Update EgyptianFraction.java

Egyptian Fraction Greedy Algorithm

Author: AtulSisodiya

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

@@ -4,49 +4,28 @@
 // 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<>();
+    
+    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 that can be subtracted
-            if (denominator % numerator == 0) {
-                result.add("1/" + (denominator / numerator));
-                break;
-            }
-            int x = denominator / numerator + 1;
+            // Find the smallest unit fraction
+            int x = (denominator + numerator - 1) / numerator; // Ceiling of (denominator / numerator)
+            fractions.add("1/" + x);
 
-            result.add("1/" + x);
-            // Update numerator and denominator for the next iteration
+            // Update the numerator and denominator
             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;
+        return fractions;
     }
 
-    private static int gcd(int a, int b) {
-        if (b == 0)
-            return a;
+    private int gcd(int a, int b) {
+        if (b == 0) return a; // Compact if statement for readability
         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 + " ");
-        }
-    }
 }