find the happy number
Write an algorithm to determine if a number 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, and 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 numbers.
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
the value of this question: how to define it will loops endlessly? 100, 1000, 10000 or more times without end in 1? maybe all of them not right.
unless we find that there have a cycle, we make sure that there have a endless loop.
So we need to use two point, if the fast point = the slow point, then it approved that there have a cycle. this is a endless loop.
java solution as below:
public boolean isHappy(int n) {
if(n <= 0) return false;
int times = 100;
int slow = n;
int fast = n;
do{
slow = nextNumber(slow);
fast = nextNumber(fast);
fast = nextNumber(fast);
if(fast == 1) return true;
}while(slow != fast);
return false;
}
private int nextNumber(int n){
int result = 0;
while(n > 0){
result += Math.pow(n%10, 2);
n = n/10;
}
return result;
}
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