Splitting A String Into Descending Consecutive Values Leetcode 1849 [Python]

View on GitHub ➹
class Solution:
    def splitString(self, s: str) -> bool:

        def dfs(index, prev):
            if index == len(s):
                return True

            for j in range(index, len(s)):
                val = int(s[index:j+1])
                if val + 1 == prev and dfs(j+1, val):
                    return True
            return False

        for i in range(len(s) - 1):
            val = int(s[:i + 1])
            if dfs(i + 1, val):
                return True

        return False

This code snippet defines the splitString function, which takes an input string s.

Inside the function, we have a nested dfs function, which performs the depth-first search.

Let’s analyze the key components of the code:

• The outer loop iterates through the string s, starting from the first character and extending to the second-to-last character.

This loop determines different initial values that we can try.

• Inside the loop, we extract the initial value, val, by converting a substring of s from the beginning up to the current index i.
• We call the dfs function with the current index i + 1 and the initial value val.

This is where the recursive exploration of possible splits occurs.

• In the dfs function, we check if we’ve reached the end of the string (index == len(s)).

If so, we return True, indicating that we successfully split the string into descending consecutive values.

• Within the dfs function, we iterate through the remaining characters of the string (s) and check if we can form descending consecutive values.

If we find a valid split, we return True.

This code efficiently explores various splitting options and returns True if any valid split is found, as per the problem requirements.

Time and Space Complexity

Now, let’s analyze the time and space complexity of our solution:

• Time Complexity: The time complexity of our approach depends on the size of the search space.

In the worst case, we may explore all possible splits of the string, which results in a time complexity of O(2^n), where n is the length of the string.

However, due to backtracking and pruning, the actual time complexity is much better in practice.

We can think of it as an optimization of the brute force approach.

• Space Complexity: The space complexity is primarily determined by the depth of the recursion, which is limited by the length of the string s.

Therefore, the space complexity is O(n), where n is the length of the string.

Reasoning Behind Our Approach

Our approach to solving the problem is based on the idea of backtracking.

We systematically explore different splits of the string, starting with various initial values, and check if the subsequent values form descending consecutive integers.

Here’s the reasoning behind our approach:

1. Initial Value Exploration: We start by considering different initial values by iterating through the input string s.

These initial values represent the first integer in a potential split.

Since there are no restrictions on the first value, we can explore various options.

2. Depth-First Search (DFS): Once we have an initial value, we use a depth-first search (DFS) approach to explore the possible splits of the remaining string.

The DFS function recursively tries different substrings, checking if they form descending consecutive integers with a difference of 1. This exploration continues until we reach the end of the string or find a valid split.

3. Pruning and Optimization: To optimize our solution, we implement pruning.

If, during the DFS, we encounter a substring that does not meet the descending consecutive values condition, we immediately backtrack, avoiding unnecessary exploration.

This pruning helps improve the efficiency of our solution.

4. Returning Results: If the DFS function finds a valid split, it returns True, indicating that the string can be split as required.

If no valid split is found for a particular initial value, we continue iterating through different initial values.

If none of them lead

to a valid split, we return False, indicating that it’s not possible to split the string as described in the problem.

Overall, our approach explores the search space efficiently, considering different starting values and pruning unproductive paths, ultimately providing a solution to the problem.

Related Interview Questions By Company:

• Walls And Gates LeetCode
• Reorganize String LeetCode
• Combinations LeetCode

Related Interview Questions By Difficulty:

• Permutations LeetCode
• Combination Sum LeetCode
• N Queens II LeetCode

Related Interview Questions By Category:

• Palindrome Partitioning LeetCode
• Alien Dictionary LeetCode
• Word Ladder LeetCode

Conclusion

In this blog post, we’ve tackled the LeetCode problem 1849, “Splitting a String Into Descending Consecutive Values,” using a backtracking approach.

We’ve provided a Python solution that efficiently explores various split possibilities and checks for descending consecutive values.

The code optimally handles the problem’s constraints, and the use of recursion and pruning makes it a practical solution.

We hope this step-by-step guide has been helpful in understanding the problem and our approach.

If you have any questions, suggestions, or comments, please feel free to share them.

We encourage you to experiment with the code, explore different test cases, and deepen your understanding of backtracking algorithms.

For the original problem statement and more details, you can visit the LeetCode problem page: Splitting a String Into Descending Consecutive Values.

Thank you for joining us in solving this coding challenge, and we look forward to bringing you more exciting problems and solutions in the future.

Happy coding!