Python - Adjacent Coordinates in N dimension

Sometimes, while working with Python Matrix, we can have a problem in which we need to extract all the adjacent coordinates of the given coordinate. This kind of problem can have application in many domains such as web development and school programming. Lets discuss certain way in which this task can be performed.

Input : test_tup = (1, 2, 3) Output : [[0, 1, 2], [0, 1, 3], [0, 1, 4], [0, 2, 2], [0, 2, 3], [0, 2, 4], [0, 3, 2], [0, 3, 3], [0, 3, 4], [1, 1, 2], [1, 1, 3], [1, 1, 4], [1, 2, 2], [1, 2, 3], [1, 2, 4], [1, 3, 2], [1, 3, 3], [1, 3, 4], [2, 1, 2], [2, 1, 3], [2, 1, 4], [2, 2, 2], [2, 2, 3], [2, 2, 4], [2, 3, 2], [2, 3, 3], [2, 3, 4]] Input : test_tup = (5, 6) Output : [[4, 5], [4, 6], [4, 7], [5, 5], [5, 6], [5, 7], [6, 5], [6, 6], [6, 7]]

Method : Using recursion + yield The combination of above functionalities can be used to solve this problem. In this, we extract the elements dynamically using yield for the coordinates around the query coordinate and using recursion, process for next column and row. 

# Python3 code to demonstrate working of 
# Adjacent Coordinates in N dimension
# Using recursion + yield

# helper_fnc
def adjac(ele, sub = []):
  if not ele:
     yield sub
  else:
     yield from [idx for j in range(ele[0] - 1, ele[0] + 2)
                for idx in adjac(ele[1:], sub + [j])]

# initializing tuple
test_tup = (3, 4)

# printing original tuple
print("The original tuple : " + str(test_tup))

# Initialize dictionary keys with Matrix
# Using deepcopy()
res = list(adjac(test_tup))

# printing result 
print("The adjacent Coordinates : " + str(res)) 

The original tuple : (3, 4)
The adjacent Coordinates : [[2, 3], [2, 4], [2, 5], [3, 3], [3, 4], [3, 5], [4, 3], [4, 4], [4, 5]]

Using itertools.product() function:

Approach:

We can generate all possible combinations of adjacent coordinates by using itertools.product() function. We need to generate a list of offsets for each dimension, which will be used to calculate adjacent coordinates. For example, for a 2-dimensional coordinate, we need to generate the following offsets: (-1,-1), (-1,0), (-1,1), (0,-1), (0,0), (0,1), (1,-1), (1,0), (1,1). Then, we can use itertools.product() to generate all possible combinations of these offsets and add them to the input coordinate to get all adjacent coordinates.

import itertools

def adjacent_coordinates(coord):
    offsets = [-1, 0, 1]
    combinations = itertools.product(offsets, repeat=len(coord))
    adj_coords = []
    for c in combinations:
        if all(o == 0 for o in c):
            continue
        adj_coord = tuple(coord[i] + c[i] for i in range(len(coord)))
        adj_coords.append(adj_coord)
    return adj_coords
test_tup = (1, 2, 3)
print("Input:", test_tup)
print("Output:", adjacent_coordinates(test_tup))

Input: (1, 2, 3)
Output: [(0, 1, 2), (0, 1, 3), (0, 1, 4), (0, 2, 2), (0, 2, 3), (0, 2, 4), (0, 3, 2), (0, 3, 3), (0, 3, 4), (1, 1, 2), (1, 1, 3), (1, 1, 4), (1, 2, 2), (1, 2, 4), (1, 3, 2), (1, 3, 3), (1, 3, 4), (2, 1, 2), (2, 1, 3), (2, 1, 4), (2, 2, 2), (2, 2, 3), (2, 2, 4), (2, 3, 2), (2, 3, 3), (2, 3, 4)]

Time Complexity: O(3^n), where n is the number of dimensions.
Auxiliary Space: O(3^n), because we need to generate all possible combinations of offsets.