Server Grouping to Target

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Problem

Nutanix Prism Central needs to select servers whose available request capacities meet an exact target. Given a list of nonnegative server capacities and a target T, return indices of a subset with the minimum number of servers whose capacities sum exactly to T. Return any valid minimum-size subset. If no subset exists, return an empty list.

The empty subset is valid when T = 0.

Formal Specification

Implement minimum_servers(capacities, T), where capacities is a list of nonnegative integers and T is a nonnegative integer. Return a list of distinct zero-based indices. The selected capacities must sum to T, and no smaller valid subset may exist.

Constraints

1 <= len(capacities) <= 40
0 <= capacities[i] <= 10^12
0 <= T <= 10^15
Each index may be selected at most once
Return any minimum-size valid subset

Function Signature

def minimum_servers(capacities, T):

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