Created potd_21_10_2024.java

Added the solution for GFG problem of the day 21 oct 2024.

october_2024/potd_21_10_2024.java

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+/*
+Problem:
+Given an array arr[] of integers, the task is to count the number of ways to split given array elements into two non-empty subsets such that the XOR of elements of each group is equal. Each element should belong to exactly one subset.
+Note:
+The answer could be very large so print it by doing modulo with 109 + 7. 
+Subsets with the same elements but derived from different indices are different.
+
+Example:
+Input : arr[] = [1, 2, 3]
+Output : 3
+Explanation: {(1),(2, 3)}, {(2),(1, 3)}, {(3),(1, 2)} are three ways with equal XOR value of two groups.
+
+*/
+
+import java.util.*;
+
+public class EqualXORSubsets {
+
+    static final int MOD = 1_000_000_007;
+
+    // Function to calculate (base^exp) % MOD using modular exponentiation.
+    static long modPow(long base, long exp, long mod) {
+        long result = 1;
+        while (exp > 0) {
+            if ((exp & 1) == 1) { // If exp is odd, multiply the result with base.
+                result = (result * base) % mod;
+            }
+            base = (base * base) % mod; // Square the base.
+            exp >>= 1; // Divide exp by 2.
+        }
+        return result;
+    }
+
+    // Function to count the number of ways to split the array.
+    static int countWays(int[] arr) {
+        int totalXOR = 0;
+
+        // Calculate the XOR of all elements in the array.
+        for (int num : arr) {
+            totalXOR ^= num;
+        }
+
+        // If the total XOR is not zero, no valid split is possible.
+        if (totalXOR != 0) {
+            return 0;
+        }
+
+        int n = arr.length;
+
+        // Calculate (2^(n-1) - 1) % MOD.
+        long ways = modPow(2, n - 1, MOD) - 1;
+        if (ways < 0) {
+            ways += MOD; // Ensure the result is non-negative.
+        }
+
+        return (int) ways;
+    }
+
+    public static void main(String[] args) {
+        int[] arr = {1, 2, 3};
+        int result = countWays(arr);
+        System.out.println("Number of ways to split the array: " + result);
+    }
+}
+
+