Count Numbers with N digits which consists of even number of 0's in C++

We are given a number N as input. The goal is to find all N digit numbers that have an even number of 0’s as digits. The number also could have preceding zeros like in case of N=3 numbers included will be 001,002,003….010….so on.

Let us understand with examples.

Input − N=4

Output − Count of no. with N digits which consists of even number of 0's are − 7047

Explanation − All 4 digits numbers would be like −

Smallest will be 0000, then 0011,0012,0013,0014…..Highest will be 9900.

Input − N=5

Output − Count of no. with N digits which consists of even number of 0's are − 66383

Explanation − All 5 digit numbers would be like −

Smallest will be 00001, then 00002,00003,00004…..Highest will be 99900.

The approach used in the below program is as follows

We will first calculate the total N digit numbers that are T=10N-1. Then calculate all N digit numbers with odd 0’s as digits, that is O=10N-8N . The remaining numbers with Even 0’s in digits will be T-O/2.

• Take an integer N as input.

• Function count_even(int N) takes N and returns the count of N digit numbers with even 0’s.

• Total N digit numbers are total=pow(10,N)-1

• Total N digit numbers with odd 0’s in digit are odd=pow(10,N)-pow(8,N).

• Leftover even 0’s in digit are even=total-odd/2.

• Return even as a count of N digit numbers with even numbers of 0’s.

Example

 Live Demo

#include <bits/stdc++.h>
using namespace std;
int count_even(int N){
   int total = pow(10, N) - 1;
   int odd = pow(10, N) - pow(8, N);
   int even = total - odd / 2;
   return even;
}
int main(){
   int N = 3;
   cout<<"Count of Numbers with N digits which consists of even number of 0's are: "<<count_even(N);
   return 0;
}

Output

If we run the above code it will generate the following output- −

Count of Numbers with N digits which consists of even number of 0's are: 755

Sunidhi Bansal

Updated on 01-Dec-2020 12:02:25

• Related Questions & Answers
• Count Numbers with N digits which consists of odd number of 0's in C++
• Fetch Numbers with Even Number of Digits JavaScript
• Find Numbers with Even Number of Digits in Python
• Program to count number of stepping numbers of n digits in python
• Total number of non-decreasing numbers with n digits
• Count digits in given number N which divide N in C++
• Find the number of integers from 1 to n which contains digits 0’s and 1’s only in C++
• Count of N-digit Numbers having Sum of even and odd positioned digits divisible by given numbers - JavaScript
• Count rotations of N which are Odd and Even in C++
• Design a DFA machine accepting odd numbers of 0’s or even numbers of 1’s
• Count number of binary strings of length N having only 0’s and 1’s in C++
• C++ code to count number of lucky numbers with k digits
• Count subarrays with equal number of 1’s and 0’s in C++
• Design DFA for language over {0,1} accepting strings with odd number of 1’s and even number of 0’s
• Program to count total number of set bits of all numbers in range 0 to n in Python