Add Digital Root (#2637)

Maths/DigitalRoot.java

@@ -0,0 +1,92 @@
+/** Author : Suraj Kumar Modi
+ * https://github.com/skmodi649
+ */
+
+
+/** You are given a number n. You need to find the digital root of n.
+ * DigitalRoot of a number is the recursive sum of its digits until we get a single digit number.
+ *
+ * Test Case 1:
+ * Input:
+ * n = 1
+ * Output:  1
+ * Explanation: Digital root of 1 is 1
+ *
+ * Test Case 2:
+ * Input:
+ * n = 99999
+ * Output: 9
+ * Explanation: Sum of digits of 99999 is 45
+ * which is not a single digit number, hence
+ * sum of digit of 45 is 9 which is a single
+ * digit number.
+ */
+
+
+
+/** Algorithm :
+ * Step 1 : Define a method digitalRoot(int n)
+ * Step 2 : Define another method single(int n)
+ * Step 3 : digitalRoot(int n) method takes output of single(int n) as input
+            if(single(int n) <= 9)
+               return single(n)
+            else
+               return digitalRoot(single(n))
+ * Step 4 : single(int n) calculates the sum of digits of number n recursively
+              if(n<=9)
+              return n;
+              else
+              return (n%10) + (n/10)
+ * Step 5 : In main method simply take n as input and then call digitalRoot(int n) function and print the result
+ */
+
+
+
+
+
+package Maths;
+
+import java.util.*;
+import java.io.*;
+import java.lang.*;
+
+class DigitalRoot
+{
+
+    public static int digitalRoot(int n)
+    {
+        if(single(n) <= 9)       // If n is already single digit than simply call single method and return the value
+            return single(n);
+        else
+            return digitalRoot(single(n));
+    }
+
+
+
+    // This function is used for finding the sum of digits of number
+    public static int single(int n)
+    {
+        if(n<=9)          // if n becomes less than 10 than return n
+            return n;
+        else
+            return (n % 10) + single(n / 10);                     // n % 10 for extracting digits one by one
+    }                                                             // n / 10 is the number obtainded after removing the digit one by one  
+                                                                  // Sum of digits is stored in the Stack memory and then finally returned
+
+
+
+    public static void main(String[] args)
+    {
+        Scanner sc = new Scanner(System.in);
+        System.out.println("Enter the number : ");
+        int n = sc.nextInt();                                     // Taking a number as input from the user
+        System.out.println("Digital Root : "+digitalRoot(n));     // Printing the value returned by digitalRoot() method
+    }
+}
+
+
+/**
+ * Time Complexity : O((Number of Digits)^2)
+ * Auxiliary Space Complexity : O(Number of Digits)
+ * Constraints :     1 <= n <= 10^7
+ */