Decode Ways
Recognize the pattern
Brute force idea
If you approach Decode Ways in the most literal way possible, you get this: Recursively try decoding one or two digits at each position. Many substrings are re-decoded across different branches. It is a fair place to begin because it matches the surface of the question, yet it does not capture the deeper structure that makes the problem simpler.
Better approach
The real unlock in Decode Ways comes when you notice this: DP: dp[i] = (ways using single digit) + (ways using two digits). If s[i] is valid (1-9), add dp[i-1]. If s[i-1.i] forms 10-26, add dp[i-2]. Instead of recomputing the world every time, you preserve just enough context to let the next decision become obvious.
Key invariant
At the center of Decode Ways is one steady idea: At each position, you either decode one character or two. The total decodings is the sum of both valid choices. dp[i] depends only on dp[i-1] and dp[i-2]. When you keep that truth intact, each local choice supports the larger solution instead of fighting it.
Watch out for
One easy way to drift off course in Decode Ways is this: Forgetting that '0' cannot be decoded alone — if s[i] = '0', there are zero ways from single-digit decoding. Also, leading zeros in two-digit codes (like '06') are invalid. The fix is usually to return to the meaning of each move, not just the steps themselves.