Sequence of Differences in Python

Carvia Tech | September 15, 2019 | 2 min read | 26 views | Python Coding Problems


Given a set of four numbers representing a “circular array” we can test to see if the absolute values of the differences between each adjoining element will eventually coalesce into a single value.

For example, consider the set of four numbers: {1, 10, 8, 3}.

We can repeatedly take the absolute values of the differences of the adjoining numbers. Since this is a circular array, calculate the value of the last element in the new array as the last number minus the first number.

For example, starting with {1, 10, 8, 3}

  • The first iteration will produce {9, 2, 5, 2} calculated as |1 - 10|, |10 - 8|, |8 - 3|, |3 - 1|.

  • The second iteration will produce {7, 3, 3, 7} calculated as |9 - 2|, |2 - 5|, |5 - 2|, |2 - 9|.

  • The third iteration will produce {4, 0, 4, 0} calculated as |7 - 3|, |3 – 3|, |3 - 7|, |7 – 7|.

  • The fourth iteration will produce {4, 4, 4, 4} calculated as |4 - 0|, |0 - 4|, |4 - 0|, |0 - 4|.

Test Data
Input Output

1 0 0 0

3 iterations were required for 1 0 0 0

0 1 4 11

5 iterations were required for 0 1 4 11

0 0 0 2

3 iterations were required for 0 0 0 2

34 12 19 28

4 iterations were required for 34 12 19 28

100 200 321 345

4 iterations were required for 100 200 321 345

def seq_diff(list_of_nums):
    orig_list = list_of_nums
    j = 0
    while len(set(list_of_nums)) != 1:
        lis = []
        for i in range(len(list_of_nums)):
            try:
                lis.append(abs(list_of_nums[i]-list_of_nums[i+1]))
            except:
                lis.append(abs(list_of_nums[i]-list_of_nums[0]))
        list_of_nums = lis
        j = j+1
    return orig_list, j
Input
print(seq_diff([9934, 8543, 812, 1001]))
Output
([9934, 8543, 812, 1001], 3)

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