The base logic clicked pretty fast for me, single digit or two digit, build up a dp array.
Use dynamic programming where dp[i] represents the number of ways to decode the substring s[0..i-1]. For each position, consider one-digit and two-digit decodings, checking validity (1-9 for one-digit, 10-26 for two-digit), and sum the valid ways. Optimize space by keeping only the last two dp values.
Pro tip: Clarify edge cases upfront, such as empty string, leading zeros, and strings with zeros in the middle, to show thoroughness. Also, mention that you can optimize space to O(1) by using two variables, which demonstrates awareness of efficiency.
Let dp[i] be the number of ways to decode the first i characters of the string. Initialize dp[0] = 1 (empty string) and dp[1] = 1 if the first character is not '0', else 0.
For each i from 2 to n, dp[i] = 0. If the current digit s[i-1] is between '1' and '9', add dp[i-1]. If the two-digit number s[i-2..i-1] is between 10 and 26, add dp[i-2].
If the string is empty or starts with '0', return 0. Also, if any '0' is encountered, it must be part of a valid two-digit number (10 or 20), otherwise the decoding is invalid.
Since dp[i] depends only on dp[i-1] and dp[i-2], use two variables to store these values and update iteratively, achieving O(1) space.
After iterating through the string, return the final dp value, which represents the total number of valid decodings.
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