Calculating the number of digits in a series of numbers, experiencing a timeout issue (What is the page count of a book? from codewars)

Question

Calculating the number of digits in a series of numbers, experiencing a timeout issue (What is the page count of a book? from codewars)

Solving the Digits in a Book Problem

Find the number of pages in a book based on its summary.

For example, if the input summary is 25, then the output should be n=17. This means that the numbers 1 to 17 have a total of 25 digits: 1234567891011121314151617.

It is guaranteed that all inputs will be valid.

Here is my current solution:

function amountOfPages(summary){

    let n=1;   
    let arrKc=[1]
        
    while((arrKc.join('').toString().length)!=summary){
        arrKc.push( n.toString())
        n++
    }
        
    return n
  
}

All tests are passing successfully, but I am encountering a timeout error when running the function.

https://i.sstatic.net/b1qKf.png

javascript arrays string algorithm while-loop

Answer 1

Answer №1

My code snippet:

I have identified a recurring pattern for finding the count of digits, which follows this formula:

9 + 9 * 10^1 * 2 + 9 * 10^2 * 3 + ...+ 9 * 10^(n-1) * n

This solution is based on the above pattern:

function initialLoad() {
      document.getElementById("outcome").innerHTML = "Answer: "+  amountOfPages(25);
}

function amountOfPages(summary) {
        var n = summary;
        var totalNumbersSoFar = 0;
        var pagesSoFar = 0;
        var ninthDigit = "9";
        while (parseInt(ninthDigit) < (n / ninthDigit.length)) {
                var numbersInRange = Math.pow(10, ninthDigit.length - 1) * 9;
                pagesSoFar += numbersInRange * ninthDigit.length;
                n -= numbersInRange;
                totalNumbersSoFar += numbersInRange;
                ninthDigit += "9";
        };
        return ((summary - pagesSoFar) / ninthDigit.length) + totalNumbersSoFar;
    };

 <HTML>
        <HEAD>
        </HEAD>
        <BODY id="outcome" onload="initialLoad()">
            <h1>

        </h1>
        </BODY>
    </HTML>

Answer 2

My code snippet:

I have identified a recurring pattern for finding the count of digits, which follows this formula:

9 + 9 * 10^1 * 2 + 9 * 10^2 * 3 + ...+ 9 * 10^(n-1) * n

This solution is based on the above pattern:

function initialLoad() {
      document.getElementById("outcome").innerHTML = "Answer: "+  amountOfPages(25);
}

function amountOfPages(summary) {
        var n = summary;
        var totalNumbersSoFar = 0;
        var pagesSoFar = 0;
        var ninthDigit = "9";
        while (parseInt(ninthDigit) < (n / ninthDigit.length)) {
                var numbersInRange = Math.pow(10, ninthDigit.length - 1) * 9;
                pagesSoFar += numbersInRange * ninthDigit.length;
                n -= numbersInRange;
                totalNumbersSoFar += numbersInRange;
                ninthDigit += "9";
        };
        return ((summary - pagesSoFar) / ninthDigit.length) + totalNumbersSoFar;
    };

 <HTML>
        <HEAD>
        </HEAD>
        <BODY id="outcome" onload="initialLoad()">
            <h1>

        </h1>
        </BODY>
    </HTML>

Calculating the number of digits in a series of numbers, experiencing a timeout issue (What is the page count of a book? from codewars)

Answer №1

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