算法百题005：数字根（Digital Roots）

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于 2011-05-10 12:14:00 发布 · 2.9k 阅读

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#算法 #integer #string #input #iterator #output

本文介绍了如何计算数字根，即通过不断求和各位数字直到得到一位数的过程。提供了两种不同的实现方法，一种通过整数除法逐次剥离，另一种以字符串形式处理，尤其适用于大数计算。给出了具体代码实现，包括思路一的`calc_digi_root_v1`和两种思路二的`calc_digi_root_v2`与`calc_digi_root_v3`。

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Background

The digital root of a positive integer is found by summing the digits of the integer. If the resulting value is a single digit then that digit is the digital root. If the resulting value contains two or more digits, those digits are summed and the process is repeated. This is continued as long as necessary to obtain a single digit.

For example, consider the positive integer 24. Adding the 2 and the 4 yields a value of 6. Since 6 is a single digit, 6 is the digital root of 24. Now consider the positive integer 39. Adding the 3 and the 9 yields 12. Since 12 is not a single digit, the process must be repeated. Adding the 1 and the 2 yeilds 3, a single digit and also the digital root of 39.

Input

The input file will contain a list of positive integers, one per line. The end of the input will be indicated by an integer value of zero.

Output

For each integer in the input, outp