Start by clearly stating the recursive solution: move N-1 disks from source to auxiliary, move the largest disk to target, then move N-1 disks from auxiliary to target. Then analyze the recursion depth (O(N)) and discuss iterative approaches, such as using a stack to simulate recursion or the binary counting method, highlighting trade-offs in clarity and performance.
Pro tip: Mention that the iterative solution can be derived from the binary representation of move numbers, which is elegant but less intuitive; showing awareness of both approaches demonstrates depth. Also, note that the recursive solution is optimal in terms of moves (2^N - 1) and that any correct solution must use exactly that many moves.
Restate the rules: only one disk moved at a time, no larger disk on smaller, all disks start on source and must end on target. Confirm N is given and output should be a sequence of moves.
Explain the base case (N=1: move disk directly) and recursive case (move N-1 to auxiliary, move largest to target, move N-1 from auxiliary to target). Provide pseudocode or actual code.
State that recursion depth is O(N) and total moves are 2^N - 1, which is optimal. Discuss potential stack overflow for large N and tail recursion possibilities (none here).
Describe two common iterative methods: (1) simulate recursion with an explicit stack, (2) use the binary counting method where the disk moved at step k is the position of the least significant 1-bit in k. Compare trade-offs: iterative avoids recursion overhead but is less readable.
Summarize when to use recursion (clarity, small N) vs iteration (large N, memory constraints). Mention that the problem is a classic example of recursion and has no closed-form move sequence without recursion or iteration.
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