202 Happy number

Question

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

Idea

int型的数据有10位数字，最大的值即为，平方和为，所以个一个810大小的数组即可表示所以可能被计算出来的平方和。

给一个n值，先计算这个n的各位数的平方和，如果这个和以前出现过（m==n也算出现过），那么这个数就不是happy number。

原因：If a number is happy, then all members of its sequence are happy; if a number is unhappy, all members of the sequence are unhappy.
如果一个数是happy number，那么他的各位数字的顺序无论怎么颠倒，新的数仍然是happy number。同理，如果不是，无论怎么颠倒，也不是happy number。如果算出来的和以前算过，那么说明这一步是从那个和算过来的，现在从这个和再算的话，就又回去了，就是一个无限循环了。

Code

bool isHappy(int n) {
    bool hash[810] = {false};
    int m = n;
    while (1) {
        int sum = 0;
        while (m) {
            sum += (m % 10) * (m % 10);
            m /= 10;
        }
        if (sum == 1) return true;
        else if (hash[sum] || m == n) return false;
        hash[sum] = true;
        m = sum;
    }
    return false;
}