Adding Egyptian Fraction Greedy Algorithm

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

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+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 {
+
+    public List<String> getEgyptianFraction(int numerator, int denominator) {
+        List<String> fractions = new ArrayList<>();
+
+        // Loop until the numerator becomes zero
+        while (numerator != 0) {
+            // Find the smallest unit fraction
+            int x = (denominator + numerator - 1) / numerator; // Ceiling of (denominator / numerator)
+            fractions.add("1/" + x);
+
+            // Update the numerator and denominator
+            numerator = numerator * x - denominator;
+            denominator = denominator * x;
+        }
+
+        return fractions;
+    }
+
+    private int gcd(int a, int b) {
+        if (b == 0) return a; // Compact if statement for readability
+        return gcd(b, a % b);
+    }
+}
+
+

src/test/java/com/thealgorithms/greedyalgorithms/EgyptianFractionTest.java

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+package com.thealgorithms.greedyalgorithms;
+
+import static org.junit.jupiter.api.Assertions.*;
+import org.junit.jupiter.api.Test;
+
+import java.util.List;
+
+public class EgyptianFractionTest {
+    EgyptianFraction ef = new EgyptianFraction();
+
+    @Test
+    public void testGetEgyptianFraction_NormalCase() {
+        List<String> result = ef.getEgyptianFraction(5, 6);
+        assertEquals(List.of("1/2", "1/3"), result);
+    }
+
+    @Test
+    public void testGetEgyptianFraction_SimpleFraction() {
+        List<String> result = ef.getEgyptianFraction(1, 2);
+        assertEquals(List.of("1/2"), result);
+    }
+
+    @Test
+    public void testGetEgyptianFraction_WholeNumber() {
+        List<String> result = ef.getEgyptianFraction(2, 1);
+        assertEquals(List.of("1/1", "1/2", "1/3", "1/6"), result); // Example output
+    }
+
+    @Test
+    public void testGetEgyptianFraction_OneOverOne() {
+        List<String> result = ef.getEgyptianFraction(1, 1);
+        assertEquals(List.of("1/1"), result);
+    }
+
+    @Test
+    public void testGetEgyptianFraction_OneOverThree() {
+        List<String> result = ef.getEgyptianFraction(1, 3);
+        assertEquals(List.of("1/3"), result);
+    }
+}