#1849

Medium

auto_awesomeBacktracking search with pruning

LeetCode Problem Workspace

Splitting a String Into Descending Consecutive Values

Check if a string of digits can be split into descending consecutive values where the difference between them is 1.

Problem Statement

You are given a string s consisting of digits, and you need to check if it can be split into two or more non-empty substrings. These substrings should represent descending numerical values where the difference between the numerical values of adjacent substrings is exactly 1.

Return true if such a split is possible, or false if no valid split exists. The solution requires checking all potential splits and verifying that they meet the descending order condition with a difference of 1.

Examples

Example 1

Input: s = "1234"

Output: false

There is no valid way to split s.

Example 2

Input: s = "050043"

Output: true

s can be split into ["05", "004", "3"] with numerical values [5,4,3]. The values are in descending order with adjacent values differing by 1.

Example 3

Input: s = "9080701"

Output: false

There is no valid way to split s.

Constraints

1 <= s.length <= 20
s only consists of digits.

Solution Approach

Backtracking Search with Pruning

Use a backtracking approach to explore all possible ways to split the string into substrings. At each split, verify if the numbers are in descending order and if the difference between adjacent substrings is exactly 1. Prune invalid paths early to save computation.

String Manipulation

Handle the string carefully, ensuring that substrings are parsed into integer values without leading zeros unless the value is exactly zero. This step is crucial for comparing the numbers correctly and avoiding invalid splits.

Efficient Pruning

Apply pruning by cutting off branches of the recursion that cannot possibly form a valid sequence of consecutive numbers. If at any point the difference between adjacent numbers is greater than 1, stop exploring further splits.

Complexity Analysis

Metric	Value
Time	Depends on the final approach
Space	Depends on the final approach

The time and space complexity depend on the backtracking approach used. In the worst case, the time complexity is O(2^n), where n is the length of the string, as we explore all possible ways to split the string. Space complexity can vary based on the depth of recursion, but it is generally O(n).

What Interviewers Usually Probe

The candidate demonstrates a strong understanding of backtracking and can apply pruning techniques to avoid unnecessary computations.
The candidate is careful with string parsing, ensuring that leading zeros are handled appropriately.
The candidate is able to explain the trade-offs between exhaustive search and efficient pruning in solving the problem.

Common Pitfalls or Variants

Common pitfalls

Failing to handle leading zeros correctly, which can lead to incorrect number comparisons.
Not pruning the search space effectively, leading to excessive computation time.
Overlooking edge cases, such as very short strings or strings where no valid split is possible.

Follow-up variants

Allowing strings to have leading zeros in some cases.
Trying a more optimized approach that uses dynamic programming instead of backtracking.
Increasing the string length limit to test the scalability of the solution.

FAQ

What is the primary algorithmic technique used to solve the Splitting a String Into Descending Consecutive Values problem?

The primary technique is backtracking with pruning, where you explore all possible splits of the string and prune invalid paths early.

How do I handle strings with leading zeros when solving this problem?

Ensure that leading zeros are only allowed when the value is exactly zero, as any other number with leading zeros would be invalid.

What should I do if the backtracking search becomes too slow?

You can apply more aggressive pruning, such as checking for invalid sequences earlier or using dynamic programming for optimization.

What is the expected time complexity for solving this problem?

The time complexity in the worst case is O(2^n), where n is the length of the string, as you explore all possible splits.

What are common mistakes to avoid when solving the Splitting a String Into Descending Consecutive Values problem?

Common mistakes include not handling leading zeros correctly, failing to prune invalid paths early, and missing edge cases like very short strings.

terminal

Solution

Solution 1: DFS

We can start from the first character of the string and try to split it into one or more substrings, then recursively process the remaining part.

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class Solution:
    def splitString(self, s: str) -> bool:
        def dfs(i: int, x: int) -> bool:
            if i >= len(s):
                return True
            y = 0
            r = len(s) - 1 if x < 0 else len(s)
            for j in range(i, r):
                y = y * 10 + int(s[j])
                if (x < 0 or x - y == 1) and dfs(j + 1, y):
                    return True
            return False

        return dfs(0, -1)

Continue Practicing

#2014 longest subsequence repeated k times #949 largest time for given digits #1863 sum of all subset xor totals