Dynamic Programming

Dynamic Programming is an algorithmic model that solves a given complex problem by breaking it down into a collection of simpler subproblems and stores the results of subproblems to avoid computing the same results again.

A problem has two below properties can be solved using Dynamic programming.

1) Overlapping subproblems

2) Optimal substructure

1) Overlapping subproblems

If the problem can be broken down into subproblems which are reused several times or a recursive algorithm for the problem solves the same subproblem over and over rather than always generating new subproblems. Computed solutions to subproblems are stored in a table so that these don’t have to recomputed.

So Dynamic Programming is not useful when there are no common (overlapping) subproblems because there is no point storing the solutions if they are not needed again.

2) Optimal substructure

A problem is said to have optimal substructure if an optimal solution of the given problem can be obtained by using optimal solutions of its subproblems. This property is used to determine the usefulness of dynamic programming and greedy algorithms for a problem.