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Count of m digit integers that are divisible by an integer n in C++
We are given two integers m and n. The goal is to count m digit numbers that are divisible by n.
If m=1, then numbers are 0,1,2,3,4,5,6,7,8,9 and n=3 then numbers divisible by 3=0,3,6,9 count=4.
Let’s understand with examples.
Input − m=2, n=9
Output − Count of m digit numbers divisible by n − 10
Explanation − between 10 and 99 numbers divisible by 9 are −
18, 27, 36, 45, 54, 63, 72, 81, 90, 99
Input m=3, n=300
Output − Count of m digit numbers divisible by n: 3
Explanation − between 100 and 999 numbers divisible by 300 are −
300, 600, 900
Approach used in the below program is as follows
We take integers m and n.
Calculate largest m-1 digit number as num1
Calculate largest m digit number as num2
Function findCount(int n, int L, int R) takes n and range ( between num1 and num2 ) as input and returns all numbers in that range which are divisible by n.
Take the initial count as 0.
Starting from i=L to i=R. If i%n==0, increment count.
Return count as result.
Example
#include<bits/stdc++.h>
using namespace std;
// Returns count of m digit numbers having n
// as divisor
int findCount(int n, int L, int R){
int count=0;
int i;
for(int i=L;i<=R;i++){
if(i%n==0)
{ count++; }
}
return count;
}
int main(){
int M = 2, N = 9;
int i;
int num1 = 0; //largest m-1 digit no.
for (i = 0; i < (M - 1); i++)
num1 = (num1 * 10) + 9;
int num2 = 0; //largest m digit no.
for (i = 0; i < M; i++)
num2 = (num2 * 10) + 9;
cout<<"Count of M digit no.s divisible by N:"<<findCount(N,num1+1,num2);
return 0;
}Output
If we run the above code it will generate the following output−
Count of M digit no.s divisible by N:11
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