Added happy_number.cpp

Famous-Coding-Interview-Problems/happy_number.cpp

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+/*
+ * Detect if a number is a happy number. A number is happy number if
+ * sequence of operations where number is replaced by sum of square
+ * of its digits leads eventually to 1. A number is not a happy number
+ * if we are in an infinite loop when above operations are performed.
+ * 
+ * Input: 49
+ * 4^2 + 9^2 = 16 + 81 = 97
+ * 9^2 + 7^2 = 81 + 49 = 130
+ * 1^2 + 3^2 + 0^2 = 1 + 9 + 0 = 10
+ * 1^2 + 0^2 = 1
+ * Thus 49 is a happy number.
+ * Approach:
+ * 
+ * We can treat this problem same as finding a cycle in a linked list.
+ * Imagine intermediate numbers as node and operation of square and sum
+ * as link.
+ * If we find the cycle, and the cycle is at 1, number is a happy number.
+ * Else, the number is not a happy number.
+ */
+
+#include <iostream>
+
+int square_sum(int num)
+{
+    int squared_sum = 0;
+    while (num > 0) {
+        squared_sum += (num % 10) * (num % 10);
+        num /= 10;
+    }
+    return squared_sum;
+}
+
+bool is_happy(int num)
+{
+    int slow = num;
+    int fast = num;
+
+    do {
+        slow = square_sum(slow);
+        fast = square_sum(square_sum(fast));
+    } while (slow != fast);
+    return slow == 1;
+}
+
+int main()
+{
+    int num = 45;
+    if (is_happy(num)) {
+        std::cout << num << " is a happy number." << std::endl;
+    } else {
+        std::cout << num << " is not a happy number." << std::endl;
+    }
+    num = 49;
+    if (is_happy(num)) {
+        std::cout << num << " is a happy number." << std::endl;
+    } else {
+        std::cout << num << " is not a happy number." << std::endl;
+    }
+    return 0;
+}