Happy Number

【问题描述】

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

• 12 + 92 = 82
• 82 + 22 = 68
• 62 + 82 = 100
• 12 + 02 + 02 = 1

【解题思路】

#define CACHE 256
enum { h_unknown = 0, h_yes, h_no };
unsigned char buf[CACHE] = {0, h_yes, 0};

bool isHappy(int n) {
    int sum = 0, x, nn;
    if (n < CACHE) {
        if (buf[n]) return 2 - buf[n];
        buf[n] = h_no;
    }

    for (nn = n; nn; nn /= 10) x = nn % 10, sum += x * x;

    x = isHappy(sum);
    if (n < CACHE) buf[n] = 2 - x;
    return x;
}