Dynamic Programming is an algorithmic paradigm that solves a given complex problem by breaking it into subproblems and stores the results of subproblems to avoid computing the same results again. Following are the two main properties of a problem that suggests that the given problem can be solved using Dynamic programming.
As we discussed in Set 1 , following are the two main properties of a problem that suggest that the given problem can be solved using Dynamic programming: 1) Overlapping Subproblems 2) Optimal Substructure We have already discussed Overlapping Subproblem property in the Set 1 . Let us discuss Optimal Substructure property here. 2) Optimal Substructure: A given problems has Optimal Substructure Property if optimal solution of the given problem can be obtained by using optimal solutions of its subproblems. For example, the Shortest Path problem has following optimal substructure property: If a node x lies in the shortest path from a source node u to destination node v then the shortest path from u to v is combination of shortest path from u to x and shortest path from x to v. The standard All Pair Shortest Path algorithm like Floyd–Warshall and Single Source Shortest path algorithm for negative weight edges like Bellman–Ford are typical examples of Dynamic Programming. O