Smith Number

Author: sathishmepco

InterviewPrograms/src/com/java/numbers/SmithNumber.java

@@ -0,0 +1,91 @@
+package com.java.numbers;
+
+import java.util.ArrayList;
+import java.util.Scanner;
+
+/*
+ * 	Smith Number
+ * 
+ * A Smith number is a composite number 
+ * the sum of whose digits is the sum of 
+ * the digits of its prime factors (excluding 1)
+ * 
+ * Say given number is 22
+ * prime factors of 22 are
+ * 		2, 11
+ * 
+ *  sum of digits of 22 = 4
+ *  sum of digits of prime factors 
+ *  2 * 11 = 2 + 1 + 1 = 4
+ *  
+ *  given number is 27
+ *  prime factors = 3, 3, 3
+ *  sum of digits of 27 = 2+7 = 9
+ *  sum of digits of prime factors
+ *  					3+3+3 = 9
+ *  
+ *  Other examples are
+ *  4, 22, 27, 58, 85, 94, 121, 166, 202, 265
+ */
+public class SmithNumber {
+	public static void main(String[] args) {
+		Scanner scanner = new Scanner(System.in);
+		System.out.println("Enter any positive integer :: ");
+		int num = Integer.parseInt(scanner.nextLine().trim());
+		
+		if(sumOfDigits(num) == getPrimeFactorsDigitSum(num))
+			System.out.println("Given number : "+num+" is a Smith Number");
+		else
+			System.out.println("Given number : "+num+" is NOT a Smith Number");
+		scanner.close();
+	}
+	
+	private static int getPrimeFactorsDigitSum(int n){
+		int sum =0;
+		ArrayList<Integer> primeFactors = getPrimeFactors(n);
+		for(int v : primeFactors)
+			sum += sumOfDigits(v);
+		return sum;
+	}
+	
+	private static ArrayList<Integer> getPrimeFactors(int n){
+		ArrayList<Integer> factors = new ArrayList<>();
+		int len = (int) Math.sqrt(n);
+		for(int i=2; i<= len;i++){
+			while( n%i == 0 ){
+				factors.add(i);
+				n = n/i;
+			}
+		}
+		if( n > 2 )
+			factors.add(n);
+		System.out.println("Prime Factors are : "+factors);
+		return factors;
+	}
+	
+	private static int sumOfDigits(int n){
+		int sum = 0;
+		while( n > 0 ){
+			int digit = n % 10;
+			sum += digit;
+			n = n / 10;
+		}
+		return sum;
+	}
+}
+/*
+	OUTPUT
+	
+	Enter any positive integer :: 22
+	Prime Factors are : [2, 11]
+	Given number : 22 is a Smith Number
+	
+	Enter any positive integer :: 85
+	Prime Factors are : [5, 17]
+	Given number : 85 is a Smith Number
+
+	Enter any positive integer :: 150
+	Prime Factors are : [2, 3, 5, 5]
+	Given number : 150 is NOT a Smith Number
+
+*/