My first instinct was to dump everything into a set and sort descending, which works but they pushed back immediately asking if I could do better given the inputs are already sorted.
Use a modified binary search to find the K-th largest unique element by leveraging the sorted order of both arrays. At each step, pick a candidate value and count how many unique elements are greater than or equal to it using binary search in both arrays, adjusting the search range based on the count. This achieves O(log(min(m,n)) * log(max_value)) time, or O(log(m+n)) with a more optimized approach.
Pro tip: Clarify upfront whether K is 1-indexed (K=1 means largest) and confirm that duplicates are ignored. Also, mention that if K exceeds the number of unique elements, you should return an appropriate error or sentinel value.
Confirm indexing of K, handling of duplicates, and behavior when K is larger than the number of unique elements. Discuss constraints like array sizes and value ranges.
Design a function that, given a value X, returns the number of unique elements >= X across both arrays. Use binary search to find the first occurrence of X in each array and count elements from there, being careful to avoid double-counting duplicates across arrays.
Perform binary search over the possible value range (from min to max of both arrays) to find the smallest value X such that count(X) >= K. That X is the K-th largest unique element.
When counting, ensure that if the same value appears in both arrays, it is counted only once. This can be done by checking if the value is present in both arrays and adjusting the count accordingly.
State the time complexity (O(log(range) * (log m + log n))) and space complexity (O(1)). Walk through examples, including edge cases like empty arrays, K=1, and all duplicates.
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