Greedy Method vs. Dynamic Programming — What's the Difference?

Greedy Method is a problem-solving approach that makes the most advantageous choice at each step, aiming for the overall optimal solution. It doesn't reconsider choices once made and often leads to a local optimum. On the other hand, Dynamic Programming is a method of solving complex problems by breaking them down into simpler subproblems and storing the results of these subproblems to avoid redundant work.

The Greedy Method is easier to implement and usually more efficient in terms of computational resources. It's used when a problem guarantees an optimal solution through local optimizations, like in the case of the Kruskal’s or Prim’s algorithms for finding the Minimum Spanning Tree. In contrast, Dynamic Programming is used in scenarios where the problem can be divided into overlapping subproblems, like the Fibonacci sequence or the Knapsack problem.

Dynamic Programming can be implemented using either a top-down approach with memoization or a bottom-up approach. It is particularly effective for problems with optimal substructure and overlapping subproblems. Conversely, the Greedy Method follows a single pass approach, making the best choice at each step without considering future consequences.

While the Greedy Method can lead to suboptimal solutions in some problems, it's highly efficient in problems where local optimization aligns with global optimization. Dynamic Programming, although providing a more accurate solution for a wider range of problems, can be more complex and consume more memory, especially in problems with a large number of subproblems.

Greedy Method is generally preferred for problems with a 'greedy choice property,' ensuring that locally optimal choices lead to a globally optimal solution. In contrast, Dynamic Programming is chosen for problems where decisions affect future choices, requiring a more comprehensive approach to find the global optimum.