Print out all permutations of an Array

Question

I am working on a program, and I have a function that swaps the positions in an Array of length that is input by a user. However, I am trying to figure out how to print out this function call N! times, which would list all the permutations in the function.

My code for the permutation function is:

static void nextPerm(int[] A){
    for( int i = (n-1); i > 0; i-- ){
        if( A[i] < A[i+1] ){
            A[i] = pivot;
            continue;
        }
        if( A[i] >= A[i+1] ){
            reverseArray(A);
            return;
        }
    }

    for( int i = n; i > 0; i--){
        if( A[i] > pivot ){
            A[i] = successor;
            continue;
        }
    }

    Swap(pivot, successor);

    int[] B = new int[pivot+1];
    reverseArray(B);

    return;
}

Should I write a loop in function main, that will print this out n! times?

Answer 1

Creating (or printing) the permutations of an array is much easier done as a combination of recursively and iteratively than purely iteratively. There are surely iterative ways to do it, but it is particularly simple with a combination. Specifically, note that there are by definition N! permutations of a length N array - N choices for the first slot, N-1 choices for the 2nd, etc etc. So, we can break an algorithm down into two steps for each index i in the array.

1. Select an element in the sub-array arr[i....end] to be the ith element of the array. Swap that element with the element currently at arr[i].
2. Recursively permute arr[i+1...end].

We note that this will run in O(N!), as on the 1st call N sub calls will be made, each of which will make N-1 sub calls, etc etc. Moreover, every element will end up being in every position, and so long as only swaps are made no element will ever be duplicated.

public static void permute(int[] arr){
    permuteHelper(arr, 0);
}

private static void permuteHelper(int[] arr, int index){
    if(index >= arr.length - 1){ //If we are at the last element - nothing left to permute
        //System.out.println(Arrays.toString(arr));
        //Print the array
        System.out.print("[");
        for(int i = 0; i < arr.length - 1; i++){
            System.out.print(arr[i] + ", ");
        }
        if(arr.length > 0) 
            System.out.print(arr[arr.length - 1]);
        System.out.println("]");
        return;
    }

    for(int i = index; i < arr.length; i++){ //For each index in the sub array arr[index...end]

        //Swap the elements at indices index and i
        int t = arr[index];
        arr[index] = arr[i];
        arr[i] = t;

        //Recurse on the sub array arr[index+1...end]
        permuteHelper(arr, index+1);

        //Swap the elements back
        t = arr[index];
        arr[index] = arr[i];
        arr[i] = t;
    }
}

Sample input, output:

public static void main(String[] args) {
    permute(new int[]{1,2,3,4});
}

[1, 2, 3, 4]
[1, 2, 4, 3]
[1, 3, 2, 4]
[1, 3, 4, 2]
[1, 4, 3, 2]
[1, 4, 2, 3]
[2, 1, 3, 4]
[2, 1, 4, 3]
[2, 3, 1, 4]
[2, 3, 4, 1]
[2, 4, 3, 1]
[2, 4, 1, 3]
[3, 2, 1, 4]
[3, 2, 4, 1]
[3, 1, 2, 4]
[3, 1, 4, 2]
[3, 4, 1, 2]
[3, 4, 2, 1]
[4, 2, 3, 1]
[4, 2, 1, 3]
[4, 3, 2, 1]
[4, 3, 1, 2]
[4, 1, 3, 2]
[4, 1, 2, 3]