GATE CS 2021 Set 1 — Question 50
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Algorithms → Dynamic Programming
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Question
Define to be the maximum amount earned by cutting a rod of length meters into one or more pieces of integer length and selling them. For , let denote the selling price of a rod whose length is meters. Consider the array of prices:Which of the following statements is/are correct about ?
Correct answer
(A) R₇ = 18; (C) R₇ is achieved by three different solutions.
Solution
The rod cutting problem can be solved using dynamic programming with the recurrence relation , where .Given the prices: .Calculating values step-by-step:
- .
1.From : (a single piece of length 7)
2.From : (two pieces of lengths 1 and 6)
3.From : (three pieces of lengths 2, 2, and 3)
Note: also yields , which is the same set as above. Similarly, yields .There are exactly 3 different solutions. Option (C) is correct.Since is a valid solution consisting of three pieces, option (D) is incorrect.Continue learning with Success Tracker
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