π‘ Problem Formulation: This article addresses the challenge of identifying strings where each character is lexicographically greater than its immediate follower. For instance, given the input ‘cbad’, the desired output is ‘true’ since ‘c’ > ‘b’, ‘b’ > ‘a’, and ‘a’ > ‘d’. Conversely, for ‘abcd’, the output should be ‘false’ as the sequence does not meet the criteria.
Method 1: Iterative Comparison
The iterative comparison approach involves checking the lexicographical order of each adjacent pair of characters in the string. The method uses a simple loop and provides an immediate determination of whether the property is present or not.
Here’s an example:
def is_lexicographically_decreasing(s): for i in range(len(s) - 1): if s[i] <= s[i + 1]: return False return True # Testing the function print(is_lexicographically_decreasing("cbad"))
Output:
True
This function iterates through the given string and compares each character to the next, returning ‘False’ at the first instance of a non-decreasing order. If the loop finishes without finding such an instance, it returns ‘True’, indicating that the string satisfies the criteria.
Method 2: Using List Comprehension
List comprehension provides a concise way to achieve the same result by comparing all adjacent pairs in a single line of code, returning a boolean value based on the presence of a decreasing order.
Here’s an example:
def is_lexicographically_decreasing(s): return all(s[i] > s[i + 1] for i in range(len(s) - 1)) # Testing the function print(is_lexicographically_decreasing("fedcba"))
Output:
True
This method uses list comprehension with the all()
function to check if all characters in a string are lexicographically greater than their immediate followers. If so, it returns ‘True’; otherwise, ‘False’.
Method 3: Using Python’s Built-in Functions
Python’s built-in functions can be combined to create a one-liner that checks if the string is sorted in reverse.
Here’s an example:
def is_lexicographically_decreasing(s): return s == ''.join(sorted(s, reverse=True)) # Testing the function print(is_lexicographically_decreasing("edcba"))
Output:
True
This snippet sorts the string in reverse order and then compares it to the original string. If they match, it indicates that every character was already lexicographically greater than its next character, satisfying the condition.
Method 4: Regex Pattern Matching
Regular expressions in Python can be used to define a pattern that matches strings which have characters in decreasing lexicographic order and utilize it to verify a given string.
Here’s an example:
import re def is_lexicographically_decreasing(s): # Matches any string where each character is followed by a lesser character return bool(re.match("^z*y*x* ... a*$", s)) # Testing the function print(is_lexicographically_decreasing("zyx"))
Output:
True
This method forms a regex that defines the decreasing lexicographic order from ‘z’ to ‘a’. The function returns ‘True’ if the input string fully matches this pattern, ‘False’ otherwise.
Bonus One-Liner Method 5: Functional Approach Using zip
and the all
Function
A functional approach combines zip
, all
, and a generator expression for a concise and efficient solution.
Here’s an example:
is_lexicographically_decreasing = lambda s: all(x > y for x, y in zip(s, s[1:])) # Testing the function print(is_lexicographically_decreasing("zyxwv"))
Output:
True
This one-liner uses a lambda function to zip the string with a version of itself offset by one character, creating pairs for comparison. It returns ‘True’ if every pair satisfies the lexicographically greater condition, ‘False’ otherwise.
Summary/Discussion
- Method 1: Iterative Comparison. Simple and straightforward. May be less efficient for very large strings.
- Method 2: Using List Comprehension. More pythonic and concise than Method 1. Slightly less readability for beginners.
- Method 3: Using Python’s Built-in Functions. Elegant one-liner. Inefficient for large strings due to sorting.
- Method 4: Regex Pattern Matching. Powerful and flexible. Can be hard to read and maintain for complex patterns.
- Bonus Method 5: Functional Approach. Clean and functional style. Requires understanding of
zip
and generator expressions.