Implement a validated strategy selector

Intermediate60 min

Implement choose_strategy(belief, strategies, budget). Validate probabilities and finite utility values, filter unaffordable strategies, and return the positive-utility winner or None.

Your task

Belief is a nonempty mapping from state names to finite nonnegative numeric probabilities summing to one within math.isclose tolerance 1e-9.
Each strategy has a unique nonempty name, a finite nonnegative cost, and a values mapping whose keys exactly match belief. Numeric fields accept int or float but reject bool, NaN, and infinity.
Budget is finite and nonnegative. Raise ValueError for any invalid data, including invalid strategies that would be over budget.
Utility is sum(belief[state] * values[state]) minus cost. Only strategies with cost <= budget are eligible.
Return the eligible strategy name with greatest strictly positive utility; break equal utilities by lexicographic name. Return None when no eligible positive-utility strategy exists. Do not mutate inputs.

Examples

EXAMPLE 1

Inputbelief simple=0.6, ambiguous=0.4; direct utility 1.4; retrieve utility 4.6; budget 2

Output'retrieve'

Reducing the budget to one selects direct despite its lower utility.

def choose_strategy(belief, strategies, budget):
    raise NotImplementedError