Get Optimal Team Size Problem

Do not manufacture an algorithm from the phrase optimal team size. Clarify whether the goal is maximum headcount, maximum total skill, minimum cost, balanced roles, or a team satisfying pairwise compatibility. Ask whether each person can be used once, whether skill values are sorted, whether there is a budget, and whether conflicts form a graph. For a common sorted-skill threshold version, sort skills and use a sliding window: while maxSkill exceeds a permitted multiple or difference of minSkill, advance left, then update best length. That works only because feasibility is monotonic after sorting. For role coverage or knapsack-like budgets, define DP state by covered roles and cost; for arbitrary incompatibility, the problem may reduce to maximum independent set and be exponential in general. Test empty input, ties, one feasible person, and extreme budgets. Sorting-window approaches are O(n log n) time and O(n) or O(1) extra space depending on sorting; do not claim this for an unspecified model.