only two rows to save space. Update the maximum length and handle the mismatch condition carefully.
State time O(m*n) and space O(n). Mention that for very large strings, suffix automaton or binary search with rolling hash could be more efficient, but DP is simpler and sufficient for most interviews.
Walk through a few examples, including cases with no mismatch, one valid mismatch, and one invalid mismatch (different classes), to verify correctness.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.