#784

Medium

auto_awesomeBacktracking search with pruning

LeetCode Problem Workspace

Letter Case Permutation

Letter Case Permutation involves generating all possible strings by changing the case of each letter in a given string.

Problem Statement

You are given a string s that consists of lowercase English letters, uppercase English letters, and digits. Your task is to generate all possible strings by changing the case of each letter independently. The final output should return all possible permutations of the string where case changes are applied to the alphabetic characters only.

Return the list of all possible strings that can be created. The order of the strings in the output does not matter, but you should consider only case transformations for alphabetic characters while leaving the digits unchanged.

Examples

Example 1

Input: s = "a1b2"

Output: ["a1b2","a1B2","A1b2","A1B2"]

Example details omitted.

Example 2

Input: s = "3z4"

Output: ["3z4","3Z4"]

Example details omitted.

Constraints

1 <= s.length <= 12
s consists of lowercase English letters, uppercase English letters, and digits.

Solution Approach

Backtracking

Utilize backtracking to explore all possible combinations of uppercase and lowercase letters. For each letter, decide whether to change its case or leave it as is. Continue this process recursively until all characters have been processed.

Pruning the Search Space

When backtracking, prune the search space by only changing the case of alphabetic characters and leaving digits unaffected. This reduces the number of unnecessary computations and speeds up the solution.

Efficient String Construction

As strings are generated, construct them incrementally by swapping the case of individual alphabetic characters, rather than generating all permutations first and filtering later.

Complexity Analysis

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

Time and space complexity depend on the number of alphabetic characters in the string. The number of possible permutations grows exponentially with each letter that has two case options. Specifically, for a string of length n, with k alphabetic characters, the time and space complexity are both O(2^k), as each letter has two choices (uppercase or lowercase).

What Interviewers Usually Probe

Candidate demonstrates knowledge of backtracking and its application to case permutations.
Ability to prune the search space and optimize the recursion depth for efficiency.
Candidate can explain the trade-offs between recursive and iterative solutions.

Common Pitfalls or Variants

Common pitfalls

Not correctly handling digits or non-alphabetic characters, which should remain unchanged.
Failure to optimize the backtracking approach by pruning unnecessary recursion calls.
Not understanding the exponential time complexity caused by processing alphabetic characters.

Follow-up variants

Allowing more than one non-alphabetic character in the string.
Exploring iterative methods rather than backtracking for generating permutations.
Adding constraints on the number of operations or runtime limits to challenge the approach.

FAQ

How do I approach the Letter Case Permutation problem?

Use backtracking to explore all case combinations, but optimize by pruning the search space and focusing only on alphabetic characters.

What is the time complexity of solving the Letter Case Permutation problem?

The time complexity is O(2^k), where k is the number of alphabetic characters in the string, since each character has two case options.

Can we optimize the space complexity of Letter Case Permutation?

Yes, by constructing the string incrementally during the backtracking process, you can avoid storing intermediate results and optimize space usage.

Why are pruning techniques important in the Letter Case Permutation problem?

Pruning prevents unnecessary recursion for digits and non-alphabetic characters, reducing computation and improving performance, especially for longer strings.

What variations can be applied to the Letter Case Permutation problem?

You could introduce additional constraints, explore iterative methods, or handle strings with a mix of non-alphabetic characters for more complex challenges.

terminal

Solution

Solution 1: DFS

Since each letter in $s$ can be converted to uppercase or lowercase, we can use the DFS (Depth-First Search) method to enumerate all possible cases.

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class Solution:
    def letterCasePermutation(self, s: str) -> List[str]:
        def dfs(i: int) -> None:
            if i >= len(t):
                ans.append("".join(t))
                return
            dfs(i + 1)
            if t[i].isalpha():
                t[i] = chr(ord(t[i]) ^ 32)
                dfs(i + 1)

        t = list(s)
        ans = []
        dfs(0)
        return ans

Solution 2: Binary Enumeration

For a letter, we can convert it to uppercase or lowercase. Therefore, for each letter, we can use a binary bit to represent its conversion scheme, where $1$ represents lowercase and $0$ represents uppercase.

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class Solution:
    def letterCasePermutation(self, s: str) -> List[str]:
        def dfs(i: int) -> None:
            if i >= len(t):
                ans.append("".join(t))
                return
            dfs(i + 1)
            if t[i].isalpha():
                t[i] = chr(ord(t[i]) ^ 32)
                dfs(i + 1)

        t = list(s)
        ans = []
        dfs(0)
        return ans

Continue Practicing

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