Minimize splits to generate monotonous Substrings from given String

Given a string str, the task is to find the minimum numbers of substrings that the given string S can be split into, such that each substring is monotonously increasing or decreasing.

Examples:

Input: str = "abcdcba" 
Output: 2 
Explanation: 
The string can be split into a minimum of 2 monotonous substrings {"abcd"(increasing), "cba"(decreasing)}
Input: str = "aeccdhba" 
Output: 3 
Explanation: 
The generated substrings are {"ae", "ccdh", "ba"}

Approach: Follow the steps below to solve the problem:

• Initialize a variable ongoing = 'N' to keep track of order of current sequence.
• Iterate over the string and for each character, follow the steps below:
• If ongoing == 'N': 
  
  • If curr_character < prev_character then update ongoing with D(Non-Increasing).
  • Otherwise, if curr_character > prev_character, then update ongoing with I(Non-Decreasing).
  • Otherwise, update ongoing with N(neither Non-Increasing nor Non-Decreasing).
• Otherwise, if ongoing == 'I':
  • If curr_character > prev_character then update ongoing with I.
  • Otherwise, if curr_character < prev_character then update ongoing with N and increment answer.
  • Otherwise, update ongoing with I.
• else  do the following steps:
  • If curr_character < prev_character then update ongoing with D.
  • Otherwise, if curr_character > prev_character then update ongoing with N and increment answer.
  • Otherwise, update ongoing with D.
• Finally, print answer+1 is the required answer.

Below is the implementation of the above approach:

3

Time Complexity: O(N) 
Auxiliary Space: O(1)