Recursion -> memoization -> tabulation -> space optimization
- memoization - top to bottom
- tabulation - bottom-up
- Recursion -> solve every sub problem
- (there is overlapping of sub problems in recursion)
-
Memoization - tend to store the value of sub problems in some map / table.
-
Tabulation - bottom-up, from base case to required answer
-
Space optimization - for space optimization, you need to find the pattern in the problem.
1) Express the problem in terms of indexes.
2) Try out all possible choices at a given index.
3) Take the maximum/minmum of all choices (according to question)
1. copy the base case of recursion
2. for loops for changing states
3. copy the recursion
If you are doing recursion step from 0th index to n-1th index, Tabulation will always be its opposite.
unknown error while using general tabulation approach so use shifting of index technique
where i means index[i-1] to tackle if(i < 0 ) testcase of recursion
because we can't store negative index in dp as dp[-1].