You should aim for a solution as good or better than O(m * n) time and O(m * n) space, where m is the length of the string s and n is the length of the string t.

Try to think in terms of recursion and visualize it as a decision tree, as we need to explore all subsequences of s. Can you determine the possible decisions at each recursion step?

We recursively iterate through the strings using indices i and j for s and t, respectively. At each recursion step, we can either skip the current character of s or include it in the current path if it matches the current character of t. Can you determine the base conditions for this recursive function?

If index j goes out of bounds, we return 1 as a valid subsequence is found. If index i goes out of bounds first, we return 0. At each recursion step, we return the sum of both paths. This approach is exponential. Can you think of a way to optimize it?

We can use memoization to cache the results of recursive calls and avoid redundant computations. A hash map or a 2D array can be used to store these results.