Python | Find groups of strictly increasing numbers in a list

Given a list of integers, write a Python program to find groups of strictly increasing numbers. 

Examples:

Input : [1, 2, 3, 5, 6]
Output : [[1, 2, 3], [5, 6]]

Input : [8, 9, 10, 7, 8, 1, 2, 3]
Output : [[8, 9, 10], [7, 8], [1, 2, 3]]

Approach #1 : Pythonic naive This is a naive approach which uses an extra input list space. It makes use of a for loop and in every iteration, it checks if the next element increments from previous by 1. If yes, append it to the current sublist, otherwise, create another sublist. 

Python3

# Python3 program to Find groups
# of strictly increasing numbers within

def groupSequence(lst):
    res = [[lst[0]]]

    for i in range(1, len(lst)):
        if lst[i-1]+1 == lst[i]:
            res[-1].append(lst[i])

        else:
            res.append([lst[i]])
    return res

# Driver program
l = [8, 9, 10, 7, 8, 1, 2, 3]
print(groupSequence(l))

Output:

[[8, 9, 10], [7, 8], [1, 2, 3]]

Time complexity: O(n), where n is the length of the input list. 
Auxiliary space: O(n).

Approach #2 : Alternate naive This is an alternative to the above mentioned naive approach. This method is quite simple and straight. It constructs a start_bound list and an end_bound list, which contains the position of starting and ending sequence of increasing integers. Thus simply return the bounds using for loops. 

Python3

# Python3 program to Find groups
# of strictly increasing numbers within

def groupSequence(l):
    start_bound = [i for i in range(len(l)-1)
        if (l == 0 or l[i] != l[i-1]+1)
        and l[i + 1] == l[i]+1]

    end_bound = [i for i in range(1, len(l))
        if l[i] == l[i-1]+1 and
        (i == len(l)-1 or l[i + 1] != l[i]+1)]

    return [l[start_bound[i]:end_bound[i]+1]
    for i in range(len(start_bound))]

# Driver program
l = [8, 9, 10, 7, 8, 1, 2, 3]
print(list(groupSequence(l)))

Output:

[[8, 9, 10], [7, 8], [1, 2, 3]]

Time complexity: O(n), where n is the length of the input list.
Auxiliary space: O(n), as two additional lists are created with a maximum size of n.

Approach #3 : Using iterable and yield This approach uses another list ‘res’ and an iterable ‘it’. A variable ‘prev’ is used for keeping the record of previous integer and start is used for getting the starting position of the increasing sequence. Using a loop, in every iteration, we check if start element is a successor of prev or not. If yes, we append it to res, otherwise, we simply yield the res + [prev] as list element. 

Python3

# Python3 program to Find groups
# of strictly increasing numbers within

def groupSequence(x):
    it = iter(x)
    prev, res = next(it), []

    while prev is not None:
        start = next(it, None)

        if prev + 1 == start:
            res.append(prev)
        elif res:
            yield list(res + [prev])
            res = []
        prev = start

# Driver program
l = [8, 9, 10, 7, 8, 1, 2, 3]
print(list(groupSequence(l)))

Output:

[[8, 9, 10], [7, 8], [1, 2, 3]]

Time complexity: O(n), where n is the length of the input list.
Auxiliary space: O(n), as two additional lists are created with a maximum size of n.

Approach #4 : Using itertools Python itertools provides operations like cycle and groupby which are used in this method. First we form another list ‘temp_list‘ using cycle. Cycle generates an infinitely repeating series of values. Then we group the temp_list accordingly using groupby operation and finally yield the desired output. 

Python3

# Python3 program to Find groups
# of strictly increasing numbers within
from itertools import groupby, cycle

def groupSequence(l):
    temp_list = cycle(l)

    next(temp_list)
    groups = groupby(l, key = lambda j: j + 1 == next(temp_list))
    for k, v in groups:
        if k:
            yield tuple(v) + (next((next(groups)[1])), )


# Driver program
l = [8, 9, 10, 7, 8, 1, 2, 3]
print(list(groupSequence(l)))

Output:

[(8, 9, 10), (7, 8), (1, 2, 3)]

Approach #5: Using recursion

This approach uses recursion to find groups of strictly increasing numbers. The function find_groups takes two arguments – the input list and the index of the current element being processed. Initially, the index is set to 0. The function returns a list of lists, where each inner list represents a group of strictly increasing numbers.

Algorithm:

1. If the index is equal to the length of the input list, return an empty list.
2. Initialize the current element to the value at the current index.
3. Find the groups of strictly increasing numbers starting from the next index recursively.
4. If the next group starts with the current element + 1, add the current element to the start of the next group.
5. If the next group is empty or does not start with the current element + 1, create a new group starting with the current element.
6. Return the list of groups.

Python3

def find_groups(l, index=0):
    if index == len(l):
        return []

    current_element = l[index]
    groups = find_groups(l, index + 1)

    if len(groups) > 0 and groups[0][0] == current_element + 1:
        groups[0].insert(0, current_element)
    else:
        groups.insert(0, [current_element])

    return groups


# Driver program
l = [8, 9, 10, 7, 8, 1, 2, 3]
print(find_groups(l))

Output

[[8, 9, 10], [7, 8], [1, 2, 3]]

Time complexity: O(n^2), where n is the length of the input list. This is because in the worst case, we may have to check each element against every other element.
Auxiliary space: O(n), where n is the length of the input list. This is because we are creating a list of lists to store the groups.