**Problem Statement:**

Write an algorithm to determine if a number n is happy.

A happy number is a number defined by the following process:

Starting with any positive integer, replace the number by the sum of the squares of its digits.

Repeat the process until the number equals 1 (where it will stay), or it loops endlessly in a cycle which does not include 1.

Those numbers for which this process ends in 1 are happy.

Return true if n is a happy number, and false if not.

**Example 1:**

**Input:** n = 19

**Output:** true

**Explanation:**

12 + 92 = 82

82 + 22 = 68

62 + 82 = 100

12 + 02 + 02 = 1

**Example 2:**

**Input:** n = 2

**Output:** false

**Constraints:**

- 1 <= n <= 231 - 1

**Solution:**

**Algorithm:**

- Initialize slow and fast by n.
- Do following until slow and fast meet. a) Move slow by one iteration: compute square of digits of slow and add them. b) Move fast by two iteration: compute square of digits of fast and add them.
- If slow becomes 1 then return true.

**Code:**

```
public class Solution {
public boolean isHappy(int n){
int slow = n;
int fast = n;
do {
slow = squareSum(slow);
fast = squareSum(squareSum(fast));
} while (slow != fast);
return slow == 1;
}
public int squareSum(int n){
int sum = 0;
while (n > 0) {
int digit = n % 10;
sum += digit * digit;
n /= 10;
}
return sum;
}
}
```

**Time Complexity:**

O(logN). We need to compute the square of digits of n at most O(logN) times.

**Space Complexity:**

O(1)

## Top comments (0)