What is the brute force approach and complexity for Letter Case Permutation?

Loop over the 2^L masks; each bit picks the case of one letter; rebuild each string with time complexity O(2^L · N) and space complexity O(N).

What is the optimal approach and complexity for Letter Case Permutation?

Walk the string once; split only at letters into lower and upper; digits pass through with optimal time complexity O(2^L · N) and space complexity O(N).

How do you identify the pattern for Letter Case Permutation?

Look for key signals in the prompt: "transform every letter individually" indicates Each letter position makes its own decision, like Permutations: one decision per position.; "lowercase or uppercase" indicates Exactly two options per letter. This is take-one-of-two, not take-one-of-n.; "digits do not change" indicates A position with only one option makes no branch at all..

Letter Case Permutation

Medium·LeetCode #784 Pro OnlyBasic Reinforcement

LeetCode

Problem Statement

You get a string s made of letters and digits. Every letter can be changed to lower case or upper case on its own. Digits never change.

Return every string you can make this way. The answer can come back in any order.

Input

A string s of lowercase letters, uppercase letters and digits. It has between 1 and 12 characters.

Output

A list of every string you can make by choosing the case of each letter.

Example 1

Input: s = "a1b2"

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

There are two letters, a and b. Each one has two versions, so 2 × 2 = 4 strings. The digits 1 and 2 stay the same.

Example 2

Input: s = "3z4"

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

The only letter is z, which can be z or Z. The digits 3 and 4 never change.

Constraints

• 1 ≤ s.length ≤ 12
• s consists only of lowercase English letters, uppercase English letters and digits.

Pattern Recognition Clues

Recognising these key signals in the problem description immediately identifies the pattern:

“transform every letter individually”

→ Each letter position makes its own decision, like Permutations: one decision per position.

“lowercase or uppercase”

→ Exactly two options per letter. This is take-one-of-two, not take-one-of-n.

“digits do not change”

→ A position with only one option makes no branch at all.

Approach Complexity Ladder

Brute Force — bitmask over the lettersO(2^L · N)O(N)

Loop over the 2^L masks; each bit picks the case of one letter; rebuild each string

Optimal — recurse over positions, branch only on lettersO(2^L · N)O(N)

Walk the string once; split only at letters into lower and upper; digits pass through

Brute Force Intuition

Count the L letters. Loop over every mask from 0 to 2^L − 1. Bit j of the mask decides the case of the j-th letter. For each mask, rebuild the whole string from scratch.

Recognition rule for this sub-pattern:

Pick an unused element for each position; mark used, recurse, unmark.

Remember this · Backtracking

Trigger

"All subsets / permutations / combinations", place items under rules (N-Queens, Sudoku), find a path in a grid.

Think

At each step, what are my choices, and how do I undo a choice?

Key question

What is my state, when is it complete, and when do I prune?

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