Add binary addition (#5593)

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

@@ -0,0 +1,75 @@
+package com.thealgorithms.greedyalgorithms;
+
+import java.util.Collections;
+
+/**
+ * BinaryAddition class to perform binary addition of two binary strings.
+ */
+public class BinaryAddition {
+    /**
+     * Computes the sum of two binary characters and a carry.
+     * @param a First binary character ('0' or '1').
+     * @param b Second binary character ('0' or '1').
+     * @param carry The carry from the previous operation ('0' or '1').
+     * @return The sum as a binary character ('0' or '1').
+     */
+    public char sum(char a, char b, char carry) {
+        int count = 0;
+        if (a == '1') {
+            count++;
+        }
+        if (b == '1') {
+            count++;
+        }
+        if (carry == '1') {
+            count++;
+        }
+        return count % 2 == 0 ? '0' : '1';
+    }
+    /**
+     * Computes the carry for the next higher bit from two binary characters and a carry.
+     * @param a First binary character ('0' or '1').
+     * @param b Second binary character ('0' or '1').
+     * @param carry The carry from the previous operation ('0' or '1').
+     * @return The carry for the next bit ('0' or '1').
+     */
+    public char carry(char a, char b, char carry) {
+        int count = 0;
+        if (a == '1') {
+            count++;
+        }
+        if (b == '1') {
+            count++;
+        }
+        if (carry == '1') {
+            count++;
+        }
+        return count >= 2 ? '1' : '0';
+    }
+    /**
+     * Adds two binary strings and returns their sum as a binary string.
+     * @param a First binary string.
+     * @param b Second binary string.
+     * @return Binary string representing the sum of the two binary inputs.
+     */
+    public String addBinary(String a, String b) {
+        // Padding the shorter string with leading zeros
+        int maxLength = Math.max(a.length(), b.length());
+        a = String.join("", Collections.nCopies(maxLength - a.length(), "0")) + a;
+        b = String.join("", Collections.nCopies(maxLength - b.length(), "0")) + b;
+        StringBuilder result = new StringBuilder();
+        char carry = '0';
+        // Iterating over the binary strings from the least significant to the most significant bit
+        for (int i = maxLength - 1; i >= 0; i--) {
+            char sum = sum(a.charAt(i), b.charAt(i), carry);
+            carry = carry(a.charAt(i), b.charAt(i), carry);
+            result.append(sum);
+        }
+        // If there's a remaining carry, append it
+        if (carry == '1') {
+            result.append('1');
+        }
+        // Reverse the result as we constructed it from the least significant bit
+        return result.reverse().toString();
+    }
+}