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题目
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
1² + 9² = 82
8² + 2² = 68
6² + 8² = 100
1² + 0² + 0² = 1
翻译
写一个算法判断一个数是否为“happy”的。
一个happy number由下列程序进行判断：
初始为一个正整数，用这个正整数的每一位数字的平方和代替原数，
重复这个做法直到数字为1，或者进入一个不为1的无限循环。
最后能够达到1的数字就是happy number。
Tags
Hash Table Math
代码
Java Math：
public boolean isHappy(int n) {
if(n == 0) return false;
int sum = 0, tmp = 0;
while(n != 1){
sum = 0;
tmp = n;
while(tmp > 0){
sum += Math.pow(tmp % 10, 2);
tmp /= 10;
}
n = sum;
if(n < 10 && n != 1 && n != 7)
return false;
}
return true;
}
Java Hash Table:
public boolean isHappy(int n) {
if(n == 0) return false;
HashSet<Integer> hashSet = new HashSet<>();
int sum = 0, tmp = 0;;
while(n != 1 && n != 7){
sum = 0;
tmp = n;
while(tmp > 0){
sum += Math.pow(tmp % 10, 2);
tmp /= 10;
}
n = sum;
if(hashSet.contains(n)) return false;
hashSet.add(n);
}
return true;
}
讲解
很容易的我们可以推断出，如果一个数为个位数，则只有1和7才是happy number，而任何数字经过有限次
的转换一定会变成个位数，如果变成的个位数不为1和7，则不是happy number，反之则是。
