Happy Number

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今天在LeetCode上刷题的时候遇到了一个有趣的问题,问题描述如下:

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

Happy Number

题目大意

题目大概意思是说将一个数按照 个、十、百、千位来分解(如果有的话),然后求他们的平方的和,得到结果后重复这个过程。最后结果为1,则该数字为happ number,则返回true,否则返回false

题目分析

第一眼看到题目其实是有点懵逼的,咋一看不知道循环结束的条件。其实循环结束的条件在题目中已经指出来——不为happly number的时候这个循环是重复的,所以说在这个循环的过程当中,推算出来的式子是有重复的部分,下面给出数字为6的时候式子的变换过程:

0^2 + 6^2 = 36
3^2 + 6^2 = 45
4^2 + 5^2 = 41
4^2 + 1^2 = 17
1^2 + 7^2 = 50
5^2 + 0^2 = 25
2^2 + 5^2 = 29
2^2 + 9^2 = 85
8^2 + 5^2 = 89    (循环起始部分
8^2 + 9^2 = 145
1^2 + 4^2 + 5^2 = 42
4^2 + 2^2 = 20
2^2 + 0^2 = 4
4^2 + 0^2 = 16
1^2 + 6^2 = 37
3^2 + 7^2 = 58    (一轮循环结束
5^2 + 8^2 = 89    (循环重新开始

可以看到当不为happy number的时候,式子在推算到一定程度,就会开始死循环,根据这个特点,这里我使用集合的特性来存储式子,通过判断式子是否重复来界定是否为happy number

AC代码

/**
 * @param {number} n
 * @return {boolean}
 */
var isHappy = function (n) {
    let result = String(n).split(''),counter = 1
    let collections = new Set()
    collections.add(result.join(''))
    while (counter === collections.size) {
        result = result.reduce((total, currentValue) => {
            return total + Math.pow(currentValue, 2)
        }, 0)
        counter++
        collections.add(String(result))
        result = String(result).split('')
        if(result[0] === '1' && result.length === 1){
            return true
        }
    }
    return false
}

其他解法

LeetCode上我发现我的思路还是具有普遍性,但是网站上我看到了两种比较有意思的解法,下面是具体的代码:

  • 解法1: Using fact all numbers in [2, 6] are not happy (and all not happy numbers end on a cycle that hits this interval):

(大意就是说利用非happy number在[2,6]这个区间的特性来判断是否为happy number

bool isHappy(int n) {
    while(n>6){
        int next = 0;
        while(n){next+=(n%10)*(n%10); n/=10;}
        n = next;
    }
    return n==1;
}
  • 解法2:I see the majority of those posts use hashset to record values. Actually, we can simply adapt the Floyd Cycle detection algorithm. I believe that many people have seen this in the Linked List Cycle detection problem. The following is my code:

(大意是说利用修改 Floyd Cycle 来判断是否为happy number

int digitSquareSum(int n) {
    int sum = 0, tmp;
    while (n) {
        tmp = n % 10;
        sum += tmp * tmp;
        n /= 10;
    }
    return sum;
}
bool isHappy(int n) {
    int slow, fast;
    slow = fast = n;
    do {
        slow = digitSquareSum(slow);
        fast = digitSquareSum(fast);
        fast = digitSquareSum(fast);
    } while(slow != fast);
    if (slow == 1) return 1;
    else return 0;
}

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