Tabulation

Algorithm

In order to avoid extra recursive stack space used in memoization approach, we can simply convert our solution into tabulation approach. We can follow these steps in order to form our tabulation solution:

Create a 2D table of boolean values with dimensions matching the memoization approach, initially setting all entries to false.
Initialize the first column to true, since achieving a target sum of zero is always possible regardless of the number of elements considered.
For the first row, mark as true only the position corresponding to the first element’s value, if it does not exceed the target.
Use nested loops to fill the table row by row, applying the same inclusion–exclusion logic from the recursive solution but replacing recursive calls with table lookups.
Continue filling the table until all states are computed.
The answer will be found at the position in the table corresponding to using all elements to achieve the required target sum.

Code

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