Satellite Signal Boosters

Problem Statement

A deep-space communications agency has placed N relay stations along a straight orbital path, each at a distinct integer coordinate. Signal quality degrades over distance — the weaker the signal between two adjacent stations, the higher the chance of data loss. The agency defines the network's weakest link [unclear] largest gap between any two consecutive stations. To strengthen the network, the agency can deploy exactly K signal repeaters anywhere along the path at integer positions. Each repeater acts as a new relay station, effectively splitting the gap it is placed in. Your task is to place the K repeaters optimally to minimize the largest gap between any two consecutive stations (including the newly added repeaters). Function Description Implement the function signalBoosters that places K repeaters optimally among N relay stations on a line and returns the minimized maximum gap between any two consecutive stations. Parameters N (int) : Number of existing relay stations. K (i