What is the brute force approach and complexity for Simplify Path?

Repeatedly collapse "//", remove "/./", and cancel "/name/../" pairs with time complexity O(N²) and space complexity O(N).

What is the optimal approach and complexity for Simplify Path?

Skip "" and ".", pop on ".." if not empty, push any other name; join with '/' with optimal time complexity O(N) and space complexity O(N).

Simplify Path

Q: How do you identify the pattern for Simplify Path?

Look for key signals in the prompt: "".." moves up one level" indicates It undoes the most recent folder still open → pop the top of a stack.; "a folder name moves down one level" indicates It opens a new level → push.; ""." and "//" change nothing" indicates Those pieces are skipped and never touch the stack..

Medium·LeetCode #71 Pro OnlySlight Variation

LeetCode

Problem Statement

You are given an absolute Unix-style file path path (it always starts with /). Rewrite it in its shortest, canonical form.

The rules of the path:

. means the current folder, so it changes nothing.
.. means the parent folder. At the root /, there is no parent, so you stay at the root.
Several slashes in a row (//, ///) count as one /.
Any other piece is a folder name, including things like ... or ..a.

The canonical path starts with a single /, has exactly one / between folder names, does not end with / (unless it is just /), and contains no . or .. pieces.

Input

A string path.

Output

The simplified canonical path as a string.

Example 1

Input: path = "/home/"

Output: "/home"

The trailing slash is dropped.

Example 2

Input: path = "/home//foo/"

Output: "/home/foo"

The double slash counts as one.

Example 3

Input: path = "/home/user/Documents/../Pictures"

Output: "/home/user/Pictures"

.. goes back up from Documents to user, then we enter Pictures.

Example 4

Input: path = "/../"

Output: "/"

The root has no parent, so .. keeps us at the root.

Example 5

Input: path = "/.../a/../b/c/../d/./"

Output: "/.../b/d"

... is an ordinary folder name. a is undone by the .. after it, c by the next .., and . changes nothing.

Constraints

• 1 ≤ path.length ≤ 3000
• path contains English letters, digits, '.', '/' and '_'
• path is a valid absolute Unix path

Pattern Recognition Clues

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

“".." moves up one level”

→ It undoes the most recent folder still open → pop the top of a stack.

“a folder name moves down one level”

→ It opens a new level → push.

“"." and "//" change nothing”

→ Those pieces are skipped and never touch the stack.

Approach Complexity Ladder

Brute Force — rewrite the string until it stops changingO(N²)O(N)

Repeatedly collapse "//", remove "/./", and cancel "/name/../" pairs

Optimal — split on '/', then a folder stackO(N)O(N)

Skip "" and ".", pop on ".." if not empty, push any other name; join with '/'

Brute Force Intuition

Add a / at the end so every name is followed by /. Then keep applying the first rule that matches, searching from the start each time: // → /, /./ → /, a leading /../ → /, and /name/../ → / (where name is not ..). When no rule matches, drop the trailing /.

Recognition rule for this sub-pattern:

Simulate a process where new items interact with the latest survivors (collisions, path folders, min tracking).

Remember this · Stack

Trigger

Matching pairs, nested structure, undo, evaluating expressions, "the last one wins".

Think

Does each new element need to look at the most recent unresolved element?

Key question

What does an item on the stack represent, and when does it get resolved?

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