LintCode 488: Happy Number

快乐数判定算法

最新推荐文章于 2020-04-07 01:22:26 发布

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本文介绍了一种用于判断一个正整数是否为快乐数的算法。快乐数是指通过反复将该数替换为其各位数字的平方和的过程，最终能够得到1的数字。文章提供了两种解法，一种使用哈希集合避免重复计算，另一种借鉴链表环的思路，通过快慢指针检测循环。

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
Example 1:

Input:19
Output:true
Explanation:

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

Example 2:

Input:5
Output:false
Explanation:

5 is not a happy number

25->29->85->89->145->42->20->4->16->37->58->89
89 appears again.

解法1：代码如下：
注意：平方不能写成n ^ 2，必须用pow()或n*n。

class Solution {
public:
    /**
     * @param n: An integer
     * @return: true if this is a happy number or false
     */
    bool isHappy(int n) {
        if (n == 0) return false;
        if (n == 1) return true;
        
        unordered_set<long long> sumSet;
        while (n > 1) {
            long long sum = getSum(n);
            if (sum == 1) return true;
            if (sumSet.find(sum) != sumSet.end()) return false;
            sumSet.insert(sum);
            n = sum;
        }
        
        return false;
    }

private:
    long long getSum(long long n) {
        long long sum = 0;
        while(n > 0) {
            int m = n % 10;
            sum += m * m; //m ^ 2 is wrong!
            n /= 10;
        }
        return sum;
    }
};

解法2：用链表环的做法

int getNext(int x) {
    int z = 0;
    while (x ) {
        z += (x % 10) * (x % 10);
        x / 10；
    }
    return z;
}

bool isHappy(int n) {
    int p = n, q = n; //注意这里q=n+1不对，因为n+1并不是n的下一个节点，getNext(n)才是。所以写成q=getNext(n)也对。
    do {
        P = getNext(p);
        q = getNext(getNext(q));
    } while (p != q && q != 1);
    return q == 1;
}