Happy Number

Description

Write an algorithm to determine if a number n 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.
• 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.

Return true if n is a happy number, and false if not.

Example 1:

Input: n = 19 Output: true Explanation: 12 + 92 = 82 82 + 22 = 68 62 + 82 = 100 12 + 02 + 02 = 1

Example 2:

Input: n = 2 Output: false

Constraints:

• 1 <= n <= 231 - 1

Code

Time Complexity: $O(N)$, Space Complexity: $O(1)$

可以使用 Floyd’s Cycle Finding Algorithm。即 Linked List Cycle 中用到的演算法。

int digitSquareSum(int n) {
    int sum = 0, tmp;
    while (n) {
        tmp = n % 10;
        sum += tmp * tmp;
        n /= 10;
    }
    return sum;
}
 
bool isHappy(int n) {
    int slow, fast;
    slow = fast = n;
    do {
        slow = digitSquareSum(slow);
        fast = digitSquareSum(fast);
        fast = digitSquareSum(fast);
    } while(slow != fast);
    if (slow == 1) return 1;
    else return 0;
}

用 hashmap 的解法，概念是一樣的。

class Solution {
public:
    bool isHappy(int n) {
        unordered_set<int> s;
        bool loop = false;
        s.insert(n);
        while(n != 1 && !loop) {
            int new_n = 0;
            int temp = n;
            while(temp >= 1) {
                int d = temp % 10;
                temp = temp / 10;
                new_n += pow(d, 2);
            }
            if(s.count(new_n)) loop = true;
            s.insert(new_n);
            n = new_n;
        }
        return loop ? false : true;
    }
};

Source

• Happy Number - LeetCode