Greedy Algorithms Questions
The Egyptian Fraction problem involves representing a given positive fraction as a sum of unique unit fractions, where a unit fraction is a fraction with a numerator of 1. The goal is to find the minimum number of unit fractions required to represent the given fraction.
A greedy algorithm can be used to solve the Egyptian Fraction problem. The algorithm starts by finding the largest possible unit fraction that is less than or equal to the given fraction. This unit fraction is added to the representation of the fraction. Then, the algorithm recursively applies the same process to the remaining fraction (subtracting the added unit fraction from it) until the remaining fraction becomes 0.
The steps to solve the Egyptian Fraction problem using a greedy algorithm are as follows:
1. Start with the given fraction.
2. Find the largest possible unit fraction that is less than or equal to the given fraction.
3. Add this unit fraction to the representation of the fraction.
4. Subtract the added unit fraction from the remaining fraction.
5. Repeat steps 2-4 until the remaining fraction becomes 0.
By following this greedy algorithm, the given fraction can be represented as a sum of unique unit fractions with the minimum number of fractions.