The third condition is the one that'll get you.
Use digit DP to count numbers <= N that satisfy the constraints, since N can be up to 10^18. The DP state should track position, tightness, mask of used digits, and the last two digits to enforce the no-sandwich condition. Precompute counts for lengths less than N's length to handle leading zeros and simplify the DP.
Pro tip: Clarify the definition of 'sandwiched' with the interviewer: it typically means a digit that is strictly smaller than both its immediate neighbors. Also, mention that the no-zero and no-repeated-digits constraints drastically reduce the search space, making digit DP efficient.
Confirm the definition of 'sandwiched' and whether numbers with fewer digits than N are included. Discuss edge cases like N < 10 or numbers with leading zeros.
Define DP state: position, tight flag, used digit mask, and last two digits. Explain how to transition by trying each possible next digit (1-9) that is unused and doesn't create a sandwich.
Since numbers can have fewer digits than N, either run DP for each length separately or incorporate a 'started' flag to handle leading zeros. Precompute counts for all lengths up to len(N)-1.
Implement memoization for the DP. Note that the mask has at most 2^10 states, and last two digits are at most 10*10, so the state space is manageable. Use bitmask operations for efficiency.
Test with small N by brute force to ensure correctness. Check edge cases like N=1, N=10, and N=10^18. Discuss time complexity: O(len(N) * 2 * 2^10 * 10^2 * 10) which is about 10^6 operations.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.