### 题目

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: 19 is a happy number

1^2 + 9^2 = 82
8^2 + 2^2 = 68
6^2 + 8^2 = 100
1^2 + 0^2 + 0^2 = 1


### 用取余%切割数字

#### 代码

public class Solution {
public boolean isHappy(int n) {
Set<Integer> memo = new HashSet<>();
while (n != 1) {
int copy = n;
int sum = 0;
while (copy != 0) {
int remainder = copy % 10;
copy /= 10;
sum += remainder * remainder;
}
if (!memo.add(sum)) { return false; } // find circle
n = sum;
}
return true;
}
}


#### 结果 ### walker,runner追逐法，空间复杂度 $O(1)$

#### 代码

public class Solution {
public boolean isHappy(int n) {
int slow = n, fast = n;
do {
slow = squareSum(slow);
fast = squareSum(fast);
fast = squareSum(fast);
if (fast == 1) { return true; }
} while (slow != fast);
return false; // find circle, but fast != 1
}
public int squareSum(int n) {
int sum = 0;
while (n != 0) {
int remainder = n % 10;
sum += remainder * remainder;
n /= 10;
}
return sum;
}
}