Way to get number of digits in an int?

Question

Is there a neater way for getting the number of digits in an int than this method?

int numDigits = String.valueOf(1000).length();

Answer 1

Can I try? ;)

based on Dirk's solution

final int digits = number==0?1:(1 + (int)Math.floor(Math.log10(Math.abs(number))));

Answer 2

We can achieve this using a recursive loop

    public static int digitCount(int numberInput, int i) {
        while (numberInput > 0) {
        i++;
        numberInput = numberInput / 10;
        digitCount(numberInput, i);
        }
        return i;
    }

    public static void printString() {
        int numberInput = 1234567;
        int digitCount = digitCount(numberInput, 0);

        System.out.println("Count of digit in ["+numberInput+"] is ["+digitCount+"]");
    }

Answer 3

Try converting the int to a string and then get the length of the string. That should get the length of the int.

public static int intLength(int num){
    String n = Integer.toString(num);
    int newNum = n.length();
    return newNum;
}

Answer 4

The fastest approach: divide and conquer.

Assuming your range is 0 to MAX_INT, then you have 1 to 10 digits. You can approach this interval using divide and conquer, with up to 4 comparisons per each input. First, you divide [1..10] into [1..5] and [6..10] with one comparison, and then each length 5 interval you divide using one comparison into one length 3 and one length 2 interval. The length 2 interval requires one more comparison (total 3 comparisons), the length 3 interval can be divided into length 1 interval (solution) and a length 2 interval. So, you need 3 or 4 comparisons.

No divisions, no floating point operations, no expensive logarithms, only integer comparisons.

Code (long but fast):

if (n < 100000){
        // 5 or less
        if (n < 100){
            // 1 or 2
            if (n < 10)
                return 1;
            else
                return 2;
        }else{
            // 3 or 4 or 5
            if (n < 1000)
                return 3;
            else{
                // 4 or 5
                if (n < 10000)
                    return 4;
                else
                    return 5;
            }
        }
    } else {
        // 6 or more
        if (n < 10000000) {
            // 6 or 7
            if (n < 1000000)
                return 6;
            else
                return 7;
        } else {
            // 8 to 10
            if (n < 100000000)
                return 8;
            else {
                // 9 or 10
                if (n < 1000000000)
                    return 9;
                else
                    return 10;
            }
        }
    }

Benchmark (after JVM warm-up) - see code below to see how the benchmark was run:

1. baseline method (with String.length): 2145ms
2. log10 method: 711ms = 3.02 times as fast as baseline
3. repeated divide: 2797ms = 0.77 times as fast as baseline
4. divide-and-conquer: 74ms = 28.99
   times as fast as baseline

Full code:

public static void main(String[] args)
throws Exception
{

    // validate methods:
    for (int i = 0; i < 1000; i++)
        if (method1(i) != method2(i))
            System.out.println(i);
    for (int i = 0; i < 1000; i++)
        if (method1(i) != method3(i))
            System.out.println(i + " " + method1(i) + " " + method3(i));
    for (int i = 333; i < 2000000000; i += 1000)
        if (method1(i) != method3(i))
            System.out.println(i + " " + method1(i) + " " + method3(i));
    for (int i = 0; i < 1000; i++)
        if (method1(i) != method4(i))
            System.out.println(i + " " + method1(i) + " " + method4(i));
    for (int i = 333; i < 2000000000; i += 1000)
        if (method1(i) != method4(i))
            System.out.println(i + " " + method1(i) + " " + method4(i));

    // work-up the JVM - make sure everything will be run in hot-spot mode
    allMethod1();
    allMethod2();
    allMethod3();
    allMethod4();

    // run benchmark
    Chronometer c;

    c = new Chronometer(true);
    allMethod1();
    c.stop();
    long baseline = c.getValue();
    System.out.println(c);

    c = new Chronometer(true);
    allMethod2();
    c.stop();
    System.out.println(c + " = " + StringTools.formatDouble((double)baseline / c.getValue() , "0.00") + " times as fast as baseline");

    c = new Chronometer(true);
    allMethod3();
    c.stop();
    System.out.println(c + " = " + StringTools.formatDouble((double)baseline / c.getValue() , "0.00") + " times as fast as baseline");

    c = new Chronometer(true);
    allMethod4();
    c.stop();
    System.out.println(c + " = " + StringTools.formatDouble((double)baseline / c.getValue() , "0.00") + " times as fast as baseline");
}


private static int method1(int n)
{
    return Integer.toString(n).length();
}
private static int method2(int n)
{
    if (n == 0)
        return 1;
    return (int)(Math.log10(n) + 1);
}
private static int method3(int n)
{
    if (n == 0)
        return 1;
    int l;
    for (l = 0 ; n > 0 ;++l)
        n /= 10;
    return l;
}
private static int method4(int n)
{
    if (n < 100000)
    {
        // 5 or less
        if (n < 100)
        {
            // 1 or 2
            if (n < 10)
                return 1;
            else
                return 2;
        }
        else
        {
            // 3 or 4 or 5
            if (n < 1000)
                return 3;
            else
            {
                // 4 or 5
                if (n < 10000)
                    return 4;
                else
                    return 5;
            }
        }
    }
    else
    {
        // 6 or more
        if (n < 10000000)
        {
            // 6 or 7
            if (n < 1000000)
                return 6;
            else
                return 7;
        }
        else
        {
            // 8 to 10
            if (n < 100000000)
                return 8;
            else
            {
                // 9 or 10
                if (n < 1000000000)
                    return 9;
                else
                    return 10;
            }
        }
    }
}


private static int allMethod1()
{
    int x = 0;
    for (int i = 0; i < 1000; i++)
        x = method1(i);
    for (int i = 1000; i < 100000; i += 10)
        x = method1(i);
    for (int i = 100000; i < 1000000; i += 100)
        x = method1(i);
    for (int i = 1000000; i < 2000000000; i += 200)
        x = method1(i);

    return x;
}
private static int allMethod2()
{
    int x = 0;
    for (int i = 0; i < 1000; i++)
        x = method2(i);
    for (int i = 1000; i < 100000; i += 10)
        x = method2(i);
    for (int i = 100000; i < 1000000; i += 100)
        x = method2(i);
    for (int i = 1000000; i < 2000000000; i += 200)
        x = method2(i);

    return x;
}
private static int allMethod3()
{
    int x = 0;
    for (int i = 0; i < 1000; i++)
        x = method3(i);
    for (int i = 1000; i < 100000; i += 10)
        x = method3(i);
    for (int i = 100000; i < 1000000; i += 100)
        x = method3(i);
    for (int i = 1000000; i < 2000000000; i += 200)
        x = method3(i);

    return x;
}
private static int allMethod4()
{
    int x = 0;
    for (int i = 0; i < 1000; i++)
        x = method4(i);
    for (int i = 1000; i < 100000; i += 10)
        x = method4(i);
    for (int i = 100000; i < 1000000; i += 100)
        x = method4(i);
    for (int i = 1000000; i < 2000000000; i += 200)
        x = method4(i);

    return x;
}

Again, benchmark:

1. baseline method (with String.length): 2145ms
2. log10 method: 711ms = 3.02 times as fast as baseline
3. repeated divide: 2797ms = 0.77 times as fast as baseline
4. divide-and-conquer: 74ms = 28.99
   times as fast as baseline

Edit: After I wrote the benchmark, I took a sneak peak into Integer.toString from Java 6, and I found that it uses:

final static int [] sizeTable = { 9, 99, 999, 9999, 99999, 999999, 9999999,
                                  99999999, 999999999, Integer.MAX_VALUE };

// Requires positive x
static int stringSize(int x) {
    for (int i=0; ; i++)
        if (x <= sizeTable[i])
            return i+1;
}

I benchmarked it against my divide-and-conquer solution:

4. divide-and-conquer: 104ms
5. Java 6 solution - iterate and compare: 406ms

Mine is about 4x as fast as the Java 6 solution.

Answer 5

Marian's solution adapted for long type numbers (up to 9,223,372,036,854,775,807), in case someone want's to Copy&Paste it. In the program I wrote this for numbers up to 10000 were much more probable, so I made a specific branch for them. Anyway it won't make a significative difference.

public static int numberOfDigits (long n) {     
    // Guessing 4 digit numbers will be more probable.
    // They are set in the first branch.
    if (n < 10000L) { // from 1 to 4
        if (n < 100L) { // 1 or 2
            if (n < 10L) {
                return 1;
            } else {
                return 2;
            }
        } else { // 3 or 4
            if (n < 1000L) {
                return 3;
            } else {
                return 4;
            }
        }           
    } else  { // from 5 a 20 (albeit longs can't have more than 18 or 19)
        if (n < 1000000000000L) { // from 5 to 12
            if (n < 100000000L) { // from 5 to 8
                if (n < 1000000L) { // 5 or 6
                    if (n < 100000L) {
                        return 5;
                    } else {
                        return 6;
                    }
                } else { // 7 u 8
                    if (n < 10000000L) {
                        return 7;
                    } else {
                        return 8;
                    }
                }
            } else { // from 9 to 12
                if (n < 10000000000L) { // 9 or 10
                    if (n < 1000000000L) {
                        return 9;
                    } else {
                        return 10;
                    }
                } else { // 11 or 12
                    if (n < 100000000000L) {
                        return 11;
                    } else {
                        return 12;
                    }
                }
            }
        } else { // from 13 to ... (18 or 20)
            if (n < 10000000000000000L) { // from 13 to 16
                if (n < 100000000000000L) { // 13 or 14
                    if (n < 10000000000000L) { 
                        return 13;
                    } else {
                        return 14;
                    }
                } else { // 15 or 16
                    if (n < 1000000000000000L) {
                        return 15;
                    } else {
                        return 16;
                    }
                }
            } else { // from 17 to ...¿20?
                if (n < 1000000000000000000L) { // 17 or 18
                    if (n < 100000000000000000L) {
                        return 17;
                    } else {
                        return 18;
                    }
                } else { // 19? Can it be?
                    // 10000000000000000000L is'nt a valid long.
                    return 19;
                }
            }
        }
    }
}

Answer 6

One wants to do this mostly because he/she wants to "present" it, which mostly mean it finally needs to be "toString-ed" (or transformed in another way) explicitly or implicitly anyway; before it can be presented (printed for example).

If that is the case then just try to make the necessary "toString" explicit and count the bits.