I'd seen the standard Jump Game before so my first instinct was to just reach for the greedy approach, which was wrong here.
Clarify the problem constraints (e.g., array size, prime step sizes, goal) and then model it as a graph where each index is a node and edges represent prime-sized jumps. Use BFS to find the minimum number of jumps, precomputing primes up to the maximum jump length. Discuss time/space complexity and potential optimizations like pruning or bidirectional BFS.
Pro tip: Mention that prime step sizes are fixed and can be precomputed once, and that BFS is optimal for unweighted graphs; also note that if the array is large, you can optimize by only considering primes up to the remaining distance to the end.
Ask questions to confirm the exact variant: Are we given an array of jump lengths (like classic Jump Game) or can we jump any prime distance? What is the goal: reach the last index, minimize jumps, or determine if possible? What are the constraints on array size and values?
Represent each index as a node. From index i, you can jump to i + p for any prime p such that i + p is within bounds. This forms a directed graph. The problem reduces to finding the shortest path (minimum jumps) from index 0 to the last index.
Use the Sieve of Eratosthenes to generate all prime numbers up to the maximum possible jump length (which is the array length minus 1). This allows O(1) prime checks during BFS.
Run BFS from index 0. For each index, iterate over all primes and enqueue unvisited reachable indices. Track the number of jumps (BFS level). If the last index is reached, return the number of jumps; if BFS exhausts, return -1.
Time complexity: O(N * P) where N is array length and P is number of primes up to N. Space: O(N). Discuss optimizations: limit primes to remaining distance, use bidirectional BFS, or precompute prime list once for multiple queries.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.