Distinct Subsequences

At each cell, you always have the option to skip s[i] (inheriting dp[i-1][j]). When characters match, you also get the option to use s[i] to match t[j] (adding dp[i-1][j-1]). Space-optimizable to O(n) with a single row iterated right-to-left. The "skip vs use" framing applies to all subsequence counting problems.