def get_points(wire):
    """
    Given a set of wire instructions, return a set of all of the points making
    up the wire along with their lengths.

    Parameters
    ----------
    wire (str)
      The list of instructions for building the wire

    Returns
    -------
    A map of all of the points comprising the wire when the instructions are
    followed. The keys for the map are the wire points, and the value is the
    length of the wire at that position.
    """
    x = 0
    y = 0
    length = 0
    result = {}

    DX = {'L': -1, 'R': 1, 'U': 0, 'D': 0}
    DY = {'L': -0, 'R': 0, 'U': -1, 'D': 1}

    for move in wire:
        direction = move[0]
        steps = int(move[1:])

        for _ in range(steps):
            x += DX[direction]
            y += DY[direction]
            length += 1

            if (x, y) not in result:
                result[(x, y)] = length

    return result