This one took me a while to even understand what was being asked.
First, clarify the problem and constraints, then model it as finding the minimum number of value groups to merge so that each value occupies one contiguous block. Use a greedy interval merging approach: for each value, compute the span from its first to last occurrence, then merge overlapping spans; the answer is the number of merges needed.
Pro tip: Mention that this is equivalent to finding the minimum number of intervals to remove so that the remaining intervals are non-overlapping, which can be solved by sorting intervals by end time and greedily keeping non-overlapping ones. This shows you recognize the underlying interval scheduling pattern.
Confirm that a global replace changes all occurrences of x to y, and the goal is to have each distinct value appear in exactly one contiguous block. Ask about constraints (e.g., array size, value range) to determine the optimal algorithm.
For each distinct value, compute its first and last index, forming an interval [first, last]. The problem reduces to merging overlapping intervals so that no two intervals overlap.
Sort intervals by end index. Use a greedy approach: iterate through intervals, keep the one with the smallest end that doesn't overlap with the last kept interval. The number of intervals to remove (merges) is the total intervals minus the maximum number of non-overlapping intervals.
Consider arrays with all same values (0 operations), all distinct values (0 operations), and values that are already contiguous. Also discuss if multiple values can be merged into one block (e.g., replacing x with y and y with z).
State that the algorithm runs in O(n log n) time due to sorting intervals, and O(n) space for storing intervals. Mention that this is optimal for comparison-based sorting.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.