Player Selection: Select an Optimal Team of Players Subject to Position and Budget Constraints

Question

## Problem

You are building a fantasy sports team. You have a list of players, each with a position, a cost, and a projected score. Select exactly `n` players (with position slots specified) to maximize total projected score without exceeding a total salary cap.

```python
def select_team(
    players: list[dict],   # {"name", "position", "cost", "score"}
    slots: dict[str, int], # {position: count_needed}, e.g. {"QB":1, "WR":3, "RB":2}
    salary_cap: int
) -> list[str] | None:     # list of player names, or None if impossible
    pass
```

**Example:**
```
players = [
  {"name": "A", "position": "QB", "cost": 8000, "score": 35},
  {"name": "B", "position": "QB", "cost": 6000, "score": 28},
  {"name": "C", "position": "WR", "cost": 5000, "score": 22},
  {"name": "D", "position": "WR", "cost": 4000, "score": 18},
]
slots = {"QB": 1, "WR": 1}, salary_cap = 12000
-> ["A", "C"]   # cost=13000 > cap; try ["A","D"]=12000 score=53 or ["B","C"]=11000 score=50
-> ["A", "D"]   # max score within cap
```

## Follow-ups

1. This is a variant of the multi-dimensional knapsack problem. What DP formulation handles both position constraints and the salary cap simultaneously?
2. How does the problem size (number of players, positions, cap) affect which approach is practical -- DP, branch-and-bound, or ILP?
3. In real DFS (daily fantasy sports) platforms, why do players also include ownership percentage, and how does that affect optimal selection strategy?
4. If you need to generate the top 100 distinct lineups (not just the best one), what search strategy would you use?

Player Selection: Select an Optimal Team of Players Subject to Position and Budget Constraints

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