From d1efd19fc9fddd2d3ffe61c0a7e3fb79d9c2e8bd Mon Sep 17 00:00:00 2001
From: Atul Sisodiya <56028094+AtulSisodiya@users.noreply.github.com>
Date: Wed, 16 Oct 2024 22:09:09 +0530
Subject: [PATCH 1/2] Create EgyptianFraction.java

Adding Greedy Algorithm for Egyptian Fraction Problem
---
 .../greedyalgorithms/EgyptianFraction.java    | 52 +++++++++++++++++++
 1 file changed, 52 insertions(+)
 create mode 100644 src/main/java/com/thealgorithms/greedyalgorithms/EgyptianFraction.java

diff --git a/src/main/java/com/thealgorithms/greedyalgorithms/EgyptianFraction.java b/src/main/java/com/thealgorithms/greedyalgorithms/EgyptianFraction.java
new file mode 100644
index 000000000000..7cb5023cc8f7
--- /dev/null
+++ b/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 + " ");
+        }
+    }
+}
+
+

From b373fd023fa8d512e3db91424f5dfcfcb2257d2e Mon Sep 17 00:00:00 2001
From: Atul Sisodiya <56028094+AtulSisodiya@users.noreply.github.com>
Date: Wed, 16 Oct 2024 22:16:07 +0530
Subject: [PATCH 2/2] Update EgyptianFraction.java

Egyptian Fraction Greedy Algorithm
---
 .../greedyalgorithms/EgyptianFraction.java    | 43 +++++--------------
 1 file changed, 11 insertions(+), 32 deletions(-)

diff --git a/src/main/java/com/thealgorithms/greedyalgorithms/EgyptianFraction.java b/src/main/java/com/thealgorithms/greedyalgorithms/EgyptianFraction.java
index 7cb5023cc8f7..893097c3669d 100644
--- a/src/main/java/com/thealgorithms/greedyalgorithms/EgyptianFraction.java
+++ b/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 + " ");
-        }
-    }
 }