I knew the basic contains-duplicate-ii problem but the twist here was returning the minimum gap AND the O(k) space constraint.
Use a hash map to store the most recent index of each element, and as you scan the array, check if the current element exists in the map and if the index difference is ≤ k. If so, update the minimum gap; otherwise, update the map with the current index. To maintain O(k) space, evict entries that are more than k indices behind the current position.
Pro tip: Emphasize that the hash map only needs to store indices within the last k positions, so you can evict stale entries by checking if the stored index is less than current_index - k. This shows you understand the space constraint and how to maintain it dynamically.
Restate the problem: find if any two equal elements are within k indices, and return the minimum such gap. Confirm that the array can be large, so O(n) time and O(k) space are required.
Use a hash map (dictionary) to store the most recent index of each element seen so far. This allows O(1) average lookup and update.
Iterate through the array with index i. For each element, if it exists in the map and i - map[element] ≤ k, update the minimum gap. Then update the map with the current index.
After processing each element, remove entries from the map whose stored index is less than i - k. This ensures the map only holds indices within the last k positions.
If a minimum gap was found, return it; otherwise, return -1 or indicate no such pair exists. Discuss time and space complexity: O(n) time, O(k) space.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Use recursion with memoization to explore all possible expressions by inserting operators or concatenating digits, while maintaining the current value and the last term to handle operator precedence. Alternatively, use dynamic programming to build expressions incrementally and store results for each position and target. The key is to avoid reparsing by evaluating expressions on the fly.
Pro tip: Emphasize that the solution should handle operator precedence correctly by tracking the last operand and its sign, and mention that memoization can reduce redundant computations when the same subproblem (position, current value, last term) is encountered.
Confirm that digits must be used in order, concatenation is allowed, and a leading sign is optional. Discuss potential constraints like target range and whether all expressions need to be found or just one.
At each digit, decide to either concatenate with the previous number, or apply '+' or '-' as a new term. Maintain the current total and the last term to correctly handle precedence.
Use a hash map to cache results for states defined by (index, current total, last term) to avoid recomputing the same subproblems, especially when searching for all solutions or when the target is large.
When all digits are processed, check if the current total equals the target. Prune branches where the remaining digits cannot possibly reach the target (e.g., using bounds).
Discuss that without memoization, the number of expressions is 3^(n-1) for n digits (plus leading sign options), but memoization can reduce redundant work. Space complexity is proportional to the recursion depth and memoization table.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.