I recognized Jump Game pretty fast and started talking through a standard BFS/DP approach.
First, clarify the problem constraints and define the allowed moves. Then, design a dynamic programming solution where dp[i] represents the minimum jumps to reach index i, initializing dp[0]=0 and others to infinity. Iterate through indices, and for each, update reachable positions by moving +1 or jumping by valid primes ending in 3, ensuring to precompute or generate such primes up to n.
Pro tip: Mention that you can precompute all valid prime jumps up to n using a sieve, and note that the +1 move ensures all indices are reachable, so the problem reduces to finding the minimum jumps efficiently.
Confirm the rules: start at index 0, moves are +1 or +p where p is prime and ends in 3. Ask if n can be 0 or 1, and if the last index is n-1.
Generate all primes up to n that end in digit 3. Use a sieve of Eratosthenes for efficiency, then filter primes ending in 3.
Define dp[i] as min jumps to reach i. Initialize dp[0]=0, others infinity. For each i from 0 to n-1, if dp[i] is finite, update dp[i+1] and dp[i+p] for each valid prime p.
After filling dp, check dp[n-1]. If finite, return it; else, return -1 (though +1 move makes it always reachable).
Time: O(n * number of valid primes) which is roughly O(n^2 / log n) worst-case, but can be optimized. Space: O(n) for dp and primes.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.