Solution: Find the Egyptian Fraction

Solution

We can generate Egyptian Fractions using Greedy Algorithm. For a given number of the form n/d, where d > n, first find the greatest possible unit fraction, then perform recursion for the remaining part.

For example, consider $6/14$. We first find the ceiling of $\lceil 14/6 \rceil$, i.e., $3$, so the first unit fraction becomes $1/3$. Now subtract $1/3$ out of $6/14$ and, then recur for $(6/14$ $–$ $1/3)$ i.e., $4/42$.