added graphs and trees in data structures

Author: Ghruank

Theory/Data-Structures/Graphs/README.md

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+## 5. Graphs
+A **Graph** is a collection of vertices (nodes) and edges (connections between nodes) representing networks.
+
+### Key Characteristics
+- **Directed** vs **Undirected**: Directed graphs have edges with direction.
+- **Weighted** vs **Unweighted**: Weighted graphs assign values to edges.
+
+### Common Representations
+- **Adjacency Matrix**: A 2D array where cells indicate edge presence.
+  - Space Complexity: \(O(V^2)\)
+- **Adjacency List**: Each vertex has a list of adjacent vertices.
+  - Space Complexity: \(O(V + E)\)
+
+### Common Operations
+- **Traversal**:
+  - **Breadth-First Search (BFS)**: Level-order traversal, useful for finding shortest paths in unweighted graphs.
+  - **Depth-First Search (DFS)**: Visits nodes as deep as possible before backtracking, useful for pathfinding.
+- **Shortest Path Algorithms**:
+  - **Dijkstra's Algorithm**: Finds shortest paths from a single source in a weighted graph.
+  - **Floyd-Warshall**: All-pairs shortest paths.
+- **Minimum Spanning Tree (MST)**:
+  - **Kruskal's and Prim's Algorithms**: Find the minimum cost to connect all nodes in a weighted graph.
+
+### Applications
+- **Networks**: Routing algorithms in communication networks.
+- **Social Networks**: Representing and analyzing relationships.
+- **Web Crawling**: Link structure of websites.
+- **Pathfinding**: Navigation systems and game AI.
+- **Scheduling**: Task scheduling with dependencies.

Theory/Data-Structures/Trees/README.md

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+## 4. Trees
+A **Tree** is a hierarchical data structure consisting of nodes with a parent-child relationship. It starts with a **root** node and expands into subtrees of children, representing various hierarchical levels.
+
+### Key Characteristics
+- Each node has data and links to child nodes.
+- Commonly represented as a **rooted tree** with a single root node.
+
+### Types of Trees
+- **Binary Tree**: Each node has at most two children.
+- **Binary Search Tree (BST)**: A binary tree with the left child <= root <= right child.
+- **Balanced Trees**: Trees like AVL, Red-Black Trees keep balance for efficient operations.
+- **Heap**: A complete binary tree used for priority queues.
+- **Trie**: A tree for storing strings, useful in search applications.
+- **B-Trees**: Balanced trees used in databases and filesystems.
+
+### Common Operations
+- **Insertion**:
+  - Adds nodes based on tree type (e.g., BST properties).
+  - Complexity: \(O(\log n)\) for balanced trees; \(O(n)\) for unbalanced.
+- **Deletion**:
+  - Removes a node while maintaining tree properties.
+  - Complexity: \(O(\log n)\) for balanced trees; \(O(n)\) for unbalanced.
+- **Traversal**:
+  - **In-order**: Left, Root, Right (BST sorted order).
+  - **Pre-order**: Root, Left, Right (used for copying).
+  - **Post-order**: Left, Right, Root (used for deletion).
+  - Complexity: \(O(n)\)
+- **Searching**:
+  - Complexity: \(O(\log n)\) for balanced trees; \(O(n)\) for unbalanced.
+
+### Applications
+- **Hierarchical Data Representation**: File systems, organizational structures.
+- **Binary Search Trees (BSTs)**: Efficient searching, insertion, and deletion.
+- **Priority Queues**: Implemented using heaps.
+- **Trie**: Used for autocomplete and dictionary implementations.
+- **Databases and Filesystems**: B-trees provide efficient data retrieval.
+