Algorithm for getting a special list of numbers

Question

I'm trying to find an algorithm in java for getting a special list of numbers. I tried writing my thoughts in code, but I feel my brain starting to melt... Maybe you can help me.

The algorithm should give me a list of all numbers:

• with a setable length

• with only numbers in a setable range

• with each number appearing once or less

So if I set the length to 3 and the range of numbers to 0-4 it should start like this:

012
013
014
021
023
024
031
032
034
041
042
043
102
103
...

I know this is not a question for something I don't know, but I already spent an eternity with this algorithm and my brain starts hurting. Maybe I'm just thinking the wrong way...

Answer 1

Base X Numeral Systems!

You can interpret generate combinations of {...}_x as count in base X

Your question, rephrased: Enumerate base X numbers, up to the highest such number with n digits

Naïve stab:

for(int i = 0; i < Math.pow(5, 3); i++) {
    System.out.println(Integer.toString(i, 5));
}

Now, a few observations:

• Your example begins with "012", I'll assume that you actually meant "000"
• The base in your example is "4 + 1 = 5"
• The base in the general case is "b - a + 1", where your range is {a..b}
• The symbols normally used to represent numbers in base X are the Arabic numerals 0..(X-1)
• The symbols that you use in your number system are the Arabic numerals, from a to b
• Numbers do not have leading zeros, string representations of numbers do.
• The highest number of length n in base X is Xⁿ - 1
• You can not customize String padding, so set width to n and replace ' ' with a

To generate your list of Strings:

1. Find the base of your number system
2. Count from 0 to Xⁿ-1
3. Generate a base X representation of each number
4. Add a to all symbols in the generated representation
5. Pad the string on the left with a

Code!

public static void main(String[] args) {
    for(String s : generate(3, 0, 4)) {
        System.out.println(s);
    }
}

private static List<String> generate(int n, int a, int b) {
    List<String> numbers = new ArrayList<>();
    int base = b - a + 1;                        // (1)
    for(int i = 0; i < Math.pow(base, n); i++) { // (2)
        String s = Integer.toString(i, base);    // (3)
        s = substituteSymbols(s, a);             // (4)
        s = String.format("%" + n + "s", s);     // (5)...
        s = replacePadding(a, s);                // ...(5)

        numbers.add(s);
    }
    return numbers;
}

private static String substituteSymbols(String s, int a) {
    char[] digits = s.toCharArray();
    StringBuilder sb = new StringBuilder();
    for(int c = 0; c < digits.length; c++) {
        int val = Character.getNumericValue(digits[c]) + a;
        sb.append(Character.forDigit(val, Character.MAX_RADIX));
    }
    return sb.toString();
}

private static String replacePadding(int a, String s) {
    return s.replace(' ', Character.forDigit(a, Character.MAX_RADIX));
}

Note:

• You could also stick to the naïve stab and discard Strings containing digits less than a
• A robust solution should handle invalid arguments
• A generic solution should not assume alphanumeric symbols
• This solution will create unnecessary garbage due to all new Strings
• If the base is higher than Character.MAX_RADIX, base 10 will be used

Answer 2

Your code should be like

public static void main (String[]args) {
    int totalNumbers=10, max=50,min =20;
    Random rand = new Random();
    Set<Integer> integers = new HashSet<Integer>();
    while(integers.size()<totalNumbers){
        integers.add(randomNumberGenerationInRange(rand, max, min));
    }
    for(Integer eachInteger: integers){
        System.out.println(String.format("%05d", eachInteger));
    }
}

private static int randomNumberGenerationInRange(Random rn,int maximum, int minimum) //This is where I'm trying to find LCM of 2 numbers
{
    int n = maximum - minimum + 1;
    int i = rn.nextInt() % n;
    return minimum + i;
}

Note String.format("%05d", eachInteger) is what adds the leading zeros to the number ... if you chafe 5 to 3 the the desired output as the question will be achieved. Set is use so that there are no duplicates.