Question

Introduction to the design and analysis of Algorithms

Question Ch 4.4.1

1. Cutting a stick A stick n inches long needs to be cut into n 1-inch pieces. Outline an algorithm that performs this task with the minimum number of cuts if several pieces of the stick can be cut at the same time. Also give a formula for the minimum number of cuts.

Answer 1

You can follow the divide and conquer method for solving this problem

The code denoting the algorithm for cutting the sticks would be:

Basically you just have to keep on dividing the length of the stick.

Let's say the length of our stick is 32. We first cut the stick in half and cut = 1. Now each stick is of length 16. We keep the one stick on top of another and cut it so cut = 2. Now each stick is of length 8. We keep the stack all sticks on each other and cut it so cut = 3. Now each stick is of length 4. We keep the stack all sticks on each other and cut it so cut = 4. Now each stick is of length 2. We keep the stack all sticks on each other and cut it so cut = 5. Now each stick is of length 1.

So we have 5 cuts on total.

Output:

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