Difference Between Divide and Conquer Algo and Dynamic Programming

Divide and Conquer

Divide and Conquer works by dividing the problem into sub-problems, conquer each sub-problem recursively and combine these solutions.

Dynamic Programming

Dynamic Programming is a technique for solving problems with overlapping subproblems. Each sub-problem is solved only once and the result of each sub-problem is stored in a table ( generally implemented as an array or a hash table) for future references. These sub-solutions may be used to obtain the original solution and the technique of storing the sub-problem solutions is known as memoization.

You may think of DP = recursion + re-use

A classic example to understand the difference would be to see both these approaches towards obtaining the nth fibonacci number. Check this material from MIT.

Divide and Conquer approach

Dynamic Programming Approach

Dynamic Programming and Divide-and-Conquer Similarities

As I see it for now I can say that dynamic programming is an extension of divide and conquer paradigm.

I would not treat them as something completely different. Because they both work by recursively breaking down a problem into two or more sub-problems of the same or related type, until these become simple enough to be solved directly. The solutions to the sub-problems are then combined to give a solution to the original problem.

So why do we still have different paradigm names then and why I called dynamic programming an extension. It is because dynamic programming approach may be applied to the problem only if the problem has certain restrictions or prerequisites. And after that dynamic programming extends divide and conquer approach with memoization or tabulation technique.

Let’s go step by step…