Print all Increasing Subsequence of a List
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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

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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 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:

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# 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)

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Output:

2
3
1
1 2
1 3

Time Complexity: O(2^{n}).