Happy Number

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202.Happy Number

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:

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

Example 2:

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Input: n = 2
Output: false

哈希表：

时间复杂度：O(logn)

空间复杂度：O(logn)

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class Solution {
public:
    bool isHappy(int n) {
        unordered_set<int> hash;
        int sum = 0;
        while (1) {
            while (n != 0) {
                sum += (n % 10) * (n % 10);
                n /= 10;
            }
            if (sum == 1)return true;
            if (hash.count(sum))return false;
            else {
                hash.insert(sum);
                n = sum;
                sum = 0;
            }
        }
    }
};

快慢指针：

时间复杂度：O(logn)

空间复杂度：O(1)

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class Solution {
    public:
    int get_next(int value) {
        int sum = 0;
        while (value) {
            sum += (value % 10) * (value % 10);
            value /= 10;
        }
        return sum;
    }
    bool isHappy(int n) {
        int slow = n;
        int fast = get_next(n);
        while (fast != 1 && fast != slow) {
            slow = get_next(slow);
            fast = get_next(get_next(fast));
        }
        return fast == 1;
    }
};