Crawler Log Folder

LeetCode 1598: Crawler Log Folder Solution & Explanation

Problem Overview

TL;DR: Use a single integer counter to track the current directory depth, incrementing for folders and decrementing (with a floor of zero) for parent operations.

The LeetCode 1598 problem, Crawler Log Folder, asks us to simulate a file system's navigation based on a series of commands. We start at the main folder (root). We receive a list of operations: moving into a child folder ("x/"), moving to the parent folder ("../"), or staying in the current folder ("./"). Our goal is to determine the minimum number of operations required to return to the main folder after processing all logs, which is equivalent to finding the current depth of the directory structure.

Brute Force Approach for Crawler Log Folder

The most intuitive way to solve this problem is to simulate the file system exactly as described using a standard Stack data structure. This approach mimics how a real file system maintains the current path.

Naive Algorithm:

1. Initialize an empty Stack of strings.
2. Iterate through each string in the logs array.
3. If the string is "../", pop the top element from the stack (if the stack is not empty).
4. If the string is "./", do nothing.
5. Otherwise (it is a folder name like "abc/"), push the string onto the stack.
6. Finally, return the size of the stack.

Why this is suboptimal: While this solution is correct and runs in linear time $O(N)$, it is spatially inefficient. By storing the actual folder names, the Space Complexity becomes $O(N \times L)$, where $N$ is the number of logs and $L$ is the maximum length of a folder name. For the purpose of calculating distance, the actual names of the folders are irrelevant; only their presence matters. This extra memory usage makes it less optimal than the pattern-based solution.

Algorithm Strategy: Two Pointer Patterns

We implement the solution using a simplified Two Pointer approach where one pointer is implicit (the loop iterator) and the other is explicit (the depth variable).

1. Initialize State: Create a variable depth initialized to 0. This represents our distance from the main folder.
2. Iterate Logs: Traverse the logs array string by string.
3. Process Backspaces: If the current log is "../", we decrement depth. We must apply the boundary check: depth can never be less than 0.
4. Process No-Ops: If the current log is "./", we simply continue to the next iteration.
5. Process Insertions: For any other string (representing a child folder), we increment depth.
6. Result: Return depth.

This strategy achieves $O(1)$ space complexity because we discard the string data and track only the topological depth.

Execution Flow

Let's trace the algorithm with Example 1: logs = ["d1/","d2/","../","d21/","./"]

1. Start: depth = 0.
2. Step 1 ("d1/"): This is a child folder.
   • Action: Increment depth.
   • State: depth = 1.
3. Step 2 ("d2/"): This is a child folder.
   • Action: Increment depth.
   • State: depth = 2.
4. Step 3 ("../"): This is a parent folder (backspace).
   • Action: Decrement depth (since depth > 0).
   • State: depth = 1.
5. Step 4 ("d21/"): This is a child folder.
   • Action: Increment depth.
   • State: depth = 2.
6. Step 5 ("./"): This is a current folder operation.
   • Action: Do nothing.
   • State: depth = 2.
7. End: Return depth, which is 2.

Proof of Correctness

The correctness relies on the invariant that depth always accurately reflects the size of the stack of folders relative to the root.

• Base Case: At the start, we are at the root, so distance is 0. Correct.
• Inductive Step:
  • If we move to a child, the path length increases by exactly 1. Our algorithm increments depth.
  • If we move to a parent, the path length decreases by exactly 1, unless we are already at the root. Our algorithm decrements depth with a check max(0, depth - 1).
  • If we stay, path length is constant. Our algorithm does nothing.
• Conclusion: Since every valid transition in the file system is mirrored 1:1 by an integer operation on depth, the final value of depth equals the minimum operations to go back (which is simply traversing up depth times).

Pattern Reuse Notes

The Two Pointers - String Comparison with Backspaces pattern is a powerful tool for simplifying simulation problems involving "undo" operations.

• LeetCode 844: Backspace String Compare: This problem is the canonical example of the pattern. Instead of folder depths, you are comparing two strings where # represents a backspace. The logic of iterating and maintaining a "valid length" or skipping characters is identical to handling ../ in the Crawler Log Folder problem.

Reference Implementation

C++ Solution for LeetCode 1598

1class Solution {
2public:
3    int minOperations(vector<string>& logs) {
4        int depth = 0;
5        
6        for (const string& log : logs) {
7            if (log == "../") {
8                // Move up one level, but not above root (0)
9                if (depth > 0) {
10                    depth--;
11                }
12            } else if (log == "./") {
13                // Stay in current folder; do nothing
14                continue;
15            } else {
16                // Move down into a child folder
17                depth++;
18            }
19        }
20        
21        return depth;
22    }
23};

Java Solution for LeetCode 1598

1class Solution {
2    public int minOperations(String[] logs) {
3        int depth = 0;
4        
5        for (String log : logs) {
6            if (log.equals("../")) {
7                // Move up one level, ensure we don't go below 0
8                if (depth > 0) {
9                    depth--;
10                }
11            } else if (log.equals("./")) {
12                // Stay in current folder
13                continue;
14            } else {
15                // Move down into a child folder
16                depth++;
17            }
18        }
19        
20        return depth;
21    }
22}

Python Solution for LeetCode 1598

1class Solution:
2    def minOperations(self, logs: List[str]) -> int:
3        depth = 0
4        
5        for log in logs:
6            if log == "../":
7                # Move up one level, max(0, depth - 1) logic
8                if depth > 0:
9                    depth -= 1
10            elif log == "./":
11                # Stay in current folder
12                continue
13            else:
14                # Move down into a child folder
15                depth += 1
16                
17        return depth