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Chapter 1: Problem 3

Write an algorithm that prints out all the subsets of three elements of a set of \(n\) elements. The elements of this set are stored in a list that is the input to the algorithm.

Short Answer

Expert verified
The algorithm involves creating a helper function to generate all subsets of size 3. The Python itertools.combinations() function can be used for this task. After generating the subsets, the algorithm will print them.

Step by step solution

01

Creating a Helper Function

Create a helper function that generates all subsets of a specific size from a given set, for this case, the size is 3. In Python, a handy function for this in the itertools module is combinations(). This function takes two parameters: the list (iterable), and the length of the subsets to be created (r). It returns an iterator that produces all possible subsets of the given length from the provided list.
02

Using the Helper Function

Use the helper function on the provided list of elements to generate all subsets of size three. As the combinations() function outputs an iterator, convert the output into a list so it's easier to work with.
03

Printing the Subsets

Print the subsets. This step could imply iterating through the list of subsets and printing each one, or just printing the entire list, depending on the specific requirements of the exercise.

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Most popular questions from this chapter

Using the Properties of Order in Section \(1.4 .2,\) show that \\[ 5 n^{5}+4 n^{4}+6 n^{3}+2 n^{2}+n+7 \in \Theta\left(n^{5}\right) \\]

Presently we can solve problem instances of size 100 in 1 minute using algorithm A, which is a \(\Theta\left(2^{n}\right)\) algorithm. On the other hand, we will soon have to solve problem instances twice this large in 1 minute. Do you think it would help to buy a faster (and more expensive) computer?

Write an algorithm that determines whether or not an almost complete binary tree is a heap.

Algorithm A performs \(10 n^{2}\) basic operations, and algorithm B performs \(300 \ln n\) basic operations. For what value of \(n\) does algorithm \(\mathrm{B}\) start to show its better performance?

Show the correctness of the following statements. (a) \(\lg n \in O(n)\) (b) \(n \in O(n \lg n)\) (c) \(n \lg n \in O\left(n^{2}\right)\) (d) \(2^{n} \in \Omega\left(5^{\ln n}\right)\) (c) \(\lg ^{3} n \in o\left(n^{a \cdot 5}\right)\)
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