Question

Infinite Spiral of Numbers (due 17 Feb 2020)

HELLO, WE ARE USING PYTHON 3 TO COMPLETE THIS PROJECT!! PLEASE FOLLOW CODE SKELETON AS GIVEN AT THE END. THIS IS DUE 17TH FEB 2020, ANY AND ALL HELP WOULD BE GREATLY APPRECIATED, THANK YOU!

Consider the natural numbers laid out in a square spiral, with 1 occupying the center of the spiral. The central 11 x 11 subset of that spiral is shown in the table below.

111	112	113	114	115	116	117	118	119	120	121
110	73	74	75	76	77	78	79	80	81	82
109	72	43	44	45	46	47	48	49	50	83
108	71	42	21	22	23	24	25	26	51	84
107	70	41	20	7	8	9	10	27	52	85
106	69	40	19	6	1	2	11	28	53	86
105	68	39	18	5	4	3	12	29	54	87
104	67	38	17	16	15	14	13	30	55	88
103	66	37	36	35	34	33	32	31	56	89
102	65	64	63	62	61	60	59	58	57	90
101	100	99	98	97	96	95	94	93	92	91

This spiral has several interesting features. The southeast diagonal has several prime numbers (3, 13, 31, 57, and 91) along it. The southwest diagonal has a weaker concentration of prime numbers (5, 17, 37) along it.

To construct the spiral we start with 1 at the center, with 2 to the right, and 3 below it, 4 to the left, and so on. A part of the problem for this assignment is to figure out the rule to fill the spiral for an arbirary size. Once you have that rule you can complete the rest of the assignment.

You will prompt the user for the following information:

Enter dimension: 11
Enter number in spiral: 42

The first line indicates the dimension of the square spiral. This number should be an odd number. If it is not then choose the dimension to be the next higher odd number. The second number must be in the range 1 and the square of the dimension. If the second number is not in that range, print an error message Number not in Range and exit the program.

You will write the sub-grid surrounding the second number. The sub-grid is a 2-D list of size (2 x 2), (2, 3), (3, 2) or (3, 3). When you print the 2-D list each row must be on a line by itself and there must be a single white space separating each number. You do not have align the numbers.

All outputs shown are for the 11 x 11 grid. If the second number was 42, then this should be your output:

72 43 44
71 42 21
70 41 20

If the second number was 64, then this should be your output:

66 37 36
65 64 63
100 99 98

If the second number was 94, then this should be your output:

60 59 58
95 94 93

If the second number was 104, then this should be your output:

105 68
104 67
103 66

If the second number was 121, then this should be your output:

120 121
81 82

For this assignment you may work with a partner. Both of you must read the paper on Pair Programming and abide by the ground rules as stated in that paper. If you are working with a partner then both of you will submit the same code. In the header make sure that you have your name and your partner's name. If you are working alone then remove the fields that has the partner's name and EID.

The file that you will be turning in will be called Spiral.py. You will follow the standard coding conventions that we have discussed. Your file will have the following template:

#  File: Spiral.py

#  Description:

#  Student's Name:

#  Student's UT EID:

#  Partner's Name:

#  Partner's UT EID:

#  Course Name: CS 313E

#  Unique Number: 

#  Date Created:

#  Date Last Modified:


#  Input: dim is a positive odd integer
#  Output: function returns a 2-D list of integers arranged
#          in a spiral
def create_spiral (dim):

#  Input: grid a 2-D list containing a spiral of numbers
#         val is a number withing the range of numbers in
#         the grid
#  Output: sub-grid surrounding the parameter val in the grid
#          sub-grid could be 1-D or 2-D list
def sub_grid (grid, val):

def main:
  # prompt user to enter dimension of grid

  # prompt user to enter value in grid

  # print subgrid surrounding the value

if __name__ == "__main__":
  main()

Answer 1

#  File: Spiral.py

#  Description:

#  Student's Name:

#  Student's UT EID:

#  Partner's Name:

#  Partner's UT EID:

#  Course Name: CS 313E

#  Unique Number:

#  Date Created:

#  Date Last Modified:

#  Input: dim and coordinates of given number

#  Output: function returns a list of integers with top left coordinate and

#          number ofrows and columns of subgrid

def get_vals(dim,x,y):

  # down right corner

  if x==dim-1 and y==dim-1:

    return list([x-1,y-1,2,2])

  # down left corner

  if x==dim-1 and y==0 :

    return list([x-1,y,2,2])

  # top left corner

  if x==0 and y==0:

    return list([x,y,2,2])

  # top right corner

  if x==0 and y==dim-1:

    return list([x,y-1,2,2])

  # top edge

  if x==0:

    return list([x,y-1,2,3])

  #bottom edge

  if x==dim-1:

    return list([x-1,y-1,2,3])

  # left edge

  if y==0:

    return list([x-1,y,3,2])

  # right edge

  if y==dim-1:

    return list([x-1,y-1,3,2])

  # internal elements

  return list([x-1,y-1,3,3])

#  Input: dim is a positive odd integer

#  Output: function returns a 2-D list of integers arranged

#          in a spiral

def create_spiral(dim):

    if dim%2 == 1:

      dim = dim+1

    N, S, W, E = (0, -1), (0, 1), (-1, 0), (1, 0) # directions

    turn_right = {N: E, E: S, S: W, W: N} # old -> new direction

    x, y = dim // 2, dim // 2 # start near the center

    dx, dy = NORTH # initial direction

    mat = [[None] * dim for _ in range(dim)]

    count = 0

    while True:

        count += 1

        mat[y][x] = count # visit

        # try to turn right

        new_dx, new_dy = turn_right[dx,dy]

        new_x, new_y = x + new_dx, y + new_dy

        if (0 <= new_x < dim and 0 <= new_y < dim and

            mat[new_y][new_x] is None): # can turn right

            x, y = new_x, new_y

            dx, dy = new_dx, new_dy

        else: # try to move straight

            x, y = x + dx, y + dy

            if not (0 <= x < dim and 0 <= y < dim):

                return mat # nowhere to go

#  Input: grid a 2-D list containing a spiral of numbers

#         val is a number withing the range of numbers in

#         the grid

#  Output: sub-grid surrounding the parameter val in the grid

#          sub-grid could be 1-D or 2-D list

def sub_grid(grid,val):

  dim = len(grid)

  nx=0

  ny=0

  for i in range(dim):

    for j in range(dim):

      if grid[i][j] == val:

        nx = i

        ny = j

  vals = get_vals(dim,nx,ny)

  for i in range(vals[2]):

    for j in range(vals[3]):

      print(grid[i+vals[0]][j+vals[1]],end=" ")

    print("")

def main:

  # prompt user to enter dimension of grid

  dim = int(input("Enter dimensions of the grid : "))

  # prompt user to enter value in grid

  val = int(input("Enter value in grid : "))

  # print subgrid surrounding the value

  create_spiral(dim)

  sub_grid(grid,val)

if __name__ == "__main__":

  main()

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