From 07a9944f414affbe7c559d77408b22548825229b Mon Sep 17 00:00:00 2001
From: theSoberSobber <109434814+theSoberSobber@users.noreply.github.com>
Date: Sun, 3 Nov 2024 15:53:45 +0530
Subject: [PATCH] Xor-Of-First-N-Natural-Numbers

---
 codes/Xor-Of-First-N-Natural-Numbers.cpp | 19 +++++++++++++++++++
 1 file changed, 19 insertions(+)
 create mode 100644 codes/Xor-Of-First-N-Natural-Numbers.cpp

diff --git a/codes/Xor-Of-First-N-Natural-Numbers.cpp b/codes/Xor-Of-First-N-Natural-Numbers.cpp
new file mode 100644
index 0000000..6b23ed5
--- /dev/null
+++ b/codes/Xor-Of-First-N-Natural-Numbers.cpp
@@ -0,0 +1,19 @@
+//Xor of first N Natural Numbers
+//based on the fact that if n%4==3 then xor till n from 1 is 0
+
+auto xorOfFirstN = [&](int n) -> int {
+    // n%4 = 3 => xor = 0
+    int t = n, ans = 0;
+    while(t%4!=3) ans^=t, --t;
+    return ans;
+};
+
+// more explicit version
+int computeXOR(int n) {
+    if (n % 4 == 0) return n;
+    if (n % 4 == 1) return 1;
+    if (n % 4 == 2) return n + 1;
+    return 0;
+}
+
+// source: https://www.geeksforgeeks.org/calculate-xor-1-n/