Explain the difference between top-down and bottom-up dynamic programming approaches.

Top-down DP involves starting from the top (the initial problem) and breaking it down into smaller subproblems, storing solutions to these subproblems in a table (memoization). Bottom-up DP, on the other hand, starts from the bottom (solving the smallest subproblems first) and builds its way up to solve the larger problem using a table (tabulation). While top-down uses recursion and memoization, bottom-up uses iteration and tabulation.