题目描述

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

Credits:
Special thanks to @mithmatt and @ts for adding this problem and creating all test cases.

分析

参考：Happy number 维基百科

1. 使用set

对每一个计算的结果进行计算，如果是1则是Happy Number；不是1且在set中出现过，则不是返回false；否则将结果加入set。

2. 利用性质，特殊数字“4”

在某一时刻，出现了4的Number肯定不Happy。

1000以内的Happy Number是：

1, 7, 10, 13, 19, 23, 28, 31, 32, 44, 49, 68, 70, 79, 82, 86, 91, 94, 97, 100, 103, 109, 129, 130, 133, 139, 167, 176, 188, 190, 192, 193, 203, 208, 219, 226, 230, 236, 239, 262, 263, 280, 291, 293, 301, 302, 310, 313, 319, 320, 326, 329, 331, 338, 356, 362, 365, 367, 368, 376, 379, 383, 386, 391, 392, 397, 404, 409, 440, 446, 464, 469, 478, 487, 490, 496, 536, 556, 563, 565, 566, 608, 617, 622, 623, 632, 635, 637, 638, 644, 649, 653, 655, 656, 665, 671, 673, 680, 683, 694, 700, 709, 716, 736, 739, 748, 761, 763, 784, 790, 793, 802, 806, 818, 820, 833, 836, 847, 860, 863, 874, 881, 888, 899, 901, 904, 907, 910, 912, 913, 921, 923, 931, 932, 937, 940, 946, 964, 970, 973, 989, 998, 1000

13和31，101和11是一样的，只是对每个数字的排列组合，那么不同序列的数字是：

1, 7, 13, 19, 23, 28, 44, 49, 68, 79, 129, 133, 139, 167, 188, 226, 236, 239, 338, 356, 367, 368, 379, 446, 469, 478, 556, 566, 888, 899

500以内的Happy Primes（质数）

7, 13, 19, 23, 31, 79, 97, 103, 109, 139, 167, 193, 239, 263, 293, 313, 331, 367, 379, 383, 397, 409, 487

代码

使用set的代码：

    public static boolean isHappy(int n) {

        if (n < 1) {
            return false;
        }

        if (n == 1) {
            return true;
        }

        Set<Integer> set = new HashSet<Integer>();
        set.add(n);

        while (true) {
            int s = 0;
            while (n > 0) {
                s += (n % 10) * (n % 10);
                n /= 10;
            }
            System.out.println(s);
            if (s == 1) {
                return true;
            } else if (set.contains(s)) {
                return false;
            }
            set.add(s);
            n = s;
        }
    }

使用特殊数字“4”的代码：

    public static boolean isHappy2(int n) {

        if (n < 1) {
            return false;
        }

        if (n == 1) {
            return true;
        } else if (n == 4) {
            return false;
        }

        int s = 0;
        while (n > 0) {
            s += (n % 10) * (n % 10);
            n /= 10;
        }

        return isHappy2(s);
    }