Day 54: Power Set
Day 54: Power Set #
Welcome to Day 54 of our 60 Days of Coding Algorithm Challenge! Today, we’ll explore the Power Set problem, a classic combinatorial problem that has applications in various areas of computer science and mathematics.
What is a Power Set? #
The power set of a set S is the set of all subsets of S, including the empty set and S itself. For a set with n elements, its power set contains 2^n elements.
For example, for the set {1, 2, 3}, its power set is: {{}, {1}, {2}, {3}, {1,2}, {1,3}, {2,3}, {1,2,3}}
Approaches to Generate Power Set #
We’ll explore three different approaches to generate the power set:
- Iterative approach using bit manipulation
- Recursive approach
- Iterative approach using itertools
1. Iterative Approach Using Bit Manipulation #
This approach uses the bit manipulation techniques we learned yesterday. We represent each subset as a binary number where each bit represents the presence (1) or absence (0) of an element.
1def power_set_bit(s):
2 n = len(s)
3 power_set = []
4 for i in range(1 << n):
5 subset = [s[j] for j in range(n) if (i & (1 << j))]
6 power_set.append( …
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