A DP (dynamic programming) table stores exact, optimal solutions to subproblems to solve a larger problem, guaranteeing an optimal solution but potentially requiring large amounts of time and memory. A heuristic is a shortcut or rule-of-thumb approach that finds a good, but not necessarily optimal, solution quickly. DP can be combined with heuristics to make the problem more manageable, such as using a heuristic to prune states in the DP table, or by creating a heuristic based on the structure of the DP solution.
DP table
- Purpose: To store and reuse the exact solutions of overlapping subproblems.
- Method: A step-by-step, exhaustive procedure that guarantees the optimal solution for the problem. It builds the solution from the bottom up.
- Pros: Guarantees the best possible solution.
- Cons: Can be very time-consuming and computationally expensive, especially for large problems. The number of states can grow impractically large.
- Use case: When finding the absolute best solution is critical and computational resources are not a constraint.
Heuristic flow
- Purpose: To find a good solution quickly, especially for complex problems where an exact solution is infeasible.
- Method: Uses a shortcut or "rule-of-thumb" strategy to approximate a solution. It doesn't guarantee optimality.
- Pros: Much faster and requires fewer computational resources than DP.
- Cons: The solution may be suboptimal or inaccurate.
- Use case: When a fast answer is needed and a "good enough" solution is acceptable, such as in real-time systems or large-scale optimization problems.