Final answer:
Dynamic Programming, Backtracking, and Brute force Approach can be used to determine if there is a subset in an array that sums to a target number, with Divide and Conquer being typically inapplicable for this problem.
Step-by-step explanation:
The question is about determining if there is a subset within an array of numbers that sums up to a given target number. The following strategies can be used:
1. Dynamic Programming: This approach is useful as it can help solve this problem by breaking it down into smaller subproblems and constructing a solution incrementally, storing the solutions of subproblems to avoid redundant computations. This is known as the Subset Sum problem which is a well-known problem that can be tackled using dynamic programming.
2. Backtracking: This technique can indeed be used, contrary to what's given in the question. Backtracking systematically searches for a solution to a problem among all available options. It builds the solution incrementally and abandons a solution as soon as it determines that the solution cannot possibly be completed to a valid solution.
3. Brute force Approach: While this method can be used to solve the problem by trying all possible subsets and check their sums, it is an inefficient approach with an exponential time complexity.
4. Divide and Conquer: This approach is typically not used for the Subset Sum problem, because dividing the array into parts doesn't help us solve the Subset Sum directly, unlike problems with more clear-cut divisions like sorting or binary search problems.
In conclusion, both Dynamic Programming and Brute force Approach can be definitely used to solve this problem, and Backtracking can also be used. The correct options for the strategies that can be used to solve this problem from the list provided are: 1) Dynamic Programming and 3) Brute force Approach, and contrary to the given options, 2) Backtracking can be used as well. Therefore, the correct answer is that 1), 2), and 3) can be used to solve this problem.