C++ Exercises: Count all the numbers with unique digits in a range

C++ Math: Exercise-29 with Solution

Write a C++ program that takes a number (n) and counts all numbers with distinct digits of length y within a specified range.

Range: 0 <= y < 10ⁿ

Example:
When n = 1, numbers with unique digits (10) between 0 and 9 are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
When n = 2, numbers with unique digits (91) between 0 and 100 are 0,1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 14, 15 …..99 except 11, 22, 33, 44, 55, 66, 77, 88 and 99.

Test Data:
1) -> 10
(2) -> 91

Sample Solution:

C++ Code :

#include <iostream>
#include <cmath>

using namespace std;

// Function to count the number of unique digit numbers given 'n' digits
int count_Unique_Digits_numbers(int n) {
    // If 'n' is 0, there's only one number (0 itself)
    if (n == 0) {
        return 1;
    }
    int ctr = 10; // Initialize the counter to 10, considering single-digit numbers
    for (int k = 2, fk = 9; k <= n; ++k) { 
        fk *= 10 - (k - 1); // Calculate the count of unique digits for 'k' digits and update 'fk'
        ctr += fk; // Add the count of unique digits for 'k' digits to the total counter
    }
    return ctr; // Return the total count of unique digit numbers for 'n' digits
}

int main() 
{
    int n = 1;
    // Display the number of unique digit numbers for 'n' digits
    cout << "\nn = " << n << ", Number of unique digits: " << count_Unique_Digits_numbers(n) << endl;   
    n = 2;  
    // Display the number of unique digit numbers for 'n' digits
    cout << "\nn = " << n << ", Number of unique digits: " << count_Unique_Digits_numbers(n) << endl;       
    return 0;    
}

Sample Output:

n = 1, Number of unique digits: 10

n = 2, Number of unique digits: 91

Flowchart:

C++ Code Editor:

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