GATE CS 2014 Set 3 — Question 47
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Algorithms → Dynamic Programming → Optimal Substructure
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Question
Suppose you want to move from 0 to 100 on the number line. In each step, you either move right by a unit distance or you take a shortcut. A shortcut is simply a pre-specified pair of integers with . Given a shortcut if you are at position on the number line, you may directly move to . Suppose denotes the smallest number of steps needed to move from to 100. Suppose further that there is at most 1 shortcut involving any number, and in particular from 9 there is a shortcut to 15. Let and be such that . Then the value of the product is _____.
Correct answer
150 to 150
Solution
From any position , we can move to (1 step). If there is a shortcut from to , we can also move to (1 step).Given:
- From 9, there is a shortcut to 15.
- is the minimum steps from to 100.
- .
1.Move by unit distance: .
2.Take the shortcut: .
Thus, the recurrence relation for is:Comparing this with the given equation , we have the set .The product .Continue learning with Success Tracker
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