Adding solution of KMP algorithm

dsa/Advance/knuth-morris-pratt.md

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+---
+id: knuth-morris-pratt
+title: Knuth-Morris-Pratt (KMP) Algorithm
+sidebar_label: 0006 - Knuth-Morris-Pratt Algorithm
+tags: [KMP, String Matching, Algorithm, C++, Problem Solving]
+description: This is a solution for implementing the Knuth-Morris-Pratt (KMP) algorithm for efficient substring searching and pattern matching.
+---
+
+## Problem Statement 
+
+### Problem Description
+
+The Knuth-Morris-Pratt (KMP) algorithm is an efficient string searching algorithm that improves the performance of substring searches within a main string. The algorithm preprocesses the pattern to create a partial match table (also known as the "lps" array), which is used to skip unnecessary comparisons during the search process.
+
+### Examples
+
+**Example 1:**
+
+```plaintext
+Input: 
+Text: "abxabcabcaby"
+Pattern: "abcaby"
+Output: 
+Pattern found at index 6
+```
+
+### Constraints
+
+- The length of the text and the pattern can be up to 10^5.
+
+## Solution of Given Problem
+
+### Intuition and Approach
+
+The KMP algorithm follows these steps:
+
+1. Preprocessing the Pattern: Compute the longest proper prefix which is also a suffix (lps) array.
+2. Searching the Text: Use the lps array to skip characters in the text while matching the pattern.
+
+### Approaches
+
+#### Codes in Different Languages
+
+<Tabs>
+  <TabItem value="cpp" label="C++">
+  <SolutionAuthor name="sjain1909"/>
+   ```cpp
+#include <bits/stdc++.h>
+using namespace std;
+void computeLPSArray(string& pat, int M, vector<int>& lps) {
+    int length = 0;  
+    lps[0] = 0;     
+    int i = 1;
+
+    while (i < M) {
+        if (pat[i] == pat[length]) {
+            length++;
+            lps[i] = length;
+            i++;
+        } else {
+            if (length != 0) {
+                length = lps[length - 1];
+            } else {
+                lps[i] = 0;
+                i++;
+            }
+        }
+    }
+}
+
+void KMPSearch(string& pat, string& txt) {
+    int M = pat.length();
+    int N = txt.length();
+
+    vector<int> lps(M);
+
+    computeLPSArray(pat, M, lps);
+
+    int i = 0; 
+    int j = 0; 
+    while (i < N) {
+        if (pat[j] == txt[i]) {
+            j++;
+            i++;
+        }
+
+        if (j == M) {
+            cout << "Pattern found at index " << i - j << "\n";
+            j = lps[j - 1];
+        } else if (i < N && pat[j] != txt[i]) {
+            if (j != 0) {
+                j = lps[j - 1];
+            } else {
+                i++;
+            }
+        }
+    }
+}
+
+int main() {
+    string txt, pat;
+    cout << "Enter the text: ";
+    cin >> txt;
+    cout << "Enter the pattern: ";
+    cin >> pat;
+
+    KMPSearch(pat, txt);
+
+    return 0;
+}
+    ```
+  </TabItem>  
+</Tabs>
+
+### Complexity Analysis
+
+- **Time Complexity:** $O(N + M)$ where N is the length of the text and M is the length of the pattern.
+- **Space Complexity:** $O(M)$ for the lps array.
+
+## Video Explanation of Given Problem
+
+    <LiteYouTubeEmbed
+      id="obWXjtg0L64"
+      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>