1.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

2.分析

3.代码

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

bool isHappy(int n) {
    if (n <= 0) return false;
    
    int fast = n;
    int slow = n;
    for (;;) {
        fast = squares(squares(fast));
        slow = squares(slow);
        if (1 == fast || 1 == slow) return true;
        if (fast == slow) break;
    }
    return false;
}