Question

2. Sum of Subset Problem. A set of positive integers S={3, 9, 2, 6, 5} is given, is there a subset of S that sums exactly to m = 10? Fill the following table using the dynamic programming approach we've discussed in the class. Backtrack from the rightmost corner and list the result. ({} means empty set).

          2. Sum of Subset Problem. A set of positive integers S={3, 9, 2, 6, 5} is given, is there a
subset of S that sums exactly to m = 10? Fill the following table using the dynamic
programming approach we've discussed in the class. Backtrack from the rightmost corner
and list the result. ({} means empty set).

2. Sum of Subset Problem. A set of positive integers S=3, 9, 2, 6, 5 is given, is there a
subset of S that sums exactly to m = 10? Fill the following table using the dynamic
programming approach we've discussed in the class. Backtrack from the rightmost corner
and list the result. ( means empty set).

Added by Julia G.

Computer Science and Information Technology

Trishna Knowledge Systems 2018 Edition

Instant Answer

Solved by Expert Donna Densmore

Step 1

The table represents the dynamic programming approach to solve the sum of subset problem. Each cell in the table represents whether a subset of the given set can sum up to the corresponding value. Show more…

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Sum of Subset Problem: Dynamic Programming Approach A set of positive integers S = {3, 9, 2, 6, 5} is given. The task is to determine if there exists a subset of S that sums exactly to m = 10. To solve this problem, we will use the dynamic programming approach discussed in class. The table below shows the step-by-step calculation using the dynamic programming approach: | | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | |---|---|---|---|---|---|---|---|---|---|---|----| | S | 0 | {} | 3 | | | | | | | | | | 2 | 9 | 3 | | | | | | | | | | | 4 | 6 | 5 | 5 | | | | | | | | | To find the subset that sums exactly to 10, we backtrack from the rightmost corner of the table. The result is as follows: Subset: {2, 3, 5}