Merge branch 'main' into principal-component-analysis

CONTRIBUTING.md

@@ -14,7 +14,7 @@ Here are some resources that may be helpful as you contribute to Algo:
 
 ## How to Contribute
 
-### 1. Fork the Repository ([Video 1](https://www.loom.com/share/4c5f309a28c444caa4e70557669979f6?sid=88202acf-3ab8-4321-bcf2-3ced94215994))
+### 1. Fork the Repository 
 Start by forking the repository to your GitHub account. This creates a copy of the repository under your account.
 
 ### 2. Clone Your Fork
@@ -24,14 +24,14 @@ Clone the repository to your local machine using:
 $ git clone https://github.com/<your-username>/algo.git
 ```
 
-### 3. Create a New Branch ([Video 2](https://www.loom.com/share/74493008c617419ea1a1f69755124dd8?sid=28379156-ff84-4e57-90a9-234b4ba15160))
+### 3. Create a New Branch 
 Create a branch for your contribution:
 
 ```bash
 $ git checkout -b <branch-name>
 ```
 
-### 4. Make Your Changes ([Video 3](https://www.loom.com/share/ea1a931b8f9a492a8994ca3d006a4526?sid=0b889369-23a4-42c7-a61e-7e7de1474494), [Video 4](https://www.loom.com/share/55b170e45b7d4cbdb4fa443b84d03a3c?sid=7a4c1db8-ae74-4a05-815c-ca6f30f8c5c4))
+### 4. Make Your Changes 
 Make your changes, which could include:
 - Adding new algorithms
 - Improving existing documentation
@@ -43,7 +43,7 @@ If your contribution involves documentation, here’s how to write effective con
 
 #### a. Markdown & MDX
 - Documentation should be written in Markdown (`.md`) or MDX (`.mdx`), which supports JSX syntax.
-- MDX allows you to use React components inside Markdown files. This is helpful for adding interactive elements or custom components.
+- MDX allows you to use React components inside Markdown files. This helps add interactive elements or custom components.
 
 #### b. Content Structure
 
@@ -63,7 +63,7 @@ tags: [<tag1>, <tag2>]
 ```
 - **id**: A unique identifier for the page.
 - **title**: The page title.
-- **sidebar_label**: The label displayed in the sidebar.
+- **sidebar_label**: The label is displayed in the sidebar.
 - **sidebar_position**: Order of the page in the sidebar.
 - **description**: A short description of the page content.
 - **tags**: Tags for categorizing content.
@@ -121,7 +121,7 @@ tags: [<tag1>, <tag2>]
     <MyComponent />
     ```
 
-### 6. Commit Your Changes ([Video 5](https://www.loom.com/share/47d2ba8e35fd4382979899fe21c29974?sid=8b5a3af6-5a80-4025-b045-76e64ff9a839))
+### 6. Commit Your Changes 
 Commit your changes with a descriptive message:
 
 ```bash
@@ -150,4 +150,4 @@ Go to the original repository and create a Pull Request (PR). Provide a clear de
 
 ---
 
-Thank you for contributing! Let's build Algo together and create an amazing learning platform for mastering Data Structures and Algorithms. ✨
+Thank you for contributing! Let's build Algo and create an amazing learning platform for mastering Data Structures and Algorithms. ✨

README.md

@@ -715,17 +715,17 @@ Thanks to these amazing people who have contributed to the **Algo** project:
                 </a>
             </td>
             <td align="center">
-                <a href="https://github.com/Bhumika-00">
-                    <img src="https://avatars.githubusercontent.com/u/178026966?v=4" width="100;" alt="Bhumika-00"/>
+                <a href="https://github.com/Lighting-pixel">
+                    <img src="https://avatars.githubusercontent.com/u/77742960?v=4" width="100;" alt="Lighting-pixel"/>
                     <br />
-                    <sub><b>Bhumika Sharma</b></sub>
+                    <sub><b>Ayan </b></sub>
                 </a>
             </td>
             <td align="center">
-                <a href="https://github.com/Lighting-pixel">
-                    <img src="https://avatars.githubusercontent.com/u/77742960?v=4" width="100;" alt="Lighting-pixel"/>
+                <a href="https://github.com/Bhumika-00">
+                    <img src="https://avatars.githubusercontent.com/u/178026966?v=4" width="100;" alt="Bhumika-00"/>
                     <br />
-                    <sub><b>Ayan </b></sub>
+                    <sub><b>Bhumika Sharma</b></sub>
                 </a>
             </td>
             <td align="center">
@@ -816,22 +816,15 @@ Thanks to these amazing people who have contributed to the **Algo** project:
                     <sub><b>Narendra Dhangar </b></sub>
                 </a>
             </td>
-            <td align="center">
-                <a href="https://github.com/Kunj05">
-                    <img src="https://avatars.githubusercontent.com/u/147203563?v=4" width="100;" alt="Kunj05"/>
-                    <br />
-                    <sub><b>Kunj Chandak</b></sub>
-                </a>
-            </td>
-		</tr>
-		<tr>
             <td align="center">
                 <a href="https://github.com/Bhum-ika">
                     <img src="https://avatars.githubusercontent.com/u/91523494?v=4" width="100;" alt="Bhum-ika"/>
                     <br />
                     <sub><b>Bhumika Sharma</b></sub>
                 </a>
             </td>
+		</tr>
+		<tr>
             <td align="center">
                 <a href="https://github.com/17arindam">
                     <img src="https://avatars.githubusercontent.com/u/65901047?v=4" width="100;" alt="17arindam"/>
@@ -867,15 +860,15 @@ Thanks to these amazing people who have contributed to the **Algo** project:
                     <sub><b>Anany Dev</b></sub>
                 </a>
             </td>
-		</tr>
-		<tr>
             <td align="center">
                 <a href="https://github.com/Grandhi-Harshitha">
                     <img src="https://avatars.githubusercontent.com/u/120390344?v=4" width="100;" alt="Grandhi-Harshitha"/>
                     <br />
                     <sub><b>Grandhi-Harshitha</b></sub>
                 </a>
             </td>
+		</tr>
+		<tr>
             <td align="center">
                 <a href="https://github.com/ADITHYA-NS">
                     <img src="https://avatars.githubusercontent.com/u/116829016?v=4" width="100;" alt="ADITHYA-NS"/>
@@ -911,15 +904,15 @@ Thanks to these amazing people who have contributed to the **Algo** project:
                     <sub><b>Shreya Tripathy</b></sub>
                 </a>
             </td>
-		</tr>
-		<tr>
             <td align="center">
                 <a href="https://github.com/vedhcet-07">
                     <img src="https://avatars.githubusercontent.com/u/176995332?v=4" width="100;" alt="vedhcet-07"/>
                     <br />
                     <sub><b>Vishwas M D</b></sub>
                 </a>
             </td>
+		</tr>
+		<tr>
             <td align="center">
                 <a href="https://github.com/yogeswari05">
                     <img src="https://avatars.githubusercontent.com/u/137740335?v=4" width="100;" alt="yogeswari05"/>
@@ -955,15 +948,15 @@ Thanks to these amazing people who have contributed to the **Algo** project:
                     <sub><b>Saiyad Uveshali</b></sub>
                 </a>
             </td>
-		</tr>
-		<tr>
             <td align="center">
                 <a href="https://github.com/Suvadip-sana">
                     <img src="https://avatars.githubusercontent.com/u/78638404?v=4" width="100;" alt="Suvadip-sana"/>
                     <br />
                     <sub><b>Suvadip Sana</b></sub>
                 </a>
             </td>
+		</tr>
+		<tr>
             <td align="center">
                 <a href="https://github.com/shivenyadavs">
                     <img src="https://avatars.githubusercontent.com/u/155547804?v=4" width="100;" alt="shivenyadavs"/>
@@ -999,15 +992,15 @@ Thanks to these amazing people who have contributed to the **Algo** project:
                     <sub><b>Rahul</b></sub>
                 </a>
             </td>
-		</tr>
-		<tr>
             <td align="center">
                 <a href="https://github.com/PRASHANTSWAROOP001">
                     <img src="https://avatars.githubusercontent.com/u/56585080?v=4" width="100;" alt="PRASHANTSWAROOP001"/>
                     <br />
                     <sub><b>PRASHANT SWAROOP</b></sub>
                 </a>
             </td>
+		</tr>
+		<tr>
             <td align="center">
                 <a href="https://github.com/nishakp3005">
                     <img src="https://avatars.githubusercontent.com/u/121110503?v=4" width="100;" alt="nishakp3005"/>
@@ -1043,15 +1036,15 @@ Thanks to these amazing people who have contributed to the **Algo** project:
                     <sub><b>PEDDIREDDY MADHAVI</b></sub>
                 </a>
             </td>
-		</tr>
-		<tr>
             <td align="center">
                 <a href="https://github.com/rajatsinghal02">
                     <img src="https://avatars.githubusercontent.com/u/112543741?v=4" width="100;" alt="rajatsinghal02"/>
                     <br />
                     <sub><b>Rajat singhal</b></sub>
                 </a>
             </td>
+		</tr>
+		<tr>
             <td align="center">
                 <a href="https://github.com/RchtDshr">
                     <img src="https://avatars.githubusercontent.com/u/58704284?v=4" width="100;" alt="RchtDshr"/>
@@ -1087,15 +1080,15 @@ Thanks to these amazing people who have contributed to the **Algo** project:
                     <sub><b>Amiya Singh</b></sub>
                 </a>
             </td>
-		</tr>
-		<tr>
             <td align="center">
                 <a href="https://github.com/ishita-1305">
                     <img src="https://avatars.githubusercontent.com/u/118795997?v=4" width="100;" alt="ishita-1305"/>
                     <br />
                     <sub><b>Ishita Srivastava</b></sub>
                 </a>
             </td>
+		</tr>
+		<tr>
             <td align="center">
                 <a href="https://github.com/Mohith1490">
                     <img src="https://avatars.githubusercontent.com/u/141254298?v=4" width="100;" alt="Mohith1490"/>
@@ -1131,15 +1124,15 @@ Thanks to these amazing people who have contributed to the **Algo** project:
                     <sub><b>Lokesh11868</b></sub>
                 </a>
             </td>
-		</tr>
-		<tr>
             <td align="center">
                 <a href="https://github.com/Saurabhchaudhary9799">
                     <img src="https://avatars.githubusercontent.com/u/106806241?v=4" width="100;" alt="Saurabhchaudhary9799"/>
                     <br />
                     <sub><b>Saurbh Kumar</b></sub>
                 </a>
             </td>
+		</tr>
+		<tr>
             <td align="center">
                 <a href="https://github.com/Aasthaa10">
                     <img src="https://avatars.githubusercontent.com/u/170360041?v=4" width="100;" alt="Aasthaa10"/>
@@ -1175,15 +1168,15 @@ Thanks to these amazing people who have contributed to the **Algo** project:
                     <sub><b>Ananya Ravikiran Vastare</b></sub>
                 </a>
             </td>
-		</tr>
-		<tr>
             <td align="center">
                 <a href="https://github.com/ChetanSingh14">
                     <img src="https://avatars.githubusercontent.com/u/153702696?v=4" width="100;" alt="ChetanSingh14"/>
                     <br />
                     <sub><b>Chetan SIngh</b></sub>
                 </a>
             </td>
+		</tr>
+		<tr>
             <td align="center">
                 <a href="https://github.com/RahulScripted">
                     <img src="https://avatars.githubusercontent.com/u/181909739?v=4" width="100;" alt="RahulScripted"/>
@@ -1219,15 +1212,15 @@ Thanks to these amazing people who have contributed to the **Algo** project:
                     <sub><b>Mahi3454</b></sub>
                 </a>
             </td>
-		</tr>
-		<tr>
             <td align="center">
                 <a href="https://github.com/Mansi-Tanwar">
                     <img src="https://avatars.githubusercontent.com/u/148472134?v=4" width="100;" alt="Mansi-Tanwar"/>
                     <br />
                     <sub><b>Mansi-Tanwar</b></sub>
                 </a>
             </td>
+		</tr>
+		<tr>
             <td align="center">
                 <a href="https://github.com/NishantRana07">
                     <img src="https://avatars.githubusercontent.com/u/126577697?v=4" width="100;" alt="NishantRana07"/>
@@ -1263,15 +1256,15 @@ Thanks to these amazing people who have contributed to the **Algo** project:
                     <sub><b>Rana Jay</b></sub>
                 </a>
             </td>
-		</tr>
-		<tr>
             <td align="center">
                 <a href="https://github.com/RohanSai22">
                     <img src="https://avatars.githubusercontent.com/u/96601297?v=4" width="100;" alt="RohanSai22"/>
                     <br />
                     <sub><b>RohanSai22</b></sub>
                 </a>
             </td>
+		</tr>
+		<tr>
             <td align="center">
                 <a href="https://github.com/sejals23">
                     <img src="https://avatars.githubusercontent.com/u/183209584?v=4" width="100;" alt="sejals23"/>
@@ -1307,15 +1300,15 @@ Thanks to these amazing people who have contributed to the **Algo** project:
                     <sub><b>aasritha-24</b></sub>
                 </a>
             </td>
-		</tr>
-		<tr>
             <td align="center">
                 <a href="https://github.com/adwityac">
                     <img src="https://avatars.githubusercontent.com/u/102909367?v=4" width="100;" alt="adwityac"/>
                     <br />
                     <sub><b>Adwitya Chakraborty</b></sub>
                 </a>
             </td>
+		</tr>
+		<tr>
             <td align="center">
                 <a href="https://github.com/pa1narendra">
                     <img src="https://avatars.githubusercontent.com/u/84829899?v=4" width="100;" alt="pa1narendra"/>
@@ -1351,15 +1344,15 @@ Thanks to these amazing people who have contributed to the **Algo** project:
                     <sub><b>Lokesh_Bijarniya_</b></sub>
                 </a>
             </td>
-		</tr>
-		<tr>
             <td align="center">
                 <a href="https://github.com/LNischala">
                     <img src="https://avatars.githubusercontent.com/u/148078708?v=4" width="100;" alt="LNischala"/>
                     <br />
                     <sub><b>LNischala</b></sub>
                 </a>
             </td>
+		</tr>
+		<tr>
             <td align="center">
                 <a href="https://github.com/krishpathak">
                     <img src="https://avatars.githubusercontent.com/u/142569867?v=4" width="100;" alt="krishpathak"/>
@@ -1395,15 +1388,15 @@ Thanks to these amazing people who have contributed to the **Algo** project:
                     <sub><b>Harsh</b></sub>
                 </a>
             </td>
-		</tr>
-		<tr>
             <td align="center">
                 <a href="https://github.com/arzoosingh147">
                     <img src="https://avatars.githubusercontent.com/u/141030187?v=4" width="100;" alt="arzoosingh147"/>
                     <br />
                     <sub><b>Arzoo Singh</b></sub>
                 </a>
             </td>
+		</tr>
+		<tr>
             <td align="center">
                 <a href="https://github.com/ArchanRD">
                     <img src="https://avatars.githubusercontent.com/u/74826173?v=4" width="100;" alt="ArchanRD"/>

docs/backtracking-algorithms/n-queens_algorithm.md → docs/algorithms/backtracking-algorithms/n-queens_algorithm.md

@@ -116,4 +116,4 @@ graph TD;
     D --> C
     E --> B
 ```
-**Note: This algorithm is adapted from GeeksforGeeks.**
+**Note: This algorithm is adapted from GeeksforGeeks.**

docs/algorithms/string-algorithm/Boyer-moore-algorithm.md → docs/algorithms/string-algorithms/Boyer-moore-algorithm.md

@@ -104,4 +104,4 @@ The Boyer-Moore algorithm is particularly effective when the alphabet size is sm
 
 The Boyer-Moore algorithm is a valuable addition to the toolkit of any programmer dealing with pattern matching tasks, especially in scenarios where efficiency is crucial. Its ability to achieve sublinear time complexity in many cases makes it a popular choice for various applications.
 
-<AdsComponent />
+<AdsComponent />

docs/algorithms/string-algorithm/Naive-search.md → docs/algorithms/string-algorithms/Naive-search.md

@@ -142,4 +142,4 @@ The naive search algorithm is a simple and intuitive approach to pattern matchin
 
 ## Conclusion
 
-The **Naive Search Algorithm** is a basic string matching technique that checks every possible position in the text for the occurrence of a given pattern. Although simple to implement, it is inefficient for large texts and patterns as it performs comparisons one by one without any optimization.
+The **Naive Search Algorithm** is a basic string matching technique that checks every possible position in the text for the occurrence of a given pattern. Although simple to implement, it is inefficient for large texts and patterns as it performs comparisons one by one without any optimization.

docs/algorithms/string-algorithm/Suffix-Tree-Algorithm.md → docs/algorithms/string-algorithms/Suffix-Tree-Algorithm.md

@@ -105,4 +105,4 @@ int main() {
 
 ## Conclusion
 
-The suffix tree is a powerful data structure for string matching and pattern searching. It allows for efficient construction and searching of substrings in linear time. Suffix trees are widely used in bioinformatics and other applications where string operations are required.
+The suffix tree is a powerful data structure for string matching and pattern searching. It allows for efficient construction and searching of substrings in linear time. Suffix trees are widely used in bioinformatics and other applications where string operations are required.

docs/algorithms/string-algorithm/aho-corasick-algorithm.md → docs/algorithms/string-algorithms/aho-corasick-algorithm.md

@@ -256,4 +256,4 @@ int main() {
 
 ## Conclusion
 
-The **Aho-Corasick Algorithm** is an optimal solution for problems involving multiple pattern matching. Its combination of a trie and failure links ensures that it can handle large datasets and multiple queries efficiently.
+The **Aho-Corasick Algorithm** is an optimal solution for problems involving multiple pattern matching. Its combination of a trie and failure links ensures that it can handle large datasets and multiple queries efficiently.

docs/algorithms/string-algorithm/rabin-karp-algorithm.md → docs/algorithms/string-algorithms/rabin-karp-algorithms.md

@@ -137,4 +137,4 @@ It is widely used for finding substrings within large text data, especially in a
 
 ## Conclusion
 
-The Rabin-Karp Algorithm is a powerful tool for pattern matching in strings, offering a balance between time complexity and practicality. By leveraging hashing and the rolling hash technique, it efficiently finds occurrences of a pattern in a text, making it a valuable algorithm in competitive programming and real-world applications.
+The Rabin-Karp Algorithm is a powerful tool for pattern matching in strings, offering a balance between time complexity and practicality. By leveraging hashing and the rolling hash technique, it efficiently finds occurrences of a pattern in a text, making it a valuable algorithm in competitive programming and real-world applications.