Code Craft: Chef Skill → Dish Profit Assignment

Assign chefs to dishes to maximize total profit. Each chef can cook at most one dish; multiple chefs can cook the same dish. Each dish has a difficulty level, and a chef can cook a dish only if their skill ≥ the dish's difficulty. Profits sorted (or queryable) by difficulty. Requirements Input: chefs (list of skill levels), difficulties (list of dish difficulties), profits (list of dish profits indexed by difficulty). A chef cooks at most one dish; can only cook dishes with difficulty ≤ chef.skill. Multiple chefs can cook the same dish. Output: maximum total profit summed across all chef assignments. Follow-up: given a single list profits where index = difficulty, how would you generate that list from raw input? (Typically: sort dishes by difficulty, take running max profit so each dish's listed profit dominates all easier dishes — guarantees monotonicity.) Notes Greedy / two-pointer / LC 826 "Most Profit Assigning Work" equivalent. Standard approach: Pair (difficulty, profit) and sort by difficulty. Sort chefs by skill ascending. Sweep chefs in order, maintaining best_profit_so_far over all dishes whose difficulty has been passed. Add best_profit_so_far to total for each chef. Total time: O((n + m) log(n + m)). The follow-up ("how to generate profits[] where index = difficulty") is asking for a monotonic-by-difficulty profit table: sort by difficulty, take prefix-max, index into the result by difficulty. Equivalent to compressing (difficulty, profit) pairs into a non-decreasing-profit array. Common bug: failing to skip dishes the chef cannot do; the two-pointer approach side-steps this by sorting chefs ascending and only advancing the dish pointer. Preparation Drill LC 826 (Most Profit Assigning Work) until automatic. Practice the sort + sweep + prefix-max pattern in under 15 minutes. Have the follow-up answer ready: "sort by difficulty, take running max profit."