1236. Web Crawler
Problem Description
The task is to implement a web crawler that crawls all URLs that are under the same hostname as the starting URL. A crawler is typically a program that systematically browses the Web or a website information to create an index of data. In this problem, you are given a starting URL and an HtmlParser interface with a getUrls method that, when called, returns all URLs found on a given webpage.
Here are the key requirements for the crawler:
- The crawler begins from the page specified by
startUrl
. - It should call the
HtmlParser.getUrls(url)
method to retrieve all URLs from the webpage at the specified URL. - The crawler should prevent visiting the same URL more than once to avoid infinite loops and redundant operations.
- Only URLs with the same hostname as the
startUrl
should be crawled. The hostname is the portion of the URL that usually includes the domain name and the top-level domain, but, for the purpose of this problem, it excludes subdomains, protocols (likehttp
), and ports. - While the question mentions that URLs with or without a trailing slash are considered different, it doesn't play a significant role in the implementation of the solution provided because the crawled URLs are obtained from the
getUrls
method, which should handle this distinction.
The description implies storing crawled URLs and making sure that new URLs are only crawled if they belong to the same domain and haven't been crawled before.
Flowchart Walkthrough
Let's apply the algorithm using the Flowchart to analyze LeetCode problem 1236, Web Crawler. Here’s a step-by-step walkthrough:
Is it a graph?
- Yes: The internet can be modeled as a graph where each URL is a node and links between websites are edges.
Is it a tree?
- No: The internet structure allows cycles and links between nodes that do not conform to a hierarchical tree structure.
Is the problem related to directed acyclic graphs (DAGs)?
- No: While we're dealing with a directional nature of URLs linking to other URLs, the internet is inherently full of cycles and not acyclic.
Is the problem related to shortest paths?
- No: The goal of a web crawler isn't to find shortest paths; instead, it is to visit all accessible pages under certain constraints.
Does the problem involve connectivity?
- Yes: The main task is to visit all reachable pages (nodes) starting from a given starting URL (root node).
Does the problem have small constraints?
- Not specified, but typically, the web is vast, implying potentially large constraints. Hence, we assume the problem expects an efficient navigation of a possibly large graph.
Conclusion: Since it's a graph problem centered around exploring reachable nodes from a given start node (URL), without small constraints or specific optimal path requirements, the flowchart would typically suggest using BFS. However, Depth-First Search (DFS) can also be effectively used for such kind of exhaustive navigation and exploration tasks, especially if the strategy involves backtracking up and down the web of links. Thus, DFS could be equally appropriate here.
Intuition
The intuition behind the solution is to perform a depth-first search (DFS) on the URLs, starting from startUrl
. Depth-first search is a recursive algorithm that uses the concept of backtracking. It involves exhaustive searches of all the nodes by going ahead, if possible, else by backtracking. This approach perfectly aligns with the nature of web crawling, where we dive deep into one link (node) before moving to adjacent links.
To implement DFS effectively and adhere to the key requirements, the following aspects are essential:
- A mechanism to determine the hostname from a given URL, so we can compare whether subsequent URLs belong to the same host as the
startUrl
. - A data structure to keep track of the URLs that have already been visited. A
set
is ideal in this scenario to avoid duplicates efficiently. - A recursive function that performs the DFS. It should:
- Add the current URL to the list of visited URLs.
- Retrieve all URLs linked from the current URL using the
getUrls
method. - For each retrieved URL, check if the hostname matches the
startUrl
's hostname and recurse only if the URL hasn't been visited yet.
This process creates a recursive traversal that explores each URL within the same hostname and builds up the set of all visited URLs, which is the final result.
The provided solution encodes this intuition. The host
function extracts the hostname from the URL, the dfs
function embodies the depth-first traversal logic, and the ans
set maintains the record of visited URLs to ensure each URL is only crawled once.
Learn more about Depth-First Search and Breadth-First Search patterns.
Solution Approach
The solution is implemented using a classic DFS algorithm. Let's walk through the implementation step by step.
First, we define a helper function named host
that parses a given URL to return its hostname. The function assumes that all URLs begin with "http://"
(length 7 characters), so it strips this part before splitting the URL by '/'
and returning the first part, which is the hostname:
1def host(url):
2 url = url[7:]
3 return url.split('/')[0]
Next, we define a recursive function dfs
that performs the depth-first search. This function takes an url
as an argument:
- It first checks if the URL is already in the set named
ans
, which is used to store crawled URLs. If the URL is already in the set, the function returns immediately to avoid processing the same URL twice. - If the URL is not in the set, it's added to
ans
. - Then, for each URL retrieved by the
HtmlParser.getUrls(url)
call, the function checks whether each of those URLs shares the same hostname as our originalstartUrl
. If it does, the function is recursively called with the new URL.
1def dfs(url):
2 if url in ans:
3 return
4 ans.add(url)
5 for next_url in htmlParser.getUrls(url):
6 if host(url) == host(next_url):
7 dfs(next_url)
Finally, we define the set ans
as an empty set, used to store the unique URLs:
1ans = set()
And we start the DFS crawl from the startUrl
:
1dfs(startUrl)
After the DFS is complete, ans
contains all the unique URLs that share the same hostname as the startUrl
and have been crawled. As per the requirements, the function returns a list of these URLs:
1return list(ans)
The beauty of this approach is its simplicity and effectiveness. Using DFS allows us to deep dive into each path of linked URLs while keeping track of visited URLs through the ans
set to avoid revisits, which could lead to infinite loops. Filter URLs with the same hostname ensures that we're adhering to the crawling boundaries set by the problem.
This solution effectively uses basic string manipulation for URL parsing, recursive DFS for navigating through links, and a set data structure to manage visited URLs.
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Start EvaluatorExample Walkthrough
Let's walk through a small example to illustrate how the solution operates. Suppose we have the following web pages and links between them and are provided with the starting URL "http://example.com/a"
:
"http://example.com/a"
links to["http://example.com/b", "http://example.com/c"]
"http://example.com/b"
links to["http://example.com/a"]
(back-link to a)"http://example.com/c"
links to[]
(no links)
The HtmlParser.getUrls
method simulates the links as follows for each URL:
1def getUrls(url):
2 links = {
3 "http://example.com/a": ["http://example.com/b", "http://example.com/c"],
4 "http://example.com/b": ["http://example.com/a"],
5 "http://example.com/c": []
6 }
7 return links[url]
Applying the solution:
- We begin with the
dfs
function called on thestartUrl
which is"http://example.com/a"
. - First, we use the
host
function to determine the hostname. For"http://example.com/a"
, the hostname is"example.com"
. - Since this URL has not been visited yet, we add it to the
ans
set. - We call
HtmlParser.getUrls("http://example.com/a")
and receive two URLs:"http://example.com/b"
and"http://example.com/c"
. - For each of these URLs, we check the hostname using the
host
function and compare it to our start URL's hostname"example.com"
. They match, so we proceed to calldfs
recursively on these URLs. - The
dfs
call on"http://example.com/b"
adds this URL to theans
set and then callsHtmlParser.getUrls
on this URL, which only returns"http://example.com/a"
. However, since"http://example.com/a"
is already in theans
set, it doesn't recurse on it to avoid a loop. - Similarly, the
dfs
call on"http://example.com/c"
adds the URL to theans
set.HtmlParser.getUrls("http://example.com/c")
returns an empty list, so there are no further URLs to process. - At the end of this process, the
ans
set contains{"http://example.com/a", "http://example.com/b", "http://example.com/c"}
, which are the unique URLs that were crawled. - We return the list form of the
ans
set, giving us our final result:["http://example.com/a", "http://example.com/b", "http://example.com/c"]
.
This walkthrough demonstrates the DFS-based crawling, visiting each unique URL starting from the startUrl
and respecting the same hostname constraint without visiting any URL more than once.
Solution Implementation
1class Solution:
2 def crawl(self, startUrl: str, htmlParser: 'HtmlParser') -> List[str]:
3 # Retrieves the hostname from a given URL.
4 def get_host_name(url: str) -> str:
5 # Trim the 'http://' part from the URL and return the hostname part.
6 # Example: "http://foo.bar.com/page" becomes "foo.bar.com"
7 return url[7:].split('/')[0]
8
9 # Performs a depth-first search to crawl all URLs that share the same host as startUrl.
10 def dfs(url: str):
11 # If the URL is already in the set, do not process it again.
12 if url in visited:
13 return
14 # Add the current URL to the visited set.
15 visited.add(url)
16 # Get all URLs from the current page using the HtmlParser API.
17 for next_url in htmlParser.getUrls(url):
18 # If the next URL shares the same host as the start URL, continue the DFS from there.
19 if get_host_name(url) == get_host_name(next_url):
20 dfs(next_url)
21
22 # Initialize a set to keep track of visited URLs.
23 visited = set()
24 # Start crawling from the starting URL.
25 dfs(startUrl)
26 # Return the list of visited URLs.
27 return list(visited)
28
1import java.util.ArrayList;
2import java.util.HashSet;
3import java.util.List;
4import java.util.Set;
5
6// This is the HtmlParser's API interface.
7// You should not implement it, or speculate about its implementation
8interface HtmlParser {
9 List<String> getUrls(String url);
10}
11
12public class Solution {
13
14 private Set<String> crawledUrls; // To store unique crawled URLs
15
16 // The crawl method initiates the crawling process from a startUrl
17 public List<String> crawl(String startUrl, HtmlParser htmlParser) {
18 crawledUrls = new HashSet<>();
19 depthFirstSearch(startUrl, htmlParser);
20 return new ArrayList<>(crawledUrls); // Convert the set of URLs to a list before returning
21 }
22
23 // Helper method to perform depth-first search on the web page's links
24 private void depthFirstSearch(String url, HtmlParser htmlParser) {
25 // Check if the url is already visited to avoid loops
26 if (crawledUrls.contains(url)) {
27 return;
28 }
29
30 // Mark the current URL as visited
31 crawledUrls.add(url);
32
33 // Iterate through all URLs obtained from the current page
34 for (String nextUrl : htmlParser.getUrls(url)) {
35 // Only continue crawling if the next URL has the same host as the start URL
36 if (extractHostName(nextUrl).equals(extractHostName(url))) {
37 depthFirstSearch(nextUrl, htmlParser); // Recursively visit the next URL
38 }
39 }
40 }
41
42 // Helper method to extract the host name from a given URL
43 private String extractHostName(String url) {
44 // Removing the protocol ("http://") part of the URL to get the hostname with possible path
45 String urlWithoutProtocol = url.substring(7);
46
47 // Split the hostname and path and return the hostname part
48 return urlWithoutProtocol.split("/")[0];
49 }
50}
51
1/**
2 * // This is the HtmlParser's API interface.
3 * // You should not implement it, or speculate about its implementation
4 * class HtmlParser {
5 * public:
6 * vector<string> getUrls(string url);
7 * };
8 */
9
10class Solution {
11public:
12 vector<string> crawledUrls; // List of all crawled URLs
13 unordered_set<string> visitedUrls; // Set to keep track of visited URLs
14
15 // Entry function to start crawling from the given startUrl
16 vector<string> crawl(string startUrl, HtmlParser htmlParser) {
17 dfsCrawl(startUrl, htmlParser);
18 return crawledUrls;
19 }
20
21 // Helper function to perform DFS crawl starting from url using htmlParser
22 void dfsCrawl(string& url, HtmlParser& htmlParser) {
23 // If the URL has already been visited, do nothing
24 if (visitedUrls.count(url)) {
25 return;
26 }
27
28 // Mark the url as visited
29 visitedUrls.insert(url);
30 // Add the url to the list of crawled URLs
31 crawledUrls.push_back(url);
32
33 // For each URL found in the current URL's page
34 for (string nextUrl : htmlParser.getUrls(url)) {
35 // Crawl the next URL if it is of the same host
36 if (extractHostName(url) == extractHostName(nextUrl)) {
37 dfsCrawl(nextUrl, htmlParser);
38 }
39 }
40 }
41
42 // Helper function to extract the hostname from a given URL
43 string extractHostName(string url) {
44 int hostNameStartIndex = strlen("http://"); // Start index for host name
45 string hostName; // Placeholder for the extracted host name
46
47 // Start from the initial index past "http://" and read until '/'
48 for (size_t index = hostNameStartIndex; index < url.size(); ++index) {
49 if (url[index] == '/') {
50 break;
51 }
52 hostName += url[index];
53 }
54
55 return hostName;
56 }
57};
58
1/**
2 * This represents the HtmlParser's API interface.
3 * Detail implementation of `getUrls` method is not given.
4 */
5interface HtmlParser {
6 getUrls(url: string): string[];
7}
8
9// Array to hold all the crawled URLs
10const crawledUrls: string[] = [];
11// Set to keep track of visited URLs
12const visitedUrls: Set<string> = new Set();
13
14/**
15 * Initiates the crawl starting from the given `startUrl` and using the
16 * provided `htmlParser` to find other URLs to crawl.
17 * @param startUrl The starting URL for the crawl process.
18 * @param htmlParser The HtmlParser instance to retrieve URLs on a page.
19 * @returns The list of URLs crawled.
20 */
21function crawl(startUrl: string, htmlParser: HtmlParser): string[] {
22 dfsCrawl(startUrl, htmlParser);
23 return crawledUrls;
24}
25
26/**
27 * Recursively crawls URLs starting from the `url` using Depth-First Search.
28 * It uses the `htmlParser` to get connected URLs and only continues with
29 * those that have the same hostname.
30 * @param url The current URL to crawl.
31 * @param htmlParser HtmlParser instance to get adjacent URLs.
32 */
33function dfsCrawl(url: string, htmlParser: HtmlParser): void {
34 // If the URL has already been visited, stop the crawl for this URL
35 if (visitedUrls.has(url)) {
36 return;
37 }
38
39 // Mark the URL as visited
40 visitedUrls.add(url);
41 // Add the URL to the list of crawled URLs
42 crawledUrls.push(url);
43
44 // Retrieve all URLs found in the current page and crawl them
45 const urlsFromPage = htmlParser.getUrls(url);
46 for (const nextUrl of urlsFromPage) {
47 // Continue the crawl on the next URL if it has the same host as the start URL
48 if (extractHostName(url) === extractHostName(nextUrl)) {
49 dfsCrawl(nextUrl, htmlParser);
50 }
51 }
52}
53
54/**
55 * Extracts the hostname from the given URL string.
56 * @param url The URL from which the hostname is to be extracted.
57 * @returns The hostname as a string.
58 */
59function extractHostName(url: string): string {
60 const hostNameStartIndex = "http://".length; // Start index for hostname
61 let hostName: string = ""; // Initialize extracted hostname
62
63 // Loop to extract the host name portion of the URL
64 for (let index = hostNameStartIndex; index < url.length; index++) {
65 if (url[index] === '/') {
66 break; // Stop at the first '/' after the protocol indicator
67 }
68 hostName += url[index];
69 }
70
71 return hostName;
72}
73
Time and Space Complexity
The given Python function implements a Depth-First Search (DFS) to crawl web pages. Here's the analysis of the time complexity and space complexity:
Time Complexity
The time complexity of the code is governed by the number of URLs that are visited and the number of out-links that each URL contains. If we assume there are N
unique URLs and each URL could have at most D
out-links we will visit:
- Each URL is processed once, and for each URL, the
getUrls
method ofHtmlParser
could be called. This operation isO(1)
for each URL since we are just processing the URL and not actually parsing HTML (parsing in reality would depend on the HTML content size). - However, each URL could link out to
D
other URLs. In the worst case where all URLs point to all other URLs, each edge (link) would effectively be visited once.
Therefore, the time complexity is O(N + N * D)
, which simplifies to O(ND)
as each URL is expanded once and then each out-link is explored.
Space Complexity
The space complexity comprises the memory required for the recursive call stack when performing DFS as well as the memory required to store the set of visited URLs:
- The recursive DFS could go as deep as
N
if there is a URL that leads to a long chain of other URLs. This contributesO(N)
to the space complexity. - The
ans
set is used to store unique URLs that are visited. In the worst-case scenario where all URLs are accessible from the starting URL, this set contributesO(N)
.
Combining the two gives us O(2N)
, which simplifies to O(N)
space complexity.
In summary:
- Time Complexity:
O(ND)
- Space Complexity:
O(N)
Learn more about how to find time and space complexity quickly using problem constraints.
Which of the following shows the order of node visit in a Breadth-first Search?
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