# 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 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]]
```

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 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]]
```

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 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]]
```

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 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)]
```

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