1408. Problem - Number in Base Representation
Base Representation

Convert number into different base representation.

1. Requirement

Convert an integer number into positive base 2 representation and negative base 2 representation.

2. Solution

2.1 Positive Base 2

Example:

Input  : n = 13, base = 2
Output : 1101
1*(8) + 1*(4) + 0*(2) + 1*(1)  = 13

Implementation.

public String base2(int n) {
    StringBuilder res = new StringBuilder();
    while (n != 0) {
        res.append(n & 1);
        n = n >> 1;
    }
    return res.length() > 0 ? res.reverse().toString() : "0";
}

2.2 Negative Base 2

Example:

Input  : n = 13, base = -2
Output : 11101
1*(16) + 1*(-8) + 1*(4) + 0*(-2) + 1*(1)  = 13

Implementation.

public String baseNeg2(int n) {
    StringBuilder res = new StringBuilder();
    while (n != 0) {
        res.append(n & 1);
        n = -(n >> 1);
    }
    return res.length() > 0 ? res.reverse().toString() : "0";
}

Test class.

public class Base2Test {
 
    @Test
    public void testBase2() {
        System.out.println("testBase2");
        Base2 instance = new Base2();
        assertEquals("101", instance.base2(5));
        assertEquals("1101", instance.base2(13));
        assertEquals("100000", instance.base2(32));
    }
 
    @Test
    public void testBaseNeg2() {
        System.out.println("testBaseNeg2");
        Base2 instance = new Base2();
        assertEquals("101", instance.baseNeg2(5));
        assertEquals("11101", instance.baseNeg2(13));
        assertEquals("1100000", instance.baseNeg2(32));
    }
}

2.3 Generic Solution

Generic solution for any base.

public class GenericBase {
    // Given a decimal number n and an integer k, Convert decimal number n to base-k.
    public String base(int n, int k) {
        if (n == 0) {
            return "0";
        }
 
        String ans = "";
        while (n != 0) {
            int r = n % k;
            n /= k;
 
            // if remainder is negative, add abs(base) to it and add 1 to n
            if (r < 0) {
                r += (-k);
                n += 1;
            }
 
            // convert remainder to string add into the result
            if (r <= 9) {
                ans = r + ans;
            } else {
                ans = (char)(r - 10 + 'A') + ans;
            }
        }
 
        return ans;
    }
}

Test class.

public class GenericBaseTest {
 
    @Test
    public void testGenericBase() {
        System.out.println("testGenericBase");
        GenericBase instance = new GenericBase();
        assertEquals("101", instance.base(5, 2));
        assertEquals("1101", instance.base(13, 2));
        assertEquals("100000", instance.base(32, 2));
 
        assertEquals("101", instance.base(5, -2));
        assertEquals("11101", instance.base(13, -2));
        assertEquals("1100000", instance.base(32, -2));
 
        assertEquals("21", instance.base(17, 8));
        assertEquals("36", instance.base(30, 8));
 
        assertEquals("11", instance.base(17, 16));
        assertEquals("1E", instance.base(30, 16));
    }
}

3. Source Files

4. References