Subjects computer science

Dp Space F46982

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1. **Problem Statement:** Determine whether the statement "To apply a dynamic programming approach to a problem that requires solving $n$ subproblems, one must always use at least $\Omega(n)$ space" is true or false. 2. **Understanding Dynamic Programming (DP):** DP solves problems by breaking them into overlapping subproblems and storing their solutions to avoid redundant computations. 3. **Space Complexity in DP:** The space used depends on how many subproblem solutions are stored simultaneously. 4. **Key Insight:** While many DP algorithms store all $n$ subproblem solutions, some can be optimized to use less space by only keeping necessary previous states. 5. **Example:** For Fibonacci numbers, naive DP stores all $n$ values (space $\Theta(n)$), but optimized DP stores only two previous values (space $O(1)$). 6. **Conclusion:** It is not always necessary to use $\Omega(n)$ space; some DP problems can be solved with less than linear space. **Final answer:** b) False