Write an algorithm to determine if a number is “happy”.
What is an happy number can be shown in the following example:
19 is a happy number 1^2 + 9^2 = 82 8^2 + 2^2 = 68 6^2 + 8^2 = 100 1^2 + 0^2 + 0^2 = 1
Analysis
The key to solve this problem is the stop condition for the loop.
Java Solution
public boolean isHappy(int n) { HashSet<Integer> set = new HashSet<Integer>(); while(!set.contains(n)){ set.add(n); n = getSum(n); if(n==1) return true; } return false; } public int getSum(int n){ int sum =0; while(n>0){ sum+=(n%10)*(n%10); n=n/10; } return sum; } |
We need a set because we know it will not be a happy number if it’ll return to a previous sum we’ve seen before. This basically means it will run in a continuous loop. A hash could also be used to store the sums previously seen for O(1) lookup time.
Why do we need set?