Distribute Candies Among Children III

Partition an array of candy values among k children to achieve a fairness objective (e.g., make each child's total equal or maximize the number of children who get full allotments) under combinatorial constraints. The core challenge is an exponential partitioning/assignment problem typically solved with state-compressed subset DP/bitmasking, DP with memoization, or advanced search/pruning rather than greedy approaches.