Example 3.2. DYNAMIC PROGRAMMING. For the various problems in area such as inventory, chemical engineering design , and control theory, Dynamic Programming is the only technique used to solve the problem. Devise the greedy algorithm that makes the change of n rupees (n<55000 and n is multiple of 10) with minimum number of notes (consider 100 notes of 10 rupees, 80 notes 20 rupees, 60 notes of 50 rupees, 50 notes of 100 rupees, 40 notes of 500 rupees and 30 notes of 1000 rupees). Dynamic Programming and Divide-and-Conquer Similarities. Like divide-and-conquer method, Dynamic Programming solves problems by combining the solutions of subproblems. Even with the correct algorithm, it is hard to prove why it is correct. Explanation: A greedy algorithm gives optimal solution for all subproblems, but when these locally optimal solutions are combined it may NOT result into a globally optimal solution. Greedy algorithm is less efficient whereas Dynamic programming is more efficient. Greedy solves the sub-problems from top down. Dynamic Programming is also used in optimization problems. But I hope this article will shed some extra light and help you to do another step of learning such valuable algorithm paradigms as dynamic programming and divide-and-conquer. Hence, a greedy algorithm CANNOT be used to solve all the dynamic programming problems. Greedy method never reconsiders its choices whereas Dynamic programming may consider the previous state. 2. A Dynamic algorithm is applicable to problems that exhibit Overlapping subproblems and Optimal substructure properties. Also, dynamic programming, if implemented correctly, guarantees that we get an optimal solution. The problem can’t be solved until we find all solutions of sub-problems. This video contains the comparison between Greedy method and Dynamic programming. It involves a lot of creativity. Dynamic Programming solves the sub-problems bottom up. Advantages 1. A greedy algorithm is one which finds optimal solution at each and every stage with the hope of finding global optimum at the end. The reason behind dynamic programming optimality is that it’s an optimization over the backtracking approach which explores all the possible choices. This video contains the comparison between Greedy method and Dynamic programming. As I see it for now I can say that dynamic programming is an extension of divide and conquer paradigm. Dynamic programming vs Greedy 1. More efficient as compared,to dynamic programming: Less efficient as compared to greedy approach Greed algorithm : Greedy algorithm is one which finds the feasible solution at every stage with the hope of finding global optimum solution. Proving that a greedy algorithm is correct is more of an art than a science. Let us say that we have a machine, and to determine its state at time t, we have certain quantities called state variables. 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