[Solved] What is the simplest way to access array (not vector) element from middle to outermost?

Question

An algorithm to list the elements from innermost to outermost is to pull off the last and first entries (pop and shift) in the array in alternation until no elements are left, then reverse the list of what you have pulled off. This works for odd and even-length arrays naturally.

For example,

1,2,3,4,5,6
1,2,3,4,5       6
2,3,4,5         6,1
2,3,4           6,1,5
3,4             6,1,5,2
3               6,1,5,2,4
                6,1,5,2,4,3
                3,4,2,5,1,6  // Reversed list from above

and

1,2,3,4,5
1,2,3,4         5
2,3,4           5,1
2,3             5,1,4
3               5,1,4,2
                5,1,4,2,3
                3,2,4,1,5  // Reversed list from above

You can use this above algorithm to create an index map array which you can use to access your main array in the order you requested. For example:

// Start with an array of indices 
// from 0..arr.length-1
0,1,2,3,4
0,1,2,3         4
1,2,3           4,0
1,2             4,0,3
2               4,0,3,1
                4,0,3,1,2
                2,1,3,0,4  // Reversed list from above

Then you have a mapping array

int[] arr = new int[]{1,2,3,4,5};
int[] map = new int[]{2,1,3,0,4};

which you can use to access your main array, for example

arr[map[0]]; // returns 3

Edit: Added Java implementation and demo.

public static int[] creatIndexMap(int length) {

    // Create a deque so elements can be removed from both ends
    Deque<Integer> tmp = new LinkedList<Integer>();
    for(int i = 0; i < length; i++) {
        tmp.add(i);
    }

    // In alternation remove the last and first entries of tmp
    // and add them in reverse order to the map array
    int[] map = new int[length];
    int index = length-1;
    while (!tmp.isEmpty()) {
        // Remove last element
        map[index--] = (int) tmp.removeLast();

        // Remove first element
        if(!tmp.isEmpty()) {
            map[index--] = (int) tmp.removeFirst();
        }
    }
    return map;
}

Demo: IDEOne

Accepted Answer