Problem Statement:
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
Solution:
Algorithm:
- Initialize slow and fast by n.
- Do following until slow and fast meet. a) Move slow by one iteration: compute square of digits of slow and add them. b) Move fast by two iteration: compute square of digits of fast and add them.
- If slow becomes 1 then return true.
Code:
public class Solution {
public boolean isHappy(int n){
int slow = n;
int fast = n;
do {
slow = squareSum(slow);
fast = squareSum(squareSum(fast));
} while (slow != fast);
return slow == 1;
}
public int squareSum(int n){
int sum = 0;
while (n > 0) {
int digit = n % 10;
sum += digit * digit;
n /= 10;
}
return sum;
}
}
Time Complexity:
O(logN). We need to compute the square of digits of n at most O(logN) times.
Space Complexity:
O(1)
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