Create EgyptianFraction.java

Adding Greedy Algorithm for Egyptian Fraction Problem

Author: AtulSisodiya

src/main/java/com/thealgorithms/greedyalgorithms/EgyptianFraction.java

@@ -0,0 +1,52 @@
+package com.thealgorithms.greedyalgorithms;
+import java.util.ArrayList;
+import java.util.List;
+// Problem Link: https://en.wikipedia.org/wiki/Greedy_algorithm_for_Egyptian_fractions
+
+public class EgyptianFraction {
+    // Function to decompose a fraction into a sum of unit fractions
+    public static List<String> getEgyptianFraction(int numerator, int denominator) {
+        List<String> result = new ArrayList<>();
+
+        while (numerator != 0) {
+            // Find the smallest unit fraction that can be subtracted
+            if (denominator % numerator == 0) {
+                result.add("1/" + (denominator / numerator));
+                break;
+            }
+            int x = denominator / numerator + 1;
+
+            result.add("1/" + x);
+            // Update numerator and denominator for the next iteration
+            numerator = numerator * x - denominator;
+            denominator = denominator * x;
+
+            // Reduce the fraction by dividing numerator and denominator by their gcd
+            int gcd = gcd(numerator, denominator);
+            numerator /= gcd;
+            denominator /= gcd;
+        }
+
+        return result;
+    }
+
+    private static int gcd(int a, int b) {
+        if (b == 0)
+            return a;
+        return gcd(b, a % b);
+    }
+
+    public static void main(String[] args) {
+        int numerator = 5;
+        int denominator = 6;
+
+        List<String> egyptianFractions = getEgyptianFraction(numerator, denominator);
+
+        System.out.println("Egyptian Fraction representation of " + numerator + "/" + denominator + " is:");
+        for (String frac : egyptianFractions) {
+            System.out.print(frac + " ");
+        }
+    }
+}
+
+