I got the basic DP solution out fast enough, two variables tracking the last two states, felt good.
Start by explaining the recursive structure: at each position, you can decode one digit (if 1-9) or two digits (if 10-26). Then derive the DP recurrence and optimize it to O(n) time and O(1) space by keeping only the last two counts. Finally, address the follow-ups: modulo arithmetic for large inputs and streaming by maintaining a sliding window of the last two digits and counts.
Pro tip: For the streaming follow-up, emphasize that you only need the previous digit and the count from two steps back, so you can process digits in O(1) space and O(1) time per digit. Also, mention that modulo operations should be applied at each step to prevent overflow, and that the streaming version naturally handles very large inputs without storing the entire string.
Confirm that digits map 1-26 to A-Z, and that '0' cannot be decoded alone. Discuss edge cases like empty string, leading zeros, and strings with '0' in the middle.
Define dp[i] as the number of ways to decode the first i characters. Then dp[i] = (dp[i-1] if s[i-1] != '0') + (dp[i-2] if 10 <= s[i-2:i] <= 26). Explain base cases dp[0]=1 and dp[1]=1 if s[0]!='0' else 0.
Observe that dp[i] only depends on dp[i-1] and dp[i-2]. Replace the array with two variables (prev2, prev1) and update them iteratively. This reduces space from O(n) to O(1).
For very large inputs, apply modulo 1,000,000,007 at each addition to keep numbers manageable. Explain that this doesn't affect the correctness of the count modulo the prime.
For streaming, process each digit as it arrives. Maintain the last digit and the counts from the previous two steps. Update the counts based on the current digit and the previous digit, then shift the window. This gives O(1) time per digit and O(1) space overall.
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