[LintCode] 488 Happy Number 解题报告

Description
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


思路
什么数字是happy number？
    squareSum(squareSum(...(n))) == 1

什么数字不是happy number？
    squareSum(...)死循环。说明有环！！！

那么我们用快慢指针（Floyd Cycle detection algorithm）的思路去做。慢指针走一步，快指针走两步。如果两个结果相等，那么就跳出来判断一下是不是1。如果是1，当然就是happy number。如果不是1，就不是happy number。

Code

public class Solution {
    /**
     * @param n an integer
     * @return true if this is a happy number or false
     */
    public boolean isHappy(int n) {
        // Write your code here
        int slow = n;
        int fast = n;
        do {
            slow = squareSum(slow);
            fast = squareSum(fast);
            fast = squareSum(fast);
        } while (slow != fast);
        return slow == 1;
    }
    
    private int squareSum(int n) {
        int sum = 0;
        while (n != 0) {
            sum += (n % 10) * (n % 10);
            n /= 10;
        }
        return sum;
    }
}