Table of Contents
- 1 How do you Recognise a problem that can be solved using dynamic programming?
- 2 Which problems Cannot be solved using dynamic programming?
- 3 When does Dynamic Programming fail?
- 4 Is optimal substructure necessary for Dynamic Programming?
- 5 What are some of the best dynamic programming examples?
- 6 When does a problem have overlapping subproblems?
How do you Recognise a problem that can be solved using dynamic programming?
7 Steps to solve a Dynamic Programming problem
- How to recognize a DP problem.
- Identify problem variables.
- Clearly express the recurrence relation.
- Identify the base cases.
- Decide if you want to implement it iteratively or recursively.
- Add memoization.
- Determine time complexity.
Which problems Cannot be solved using dynamic programming?
A problem can be solved using dynamic programming if (1) it has optimal sub-structure, i.e. it is recursive, and (2) it has overlapping sub problems. Therefore, any recursive problem that has not overlapping sub problems cannot be solved using dynamic programming.
How can I master in dynamic programming?
The best way to practice dynamic programming is:
- First, define a brute force recursive solution.
- Characterise the structure of the recursive solution.
- Identify the base cases.
- Store the computed values of overlapping subproblems.
- Convert Recursive code to Memoised code.
- Convert Memoised code to Tabular form.
How do you determine the optimal substructure?
If minimizing the local functions is a problem of “lower order”, and (specifically) if, after a finite number of these reductions, the problem becomes trivial, then the problem has an optimal substructure.
When does Dynamic Programming fail?
1. Overlapping Sub-problems. If any problem doesn’t have either of above property then problem can’t be solved using DP. for example shortest path can be solved using DP but longest path can’t solved, because longest path doesn’t hold optimal sub-structure property.
Is optimal substructure necessary for Dynamic Programming?
The tree example above is not a dynamic programming problem. And readers should notice that the optimal-substructure property is not unique for dynamic programming. Most of the problems with optimal values have this property. However, the optimal substructure is a necessary condition for dynamic programming problems.
Can all dynamic programming problems be solved using DP?
All dynamic programming problems satisfy the overlapping subproblems property and most of the classic dynamic problems also satisfy the optimal substructure property. Once, we observe these properties in a given problem, be sure that it can be solved using DP.
Does dynamic programming have an optimal substructure?
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. Now in the given example, It definitely has an optimal substructure because we can get the right answer just by combining the results of the subproblems.
What are some of the best dynamic programming examples?
Dynamic Programming Examples 1. Minimum cost from Sydney to Perth 2. Economic Feasibility Study 3. 0/1 Knapsack problem 4. Sequence Alignment problem Minimum Cost from Sydney to Perth Based on M. A. Rosenman: Tutorial – Dynamic Programming Formulation http://people.arch.usyd.edu.au/~mike/DynamicProg/DPTutorial.95.html •Problem definition
When does a problem have overlapping subproblems?
A problem has overlapping subproblems if finding its solution involves solving the same subproblem multiple times. Dynamic Programming is mainly used when solutions of the same subproblems are needed again and again. In dynamic programming, computed solutions to subproblems are stored in a table so that these don’t have to be recomputed again.