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Posted on Feb 16, 2021

## Solution: Letter Case Permutation

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## Leetcode Problem #784 ( Medium ): Letter Case Permutation

Description:

Given a string S, we can transform every letter individually to be lowercase or uppercase to create another string.

Return a list of all possible strings we could create. You can return the output **in any order .

Constraints:

• S will be a string with length between 1 and 12 .
• S will consist only of letters or digits.

When a problem asks us to deal with permutations, one of the obvious approaches is via recursion as recursion will allow us to fire off our helper function down each branching possibility.

Recursion also naturally favors a DFS approach, which is also good because it ensures that our recursion stack never gets too deep.

Our recursive helper function ( dfs ) is actually quite simple. If we start with the input string ( S ) fully lowercased, then we just need to make sure that each version of dfs calls itself down two branches: one in which the current character is left unchanged, and a second in which the character has been uppercased, but only if the character is a letter.

Then, whenever we reach the end of S , we can add the permutation to our answer array ( ans ).

Implementation:

Javascript and Python deal with string copies faster than character arrays, so dfs will maintain a string ( res ) that it will build up as the function is called recursively.

Java deals with char arrays faster than it does strings, so we can pass a reference to a singular central char array ( chArr ) and modify it as we go. This also means that we have to remember to undo our toUpperCase after the second dfs is fired off so that later recursions reaching this character start with it in lower case.

C++ alone out of the four languages has mutable strings, so we can just pass a full copy of S down and modify each char individually, rather than having to build out a res .

Javascript Code:

Python Code:

Templates let you quickly answer FAQs or store snippets for re-use.

Here's another solution. We can also use a Bit-Masking approach to solve this problem.

Solution.java

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## 784. Letter Case Permutation

• Time: \$O(2^n)\$
• Space: \$O(2^n)\$

## Similar Problems

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## Problem Statement

Given a string S, we can transform every letter individually to be lowercase or uppercase to create another string. Return a list of all possible strings we could create.

Input: S = “r2q” Output: [“r2q”, “R2q”, “r2Q”, “R2Q”]. Input: S = “678” Output: [“678”]
• S will be a string with length between 1 and 12.
• S will consist only of letters or digits.

We don’t have to take care of digits as they can’t help to find more pernutations. We only have letters with us now. Suppose a string have L letters in it. The number of possible permutation will 2 L .

This can be represented by bitmask bits.

For Example: we have g5h, we can represent all the possible permutations as g5h = 00, g5H = 01, G7h = 10, G7H = 11. Digits given in the input string are not included in bitmask.

According the possible bitmask, find out all the permutations, taking one bitmask at a time.

## Implementation

Complexity analysis.

• Time Complexity: O(2 n *n).
• Space Complexity: O(2 n *n).

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## Data Structures

Data Structures & Algorithms

System Design

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