notes/OJ notes/pages/Leetcode Happy-Number.md

Leetcode Happy-Number

2022-07-26 09:12

Algorithms:

#algorithm #Floyd_s_cycle_finding_algorithm

Difficulty:

#coding_problem #difficulty-easy

Additional tags:

#leetcode

Revisions:

N/A

Related topics:

tag:#Floyd_s_cycle_finding_algorithm 

Links:

• Link to problem

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Problem

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.

Examples

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

Thoughts

[!summary] This is a #Floyd_s_cycle_finding_algorithm

This works, because as the problem mentioned, this will result in a endless loop.

So, by using fast ans slow, we can determine whether there is a loop.

And, when fast hit 1, we know slow will eventually reach the answer, so we return early. (but in the cost of time of checking).

Solution

class Solution {
  int getDigitSqrt(int i) {
    int sum = 0;

    while (i) {
      sum += (i % 10) * (i % 10);
      i /= 10;
    }

    return sum;
  }

public:
  bool isHappy(int n) {
    // Floyd cycle finding algorighm.
    int slow, fast;
    slow = fast = n;

    do {
      slow = getDigitSqrt(slow);
      fast = getDigitSqrt(fast);
      fast = getDigitSqrt(fast);
      if (fast == 1) {
        return true;
      }
    } while (fast != slow);

    return false;
  }
};