# Python – Group Adjacent Coordinates

Sometimes, while working with Python lists, we can have a problem in which we need to perform the grouping of all the coordinates which occur adjacent on a matrix, i.e horizontally and vertically at distance 1. This is called Manhatten distance. This kind of problem can occur in competitive programming domain. Let’s discuss certain way in which this task can be performed.

Input : test_list = [(4, 4), (6, 4), (7, 8)]
Output : [[(7, 8)], [(6, 4)], [(4, 4)]]

Input : test_list = [(4, 4), (5, 4)]
Output : [[(5, 4), (4, 4)]]

Method : Using `product() + groupby()` + list comprehension
The combination of above methods can be used to solve this problem. In this, we perform the task of grouping of elements using groupby() and check for pairs using product(). The logic driving this solution is similar to union find algorithm.

 `# Python3 code to demonstrate working of  ` `# Group Adjacent Coordinates ` `# Using product() + groupby() + list comprehension ` `from` `itertools ``import` `groupby, product ` ` `  `def` `Manhattan(tup1, tup2): ` `    ``return` `abs``(tup1[``0``] ``-` `tup2[``0``]) ``+` `abs``(tup1[``1``] ``-` `tup2[``1``]) ` ` `  `# initializing list ` `test_list ``=` `[(``4``, ``4``), (``6``, ``4``), (``7``, ``8``), (``11``, ``11``),  ` `                     ``(``7``, ``7``), (``11``, ``12``), (``5``, ``4``)] ` ` `  `# printing original list ` `print``(``"The original list is : "` `+` `str``(test_list)) ` ` `  `# Group Adjacent Coordinates ` `# Using product() + groupby() + list comprehension ` `man_tups ``=` `[``sorted``(sub) ``for` `sub ``in` `product(test_list, repeat ``=` `2``) ` `                                         ``if` `Manhattan(``*``sub) ``=``=` `1``] ` ` `  `res_dict ``=` `{ele: {ele} ``for` `ele ``in` `test_list} ` `for` `tup1, tup2 ``in` `man_tups: ` `    ``res_dict[tup1] |``=` `res_dict[tup2] ` `    ``res_dict[tup2] ``=` `res_dict[tup1] ` ` `  `res ``=` `[[``*``next``(val)] ``for` `key, val ``in` `groupby( ` `        ``sorted``(res_dict.values(), key ``=` `id``), ``id``)] ` ` `  `# printing result  ` `print``(``"The grouped elemets : "` `+` `str``(res))  `

Output :

```The original list is : [(4, 4), (6, 4), (7, 8), (11, 11), (7, 7), (11, 12), (5, 4)]
The grouped elemets : [[(6, 4), (5, 4), (4, 4)], [(7, 8), (7, 7)], [(11, 12), (11, 11)]]
```

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