This one took me a while to even understand what was being asked.
First, compute the last occurrence index for each character in the string. Then, iterate through the string while maintaining the farthest last occurrence seen so far; when the current index reaches that farthest point, you've found a valid substring, so increment the count and reset for the next substring.
Pro tip: Clarify that the substrings must be contiguous and cover the entire string without overlap, and mention that the greedy approach works because extending a substring to include all occurrences of its characters is always optimal.
Restate the problem to ensure clarity: we need to partition the string into the maximum number of contiguous, non-overlapping substrings such that each substring contains all occurrences of every character it includes.
Create an array or hash map to store the last index of each character in the string. This will help determine how far a substring must extend to include all occurrences of its characters.
Iterate through the string, keeping track of the farthest last occurrence seen so far. When the current index equals this farthest point, a valid substring ends; increment the count and reset the farthest point for the next substring.
Explain that the algorithm runs in O(n) time and O(1) space (since the alphabet size is fixed), making it optimal.
Walk through a simple example like 'abac' to demonstrate the algorithm: last occurrences: a->2, b->1, c->3. Start at 0, farthest=2, at index 2 farthest=2, so substring 'aba' ends, count=1; then 'c' ends, count=2.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.