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Algorithms · Dynamic Programming
Official IIT answer key · IISc Bangalore · Audited Aug 2026
GATE CSE 2016 Set 2 Q38 · NAT · 2 marks
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Dynamic Programming in GATE CS tests both classical tabular algorithms (such as Matrix Chain Multiplication and Rod Cutting) and structural properties of DP (such as dependency graphs, evaluation orders, and state-space reductions). Questions frequently require either manual tracing of a DP table on small concrete inputs or mapping an unfamiliar problem reduction (like array replacement distance) to a standard DP formulation like Longest Non-Decreasing Subsequence. Both conceptual evaluation order questions (MCQ/MSQ) and exact numerical optimization outputs (NAT) are regularly tested.
Full Dynamic Programming guide →Let A1, A2, A3, and A4 be four matrices of dimensions 10 5, 5 20, 20 10, and 10 5, respectively. The minimum number of scalar multiplications required to find the product A1A2A3A4 using the basic matrix multiplication method is …
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