Number of N-Digit Stepping Numbers in C++

The stepping number is a number where the difference between the consecutive digits is 1. You are given a number n representing the number of digits. You need to count the total number of stepping numbers with n digits.

Let's see an example.

Input

2

Output

17

The lowest number of 2 digits is 10 and highest number of 2 digits is 99. There are 17 stepping numbers in between them.

Algorithm

• Initialise the number n.
• Initialise the count to 0.
• Find the lowest number of n digits i.e.., pow(10, n - 1).
• Find the highest number of n digits i.e.., pow(10, n) - 1.
• Write a loop that iterates from the lowest n digit number to highest n digit number.
  • Check whether the current number is stepping number or not.
  • Check the difference between consecutive pair of digits in the number.
  • If the result of the any difference is not 1, then return false else true.
  • Increment the count if the current number is a stepping number.
• Return the count.

Implementation

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

#include <bits/stdc++.h>
using namespace std;
bool isSteppingNumber(int n) {
   int previousDigit = -1;
   while (n) {
      int currentDigit = n % 10;
      if (previousDigit != -1 && abs(previousDigit - currentDigit) != 1) {
         return false;
      }
      previousDigit = currentDigit;
      n /= 10;
   }
   return true;
}
int getSteppingNumbersCount(int n) {
   int lowestNumber = pow(10, n - 1), highestNumber = pow(10, n) - 1;
   int count = 0;
   for (int i = lowestNumber; i <= highestNumber; i++) {
      if (isSteppingNumber(i)) {
         count += 1;
      }
   }
   return count;
}
int main() {
   int n = 3;
   cout << getSteppingNumbersCount(n) << endl;
   return 0;
}

Output

If you run the above code, then you will get the following result.

32