CPP: add Happy Number solution (IEEEXtreme style)

CPP/Basics/happy_number.cpp

@@ -0,0 +1,69 @@
+// Problem: Happy Number
+// Language: C++
+// Description:
+//   A number is "happy" if repeatedly replacing the number by the sum
+//   of the squares of its digits eventually leads to 1. If it enters
+//   a cycle that does not include 1, the number is not happy.
+// Input: A single positive integer n
+// Output: "YES" if n is a happy number, otherwise "NO"
+
+#include <iostream>
+
+using namespace std;
+
+// Function to compute the sum of squares of digits
+long long sum_of_squares(long long x) {
+    long long s = 0;
+    while (x > 0) {
+        int d = static_cast<int>(x % 10);
+        s += static_cast<long long>(d) * d;
+        x /= 10;
+    }
+    return s;
+}
+
+// Floyd's cycle detection algorithm
+bool isHappy(long long n) {
+    auto next = [](long long x) {
+        long long s = 0;
+        while (x > 0) {
+            int d = static_cast<int>(x % 10);
+            s += static_cast<long long>(d) * d;
+            x /= 10;
+        }
+        return s;
+    };
+
+    long long tortoise = n;
+    long long hare = n;
+
+    while (true) {
+        tortoise = next(tortoise);
+        hare = next(next(hare));
+        if (tortoise == 1 || hare == 1) return true;
+        if (tortoise == hare) return false; // cycle detected
+    }
+}
+
+int main() {
+    ios::sync_with_stdio(false);
+    cin.tie(nullptr);
+
+    long long n;
+    if (!(cin >> n)) return 0;
+
+    if (n <= 0) {
+        cout << "NO\n";
+        return 0;
+    }
+
+    cout << (isHappy(n) ? "YES\n" : "NO\n");
+    return 0;
+}
+
+/*
+Sample Input:
+19
+Sample Output:
+YES
+*/