在C++中，将给定的四个数字组成的第n个数字的位数

We need to find the number of digits in the nth number made of given four digits 1, 2, 3, and 4.

The series with the above four digits is as follows

1, 2, 3, 4, 11, 12, 13, 14, 21, 22, 23, 24...

We need to find the number of digits of the nth number from the above series. If you carefully observe the pattern, you will find the following points.

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• There are 4 numbers with digits 1.

• There are 16 numbers with digits 2.

• The pattern continues as the powers of 4.

  

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  所谓数组，就是相同数据类型的元素按一定顺序排列的集合，就是把有限个类型相同的变量用一个名字命名，然后用编号区分他们的变量的集合，这个名字称为数组名，编号称为下标。组成数组的各个变量称为数组的分量，也称为数组的元素，有时也称为下标变量。数组是在程序设计中，为了处理方便， 把具有相同类型的若干变量按有序的形式组织起来的一种形式。这些按序排列的同类数据元素的集合称为数组。 数组应用&二维数组目录 1. 数组的简单应用2. 数组排序3. 数组查找4. 数组的使用思想5. 查表法6. 二维数组7. 数组综合

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Let's see an example

Input

7

Output

2

The 7th number in the series is 13 and the number of digits in it is 2.

Algorithm

• Initialise the number n.
• Initialise two variables one to store result and another one to store total sum of numbers in the series.
• Create a loop that increased the iterative variable by the powers of 4.
  • Add the current number to the sum variable.
  • If the total sum is greater than n, then break the loop.
  • Add 1 to the result as next set of number will have one digit extra than previous set of numbers.
• Return the result.

Implementation

Following is the implementation of the above algorithm in C++

#include <bits/stdc++.h>
using namespace std;
int getDigitsCount(int n) {
   int i, result = 1, sum = 0;
   for (i = 4; ; i *= 4) {
      sum += i;
      if (sum >= n) {
         break;
      }
      result += 1;
   }
   return result;
}
int main() {
   int n = 57;
   cout << getDigitsCount(n) << endl;
   return 0;
}

输出

如果你运行上述代码，你将得到以下结果。

3

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