![]() All pair shortest path by Floyd-Warshallĭynamic programming can be used in both top-down and bottom-up manner.The following computer problems can be solved using dynamic programming approach − Dynamic algorithms use memorization to remember the output of already solved sub-problems. In contrast to divide and conquer algorithms, where solutions are combined to achieve an overall solution, dynamic algorithms use the output of a smaller sub-problem and then try to optimize a bigger sub-problem. In contrast to greedy algorithms, where local optimization is addressed, dynamic algorithms are motivated for an overall optimization of the problem. The problem should be able to be divided into smaller overlapping sub-problem.Īn optimum solution can be achieved by using an optimum solution of smaller sub-problems. ![]() The solutions of sub-problems are combined in order to achieve the best solution. Before solving the in-hand sub-problem, dynamic algorithm will try to examine the results of the previously solved sub-problems. Mostly, these algorithms are used for optimization. Rather, results of these smaller sub-problems are remembered and used for similar or overlapping sub-problems.ĭynamic programming is used where we have problems, which can be divided into similar sub-problems, so that their results can be re-used. But unlike, divide and conquer, these sub-problems are not solved independently. Dynamic programming approach is similar to divide and conquer in breaking down the problem into smaller and yet smaller possible sub-problems.
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