Adding solution of Aho-Corasick Algorithm.

dsa/Advance/aho-corasick.md

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+---
+id: aho-corasick-algorithm
+title: Aho-Corasick Algorithm for Efficient String Matching
+sidebar_label: 0011 - Aho-Corasick Algorithm
+tags: [Aho-Corasick, String Matching, Algorithm, C++, Problem Solving]
+description: This is a solution for implementing the Aho-Corasick Algorithm to search multiple patterns simultaneously in a given text.
+---
+
+## Problem Statement 
+
+### Problem Description
+
+The Aho-Corasick Algorithm is designed for searching multiple patterns simultaneously within a given text. It constructs a finite state machine that resembles a digital tree with additional links between nodes, allowing efficient transitions between patterns.
+
+### Examples
+
+**Example 1:**
+
+```plaintext
+Input: 
+Patterns: {"he", "she", "his", "hers"}
+Text: "ahishers"
+Output: 
+Pattern found: he at index 1
+Pattern found: his at index 1
+Pattern found: she at index 3
+Pattern found: hers at index 4
+
+Explanation: All the patterns are efficiently found within the text.
+```
+
+### Constraints
+
+- The input consists of multiple patterns and a single text.
+- The algorithm should handle large patterns and text sizes efficiently.
+
+## Solution of Given Problem
+
+### Intuition and Approach
+
+The Aho-Corasick Algorithm follows these steps:
+
+1. Build a Trie: Insert all patterns into a trie.
+2. Construct Failure Links: Create failure links to enable efficient transitions when a mismatch occurs.
+3. Search the Text: Use the trie and failure links to search the text for all patterns simultaneously.
+
+### Approaches
+
+#### Codes in Different Languages
+
+<Tabs>
+  <TabItem value="cpp" label="C++">
+  <SolutionAuthor name="sjain1909"/>
+   ```cpp
+    #include <bits/stdc++.h>
+    using namespace std;
+
+    struct TrieNode {
+    unordered_map<char, TrieNode*> children;
+    TrieNode* failure;
+    vector<int> output;
+    TrieNode() : failure(nullptr) {}
+};
+
+class AhoCorasick {
+    TrieNode* root;
+    vector<string> patterns;
+
+public:
+    AhoCorasick() {
+        root = new TrieNode();
+    }
+
+    void addPattern(const string& pattern, int index) {
+        TrieNode* node = root;
+        for (char c : pattern) {
+            if (node->children.find(c) == node->children.end()) {
+                node->children[c] = new TrieNode();
+            }
+            node = node->children[c];
+        }
+        node->output.push_back(index);
+    }
+
+    void buildFailureLinks() {
+        queue<TrieNode*> q;
+        root->failure = root;
+        for (auto& child : root->children) {
+            child.second->failure = root;
+            q.push(child.second);
+        }
+
+        while (!q.empty()) {
+            TrieNode* current = q.front();
+            q.pop();
+
+            for (auto& child : current->children) {
+                char c = child.first;
+                TrieNode* fail = current->failure;
+
+                while (fail != root && fail->children.find(c) == fail->children.end()) {
+                    fail = fail->failure;
+                }
+
+                if (fail->children.find(c) != fail->children.end()) {
+                    child.second->failure = fail->children[c];
+                } else {
+                    child.second->failure = root;
+                }
+
+                child.second->output.insert(child.second->output.end(),
+                    child.second->failure->output.begin(), child.second->failure->output.end());
+
+                q.push(child.second);
+            }
+        }
+    }
+
+    void search(const string& text) {
+        TrieNode* node = root;
+        for (int i = 0; i < text.size(); ++i) {
+            char c = text[i];
+            while (node != root && node->children.find(c) == node->children.end()) {
+                node = node->failure;
+            }
+
+            if (node->children.find(c) != node->children.end()) {
+                node = node->children[c];
+            } else {
+                node = root;
+            }
+
+            if (!node->output.empty()) {
+                for (int index : node->output) {
+                    cout << "Pattern found: " << patterns[index] << " at index " << i - patterns[index].size() + 1 << "\n";
+                }
+            }
+        }
+    }
+
+    void initialize(const vector<string>& patterns) {
+        this->patterns = patterns;
+        for (int i = 0; i < patterns.size(); ++i) {
+            addPattern(patterns[i], i);
+        }
+        buildFailureLinks();
+    }
+};
+
+int main() {
+    int n;
+    cout << "Enter number of patterns: ";
+    cin >> n;
+    vector<string> patterns(n);
+    cout << "Enter patterns:\n";
+    for (int i = 0; i < n; ++i) {
+        cin >> patterns[i];
+    }
+
+    string text;
+    cout << "Enter text: ";
+    cin >> text;
+
+    AhoCorasick ac;
+    ac.initialize(patterns);
+    ac.search(text);
+
+    return 0;
+}
+    ```
+  </TabItem>  
+</Tabs>
+
+### Complexity Analysis
+
+- **Time Complexity:** $O(N + M + Z)$ where `N` is the length of the text, `M` is the total length of all patterns, and `Z` is the number of pattern occurrences.
+- **Space Complexity:** $O(M)$
+
+The time complexity accounts for building the trie, constructing failure links, and searching the text. The space complexity is linear with respect to the total length of the patterns.
+
+## Video Explanation of Given Problem
+
+    <LiteYouTubeEmbed
+      id="VSvE-zpZtso"
+      params="autoplay=1&autohide=1&showinfo=0&rel=0"
+      title="Problem Explanation | Solution | Approach"
+      poster="maxresdefault"
+      webp 
+    />
+---
+
+<h2>Authors:</h2>
+
+<div style={{display: 'flex', flexWrap: 'wrap', justifyContent: 'space-between', gap: '10px'}}>
+{['sjain1909'].map(username => (
+ <Author key={username} username={username} />
+))}
+</div>