Application of dynamic programming in solving optimizing problems

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I am going to talk about applications of dynamic programming for solving optimising problems and I am giving it to attach of real world and some of the practical examples to make it more understandable for all of you.

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Dynamic programming is one of most significant process and technique for solution of optimizing problems by torn them down into smaller problems which are called sub problems which solve each only once in a time and for storing their solutions to prevent any kind of redundant computation. This technique is most significantly helpful for problems that have overlapping small problems and optimal small structures.

Now here are some of most significant practical examples of dynamic programming applications include:

1. Fibonacci sequence calculation:

We all know that there is dynamic programming which is useful for efficient computation of Fibonacci numbers when it store previously or already calculated values so that it may prevent any kind of redundant calculations.

2. Shortest path problems:

In a graph Dynamic programming seeks for the shortest path by breaking it down into smaller problems and in this way it becomes easy to solve each only once and then it also combines the overall results.

3. Knapsack problem:

Dynamic programming is helpful in optimally solving the knapsack problem by determination of the optimal items and they leads to give then constraints at different factors like weight and value.

4. Longest common subsequence:

Dynamic programming find out the longest common subsequence in one of most significant way within two strings when it builds similarity in its matrix and then it trace back the optimal solution at the end

5. Scheduling problems:

Dynamic programming is helpful in optimization of scheduling different particular tasks such as scheduling jobs or other allocation of resource by breaking large problems into small problems and solve each only once.

6. Minimum spanning tree:

Dynamic programming try to search out the minimized spanning tree in one graph when it tends to solve smaller problems and it leads to combine the results.

7. Matrix chain multiplication:

Dynamic programming is helpful in optimizing matrix multiplication when it find out order of multiplication which is most efficient.

8. Optimal binary search tree:

Dynamic programming is helpful in construction of binary search tree when it solve subproblems and then they combine final outcomes.

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There are different fields in which dynamic programming has its applications and these fields are operation research, computer science and it could also be economics but all these are most specificity and significantly useful and helpful for the solution of complex optimising problems buy overlapping some problems and significant sub structures.

That was some of the applications of dynamic programming for solving some of the optimising problems I have explained in different headings and hopefully now the topic is clear to all of you.

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Thanks

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