In this shot, we will solve an interview problem from Leetcode called Happy Number.
We will learn how to determine whether or not a number is happy. A happy number is a number that converges to a sum of $1$ after getting replaced by the sum of the square of its digits.
Let’s understand the Happy Number problem with the help of examples:
Suppose the number is $44$. We have the sum of squares of digits as below:
$4^2$ + $4^2$ = 16 + 16 = 32
$3^2$ + $2^2$ = 9 + 4 = 13
$3^2$ + $1^2$ = 9 + 1 = 10
$1^2$ + $0^2$ = 1 + 0 = 1
Finally, the sum of squares of the digits converges to 1, so 44 is a happy number. The program’s output for this input would be true
.
Now, suppose the number is 16, here we have the sum of squares of digits as below:
$1^2$ + $6^2$ = 1 + 36 = 37
$3^2$ + $7^2$ = 9 + 49 = 58
$5^2$ + $9^2$ = 25 + 49 = 74
$7^2$ + $4^2$ = 49 + 16 = 65
$6^2$ + $5^2$ = 36 + 25 = 61
$6^2$ + $1^2$ = 36 + 1 = 37
Here the sum of the digits’ squares is not converging to $37$, so it would keep repeating with the pattern (37, 58, 74, 65, 61, 37, 58, 74, … so on). Therefore, $16$ is not a happy number, and the program’s output for this input would be false
.
We first find the sum of digits using a while
loop and the modulo %
operator. Then, we will store the values within a java.util.Set
to check whether or not the sum value has been encountered previously.
The code below provides a solution to the Happy Number problem:
import java.util.*; class Solution { public static boolean isHappy(int n) { Set<Integer> set = new HashSet<>(); while (n!=1) { if(set.contains(n)) return false; set.add(n); n = sumOfDigitSquares(n); } return true; } private static int sumOfDigitSquares(int n) { int sum = 0; while (n != 0) { int digit = n % 10; sum += digit * digit; n /= 10; } return sum; } public static void main(String[] args) { System.out.printf("Is 44 happy -> %b", isHappy(44)); System.out.printf("\nIs 16 happy -> %b", isHappy(16)); } }
Line 1 imports java.util.*
(using a wildcard as we want to import both Set
and HashSet
).
Line 3 declares a Solution
class.
Line 4 defines the isHappy(int n)
method.
Line 5 declares a set
using java.util.HashSet
to store integers.
Line 7 repeats a while
loop until the value of n
equals 1
.
Line 8 checks if the value of n
is already present in Set
. If so, it returns false
denoting the number n
is not a happy number.
Line 10 adds n
to the set
.
Line 11 calculates the sum of the square of digits using the sumOfDigitSquares()
method and updates the value of n
with the returned value.
Line 12 exits the while
loop when n == 1
.
Line 14 returns true
, denoting the number as a happy number.
Line 17 declares the sumOfDigitSquares(int n)
method.
Line 18 initializes sum
to 0
.
Line 19 repeats a while
loop until n
is not equal to 0
.
Line 20 gets the current digit as n % 10
.
Line 21 updates the sum
as the current value plus square of digit
(i.e. digit * digit
).
Line 22 updates n
to n / 10
(integer division).
Lines 23 and 25 exit the while
loop if n
equals 0
and return sum
.
Line 28 declares the main()
method to verify our solution.
Lines 29 and 30 call the isHappy()
with different inputs and print the output.
The time complexity of this problem would be $O(d)$, where $d$ is the number of digits in the number input. The max value of $d$ can be $10$, as in Java, the range of integers is up to $2,147,483,647$ (which has $10$ digits). More precisely, the algorithm runs in constant time $O(1)$.
As the memory required for this program does not depend on the input value, the space complexity of this problem would be constant, i.e., $O(1)$.
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