Infectious Disease Spread (Infection Propagation)

Infectious Disease (Infection Propagation) You are given a data structure describing how infection can spread in a population (e.g., a contact graph, contact logs, or a 2D grid). Some individuals are infected at time 0. Infection spreads in discrete steps: at each step, every infected individual causes all directly connected (in-contact) uninfected individuals to become infected in the next step. Implement a function that returns: the minimum number of time steps needed to infect all reachable individuals; if there exists any individual that can never be infected (disconnected from all sources), return a sentinel value such as -1. Notes Clearly define the input representation: Graph: n nodes, edge list edges, initial infected set sources. Grid: m x n grid with encodings for infected/uninfected/blocked. Output is a single integer (steps or -1). Constraints The input can be large; aim for linear or near-linear time. Sample tests Input: graph n=4, edges=[[0,1],[1,2],[2,3]], sources=[0] => Output: 3 Input: graph n=4, edges=[[0,1],[2,3]], sources=[0] => Output: -1 Input: grid [[2,1,1],[1,1,0],[0,1,1]] (2=infected, 1=susceptible, 0=blocked) => Output: 4 Input: grid [[2,1,1],[0,1,1],[1,0,1]] => Output: -1 Input: grid [[0,2]] => Output: 0 Example Input 4 3 0 1 1 2 2 3 1 0 Output 3