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N digit numbers divisible by 5 formed from the M digits in C++
We have given a number N along with an array of M digits. Our job is to find the number of n digit numbers formed from the given M digits that are divisible by 5.
Let's see some examples to understand the problem inputs and outputs.
In −
N = 2
M = 3
arr = {5, 6, 3}Out −
2
There are 2 N digit numbers 35 and 65 possible that are divisible by 5. Let's see another example.
Input −
N = 1
M = 7
arr = {2, 3, 4, 5, 6, 7, 8}Output −
1
There is only 1 number with 1 digit in the given array that is divisible by 5. So, our task is to find the number of numbers that can be formed from the given number with N digits that are divisible by 5.
The number must end with the digits 0 or 5 to be divisible by 5. Let's see the algorithm
Algorithm
- Check for the 0 and 5 in the given array. 2. If there are both 0 and 5 then there are two ways to place a digit in the units place. Otherwise, there will be a single way to place a digit.
- Initialise the count to 2.
- Now, the remaining place can have m - 1, m - 2, m - 3, ... n ways to fill them respectively.
- Write a loop that iterates from 0 to n - 1.
- Decrement that size of the array.
- Multiply it with count.
- If there is a single digit 0 or 5 then there is only one way to place a digit in the units place.
- Initialise the count to 2.
- Now, the remaining place can have m - 1, m - 2, m - 3, ... n ways to fill them respectively.
- Write a loop that iterates from 0 to n - 1.
- Decrement that size of the array.
- Multiply it with count.
- If there are no digits 0 or 5 than we can form a number that can be divisible by 5. Return -1 in that case.
Implementation
Following is the implementation of the above algorithm in C++
#include <bits/stdc++.h>
using namespace std;
int numbers(int n, int m, int arr[]) {
bool isZeroPresent = false, isFivePresent = false;
int numbersCount = 0;
if (m < n) {
return -1;
}
for (int i = 0; i < m; i++) {
if (arr[i] == 0) {
isZeroPresent = true;
}
if (arr[i] == 5) {
isFivePresent = true;
}
}
if (isZeroPresent && isFivePresent) {
numbersCount = 2;
for (int i = 0; i < n - 1; i++) {
m--;
numbersCount = numbersCount * m;
}
} else if (isZeroPresent || isFivePresent) {
numbersCount = 1;
for (int i = 0; i < n - 1; i++) {
m--;
numbersCount = numbersCount * m;
}
} else {
return -1;
}
return numbersCount;
}
int main() {
int arr[] = {5, 6, 3};
cout << numbers(2, 3, arr) << endl;
return 0;
}Output
If you run the above code, then you will get the following result.
2
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