Algorithms · Dynamic Programming
Official IIT answer key · IIT Bombay · Audited Aug 2026
GATE CSE 2021 Set 1 Q40 · MSQ · 2 marks
Key concept
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Topic notes
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 →Define Rn to be the maximum amount earned by cutting a rod of length n meters into one or more pieces of integer length and selling them. For i > 0, let p[i] denote the selling price of a rod whose length is i meters. Consider the array of prices: p[1] = 1, p[2] = 5, p[3] = 8, p[4] = 9, p[5] = 10, p[6] = 17, p[7] = 18 Which of the following statements is/are correct about R7?
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