# Print all Increasing Subsequence of a List

Given a list or array of integer, the task is to print all such subsequences of this list such in which the elements are arranged in increasing order.

A *Subsequence* of the list is an ordered subset of that list’s element having same sequential ordering as the original list.

**Examples:**

Input:arr = {1, 2]}

Output:

2

1

1 2

Input:arr = {1, 3, 2}

Output:

2

3

1

1 2

1 3

**Approach: **

- Here, we will use recursion to find the desired output.
- The function will take two lists as an argument and the base condition will be until the list is empty.
- At each step of recursion, we will make the decision whether to include or exclude a particular element of the original list.
- For achieving this, we will maintain two list namely
**inp**and**out**, the input and output list of that step. - While including an element in output list, we will check whether that element is greater than the last element in output list, if yes then we will include that element.
- When the length of the input list becomes zero then the output list will contain the desired output. This is also a base condition too.

Below is the implementation of the above approach:

`# Python3 implementation ` `# To store all increasing subsequence of the given list ` `st ` `=` `[] ` ` ` `# Method to find increasing subsequence ` `def` `find(inp, out) : ` ` ` `if` `len` `(inp)` `=` `=` `0` `: ` ` ` `if` `len` `(out) !` `=` `0` `: ` ` ` `# storing result ` ` ` `st.append(out) ` ` ` `return` ` ` ` ` `# excluding 1st element ` ` ` `find(inp[` `1` `:], out[:]) ` ` ` ` ` `# including first element ` ` ` `# checking the condition ` ` ` `# for increasing subsequence ` ` ` `if` `len` `(out)` `=` `=` `0` `: ` ` ` `find(inp[` `1` `:], inp[:` `1` `]) ` ` ` `elif` `inp[` `0` `] > out[` `-` `1` `] : ` ` ` `out.append(inp[` `0` `]) ` ` ` `find(inp[` `1` `:], out[:]) ` ` ` `# The input list ` `ls1 ` `=` `[` `1` `, ` `3` `, ` `2` `] ` `ls2 ` `=` `[] ` ` ` `# Calling the function ` `find(ls1, ls2) ` ` ` `# Printing the lists ` `for` `i ` `in` `st: ` ` ` `print` `(` `*` `i) ` |

*chevron_right*

*filter_none*

**Output:**

2 3 1 1 2 1 3

**Time Complexity**: .

## Recommended Posts:

- Maximum Sum Increasing Subsequence | DP-14
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- Construction of Longest Increasing Subsequence (N log N)
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- Python program for Longest Increasing Subsequence
- Maximum product of an increasing subsequence of size 3
- Construction of Longest Increasing Subsequence(LIS) and printing LIS sequence
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- Number of Permutations such that no Three Terms forms Increasing Subsequence

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