Truth table array

Question

I'm stuck on how to begin coding this. I want to be able to do the following. It's a classic flipping the coin problem If I flip twice the out comes are:
T T
T F
F T
F F
I want to be able to create an array with one result at a time. To better illustrate this, it should be something like (I'm using Java by the way):
boolean[] cases = new boolean[numberOfFlips]

the first time cases will have: T T.
After I'm done doing other calculations with this result I want to move on and now make cases: T F and proceed with running other calculations.
Can someone guide me in the right direction please? I would greatly appreciate it. An algorithm in any language is fine with me. Thank you for your time! (:

Answer 1

There are many ways to store binary data in Java and it is unclear, what you want to store. If you want to store ALL possible combinations of N flippings, then you need and array new boolean[2^N][N]

Remember that Java has another syntax for raising to power.

UPDATE

Below is the code for storing all combinations of N flips.

From it you will get an idea how to generate one combination too: from binary representation of combination ordinal number. See comments.

    // number of flips
    // limit it by 31
    int N = 3;

    // number of combinations
    // using bitshift to power 2
    int NN = 1<<N;

    // array to store combinations
    boolean flips[][] = new boolean[NN][N];

    // generating an array
    // enumerating combinations
    for(int nn=0; nn<NN; ++nn) {

        // enumerating flips
        for( int n=0; n<N; ++n) {

            // using the fact that binary nn number representation
            // is what we need
            // using bitwise functions to get appropriate bit
            // and converting it to boolean with ==
            flips[nn][N-n-1] = (((nn>>n) & 1)==1);

            // this is simpler bu reversed
            //flips[nn][n] = (((nn>>n) & 1)==1);

        }

    }

    // printing an array
    for(int nn=0; nn<NN; ++nn) {

        System.out.print("" + nn + ": ");

        for( int n=0; n<N; ++n) {
            System.out.print(flips[nn][n]?"T ":"F ");
        }
        System.out.println("");
    }

Answer 2

Notice the similarity between your desired output and binary representation of an integer. Here is an example:

for(int i = 0; i < 4; ++i) {
    boolean first = (i & 1) == 0;
    boolean second = (i & 2) == 0;
    System.out.println(first + "\t" + second);
}

Prints:

true    true
false   true
true    false
false   false

Answer 3

Here is a general solution that works for any number of flips (within reason):

public class Flips {

    static void generate(boolean[] res, int start) {
        if (start == res.length) {
            System.out.println(Arrays.toString(res));
        } else {
            generate(res, start + 1);
            res[start] = true;
            generate(res, start + 1);
            res[start] = false;
        }
    }

    static void generate(int n) {
        boolean res[] = new boolean[n];
        generate(res, 0);
    }

    public static void main(String args[]) {
        generate(4);
    }
}

It produces the combinations in a different order to that in your question, but it's trivial to modify to match your order if that's important.

Answer 4

Using recursion :

public static void main(String args[]) {
int size = 3;
generateTable(0, size, new int[size]);
}

private static void generateTable(int index, int size, int[] current) {
if(index == size) { 
    for(int i = 0; i < size; i++) {
        System.out.print(current[i] + " ");
    }
    System.out.println();
} else {
    for(int i = 0; i < 2; i++) {
        current[index] = i;
        generateTable(index + 1, size, current);
    }
}
}