FreeCodeCampDynamicProgramming
Dynamic programming exercises written in C++17 from FreeCodeCamp in YouTube: https://youtu.be/oBt53YbR9Kk.
This repository serves as a very good starting point to learn or remember about dynamic programming.
Why C++?
It is my favourite language and I wanted to see the language differences in the implementation. The C++17 implementation is only a little harder to understand than the JavaScript one.
In any case, it is the small price that we pay for better performance.
Algorithms' complexity
Time complexity
| Program | Brute force | Memoization | Tabulation |
|---|---|---|---|
| Fibonacci | O(2n) | O(n) | O(n) |
| GridTraveler | O(2(n+m)) | O(n*m) | O(n*m) |
| CanSum | O(nm)) | O(n*m) | O(n*m) |
| HowSum | O(nm*m) | O(n*m2) | O(n*m2) |
| BestSum | O(nm*m) | O(n*m2) | O(n*m2) |
| CanConstruct | O(nm*m) | O(n*m2) | O(n*m2) |
| CountConstruct | O(nm*m) | O(n*m2) | O(n*m2) |
| AllConstruct | O(nm) | O(nm) | O(nm) |
Space complexity
| Program | Brute force | Memoization | Tabulation |
|---|---|---|---|
| Fibonacci | O(n) | O(n) | O(n) |
| GridTraveler | O(n+m) | O(n*m) | O(n*m) |
| CanSum | O(m) | O(m) | O(m) |
| HowSum | O(m) | O(m2) | O(m2) |
| BestSum | O(m2) | O(m2) | O(m2) |
| CanConstruct | O(m2) | O(m2) | O(m) |
| CountConstruct | O(m2) | O(m2) | O(m) |
| AllConstruct | O(m) | O(nm) | O(nm) |
Alvin's memoization recipe
- Make it work
- Visualize the problem as a tree
- Implement the tree using recursion
- Test it
- Make it efficient
- Add a memo object
- Add a base case to return memo value
- Store return values into the memo
Alvin's tabulation recipe
- Visualize the problem as a table
- Size the table based on the inputs
- Initialize the table with default values
- Seed the trivial answer into the table
- Iterate through the table
- Fill further positions based on the current position
Notes on exercises
CanSum, HowSum and BestSum notes
- CanSum: "Can you do it? yes/no"
- HowSum: "How will you do it?"
- BestSum: "What is the optimize way to do it?"
- CanSum: Decision problem
- HowSum: Combinatoric problem
- BestSum: Optimization problem
CanConstruct, CountConstruct and AllConstruct notes
- CanConstruct: "Can you do it? yes/no"
- CountConstruct: "In how many ways will you do it?"
- AllConstruct: "What are all the possible ways to do it?"
- CanSum: Decision problem
- HowSum: Combinatoric enumeration problem
- AllConstruct: Combinatoric construction problem
Conclusion
- Notice any overlapping subproblems
- Decide what is the trivially smallest input
- Think recursively to use Memoization
- Think iteratively to use Tabulation
- Draw a strategy first!