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# Happy Number

Write an algorithm to determine if a number 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, and 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 numbers.

**Example:** 

```
Input: 19
Output: true
Explanation: 
1^2 + 9^2 = 82
8^2 + 2^2 = 68
6^2 + 8^2 = 100
1^2 + 0^2 + 0^2 = 1
```

## Analysis

Tricky在于如何跳出infinite loop。可以用HashSet的add()，如果当前已经遍历过这个数，那么就要跳出循环避免进入死循环。

> Adds the specified element to this set if it is not already present. More formally, adds the specified element e to this set if this set contains no element e2 such that (e==null ? e2==null : e.equals(e2)). If this set already contains the element, the call leaves the set unchanged and returns false.

[https://docs.oracle.com/javase/7/docs/api/java/util/HashSet.html#add(E\\](https://docs.oracle.com/javase/7/docs/api/java/util/HashSet.html#add%28E\)\\)

## Solution

```java
class Solution {
    public boolean isHappy(int n) {
        long t = n;
        Set<Long> seen = new HashSet<Long>();
        while (seen.add(t)) {
            t = process(t);
            if (t == 1) {
                return true;
            }
        }
        return false;
    }

    private long process(long n) {
        long res = 0;
        while (n > 0) {
            long rem = n % 10;
            res += rem * rem;
            n /= 10;
        }
        return res;
    }
}
```

## Reference

<https://leetcode.com/problems/happy-number/discuss/56913/Beat-90-Fast-Easy-Understand-Java-Solution-with-Brief-Explanation>


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