💡 Problem Formulation: The task is to determine if a given string can be split into parts that represent descending consecutive numbers. For instance, if the input is “321”, the desired output would be True because the numbers 3, 2, 1 are consecutive and in descending order. If the input were “32123”, the output would be False, as there is no way to split it to form a sequence of descending consecutive numbers.
Method 1: Iterative Check
This method involves iterating through the string while trying to match and remove descending consecutive numeric sequences from the start. It relies on the principle that the greatest number will be at the beginning of the string. The function tries to find the longest consecutive descending sequence starting with the highest number it can form with the first few digits.
Here’s an example:
def can_split_into_descending(string):
i, n = 0, len(string)
current = float('inf')
while i < n:
num = 0
while i < n and num = current:
return False
current = num - 1
return current < 0
print(can_split_into_descending("321"))
print(can_split_into_descending("32123"))
Output:
True False
In this code snippet, the can_split_into_descending function checks for a valid descending sequence. Starting with the largest possible number from the left of the string, it iterates through and decreases its expected consecutive number by one each time it finds a valid number. If at any point the function cannot find a smaller consecutive number, it returns False.
Method 2: Recursive Approach
In the recursive approach, the function calls itself with a smaller substring, trying to find a sequence of numbers that follows the consecutive descending rule. The base case of the recursion is when the string is empty, which means a valid sequence has been found.
Here’s an example:
def is_descending_consecutive(string, prev=None):
if not string:
return True
for i in range(1, len(string) + 1):
num = int(string[:i])
if prev is None or num == prev - 1:
if is_descending_consecutive(string[i:], num):
return True
return False
print(is_descending_consecutive("321"))
print(is_descending_consecutive("32123"))
Output:
True False
The is_descending_consecutive function recursively checks if a string can be partitioned into descending consecutive numbers. If the current number is exactly one less than the previous or if there’s no previous number (the start of the recursion), it proceeds down the string. This method exhaustively searches for valid sequences but may be slower for long strings due to its recursive nature.
Method 3: Dynamic Programming
Dynamic programming is used to keep track of descending sequences using a bottom-up approach. The method first fills a boolean array where each position indicates whether the ending part of the string can form descending consecutive values starting with a particular number. After filling the array, the answer lies in the first element.
Here’s an example:
def can_partition_desc(string):
n = len(string)
# +1 because we want to include the empty substring at the end
dp = [False] * (n + 1)
dp[n] = True
for i in range(n - 1, -1, -1):
num = 0
for j in range(i, n):
num = num * 10 + int(string[j])
if (j + 1 == n or dp[j + 1]) and (j + 1 == n or num - 1 == int(string[j + 1])):
dp[i] = True
break
return dp[0]
print(can_partition_desc("321"))
print(can_partition_desc("32123"))
Output:
True False
This snippet implements a dynamic programming solution that builds up a solution from the smallest substrings. The dp array tracks whether a valid sequence can start at different points in the string. It is filled in reverse, starting with the knowledge that an empty string (an empty substring of the original string) surely has descending consecutive values.
Method 4: Using Built-in Functions
This method finds a more functional and Pythonic way to achieve the same goal by utilizing Python’s built-in functions and a generator expression. It uses itertools.groupby() combined with enumeration to filter potential split points and checks for descending order.
Here’s an example:
from itertools import groupby
def can_split(string):
groups = [(k, sum(1 for _ in g)) for k, g in groupby(enumerate(string), lambda x: x[0]-int(x[1]))]
return all(x[0] - 1 == y[0] for x, y in zip(groups, groups[1:]))
print(can_split("321"))
print(can_split("32123"))
Output:
True False
The function can_split leverages itertools.groupby() to group digits that are consecutive descending numbers and then checks each group to see if it follows a sequence with the next group. It may be less readable for those not familiar with itertools but takes advantage of Python’s powerful standard library.
Bonus One-Liner Method 5: Using List Comprehensions
This method uses a succinct one-liner list comprehension to try all possible split points in a string and checks if they form descending consecutive numbers.
Here’s an example:
can_split_desc = lambda s: any(all(int(s[i:i+l]) - 1 == int(s[i+l:i+2*l]) for i in range(0, len(s) - l, l)) for l in range(1, len(s)))
print(can_split_desc("321"))
print(can_split_desc("32123"))
Output:
True False
This compact one-liner employs a nested list comprehension where l represents the length of numbers being tried and the outer comprehension checks these lengths against every starting split point in the string. This method is terse but may lack clarity and efficiency for complex cases.
Summary/Discussion
- Method 1: Iterative Check. Efficient for most cases. May have difficulty with very large strings due to iteration.
- Method 2: Recursive Approach. Exhaustive and easy to understand. Potentially slow for long strings and can reach recursion limit.
- Method 3: Dynamic Programming. Highly efficient especially for large strings with reuse of computations. More complex to understand and implement.
- Method 4: Using Built-in Functions. Pythonic and concise. May be less clear to those unfamiliar with Python’s itertools library.
- Bonus One-Liner Method 5: Compact and uses functional programming principles. May sacrifice readability and performance for brevity.