JavaScript - Count all the numbers with unique digits in a range

JavaScript Math: Exercise-109 with Solution

Unique Digit Numbers Count

Write a JavaScript program that accepts a number (n) and counts all numbers with unique digits of length p within a specified range.

Range: 0 <= p < 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:

JavaScript Code:

/**
 * Function to calculate the count of numbers with unique digits in a given range.
 * @param {number} n - The upper limit of the range (from 0 to n).
 * @returns {number} - The count of numbers with unique digits in the specified range.
 */
function test(n) {
    // If n is 0, there's one number with a unique digit: 0 itself
    if(n===0){
        return 1;
    }       
    // Initialize result to 10, as numbers from 0 to 9 all have unique digits
    var result = 10;
    // Initialize temp to 9, representing the number of choices for the first digit (1 to 9)
    var temp = 9;    
    // Loop through the range starting from 1 (since we've already considered the case when n=0)
    for(var i=1; i<n; i++){
        // Update temp by multiplying with the number of remaining choices
        temp *= 10 - i;
        // Add temp to result, representing the count of numbers with unique digits at each iteration
        result += temp;
    }
    // Return the final count of numbers with unique digits in the range
    return result;
}

// Test cases
n = 1;
console.log("Range: " + n + " to 10");
console.log("Numbers with unique digits in the said range: " + test(n));
n = 2;
console.log("Range: " + n + " to 10");
console.log("Numbers with unique digits in the said range: " + test(n));

Output:

Range: 1 to 10
Numbers with unique digits in the said range: 10
Range: 2 to 10
Numbers with unique digits in the said range: 91

Flowchart:

Live Demo:

See the Pen javascript-math-exercise-109 by w3resource (@w3resource) on CodePen.

For more Practice: Solve these Related Problems:

• Write a JavaScript function that counts the total number of numbers with unique digits for a given length using combinatorial reasoning.
• Write a JavaScript function that generates all numbers with non-repeating digits for a specified digit length and returns their count.
• Write a JavaScript function that recursively computes the number of unique digit numbers without enumerating them explicitly.
• Write a JavaScript function that validates the input digit length and returns the count based on formula derivation.

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