Refine title and update content structure

Updated the title and improved the clarity of the content. Removed performance benchmarks section and adjusted the focus on future developments.

Author: prex03

_posts/2025-10-22-Week 10 @ Season of Commits.md

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+---
+title: Expanding the C++ Graph Backend - DFS and Bellman-Ford  
+date: 2025-10-22 23:25:31 +0530  
+categories: [Season of Commits]  
+tags: [Week 10]  
+---
+
+This week’s progress focused on extending the C++ graph backend in PyDataStructs with two major algorithmic implementations, Depth-First Search (DFS) and the Bellman-Ford shortest path algorithm. The [PR](https://github.com/codezonediitj/pydatastructs/pull/707) builds upon the existing backend architecture established in earlier commits, further accelerating computation on large graphs while maintaining full compatibility with the Python interface.
+
+---
+
+### 1. Adding DFS and Bellman-Ford to the C++ Backend
+
+The primary goal of this update was to move more core graph algorithms from Python to C++ for improved performance and scalability. With this PR, both **DFS** and **Bellman-Ford** are now available in the C++ backend, enabling faster traversal and shortest-path computations, especially on large or dense graphs.
+
+---
+
+### 2. Depth-First Search (DFS) — Iterative, Flexible, and Fast
+
+The C++ DFS implementation mirrors the behavior of the existing Python version while significantly improving runtime performance.  
+Key highlights include:
+
+- **Iterative stack-based design** — avoids recursion depth limits  
+- **Support for both graph types** — adjacency list and adjacency matrix  
+- **Custom callback operations** — users can attach operations (like node labeling or early stopping) via function arguments  
+- **Full compatibility** — results and traversal order match the Python backend for consistent testing
+
+This design not only improves efficiency but also provides a framework for extending graph traversal algorithms with user-defined logic, something that will integrate well with future backend expansion (e.g., parallel traversal in LLVM).
+
+---
+
+### 3. Bellman-Ford Algorithm — Optimized with SPFA
+
+The Bellman-Ford shortest path algorithm, implemented as `shortest_paths_bellman_ford_adjacency_list`, was enhanced with the **Shortest Path Faster Algorithm (SPFA)** optimization.  
+This approach drastically reduces redundant relaxations on sparse graphs while preserving correctness on graphs with negative weights.
+
+Key improvements include:
+
+- **SPFA optimization** for improved average-case performance  
+- **Negative weight and cycle detection**  
+- **Consistent output format** — returns distances and predecessors identical to Python’s implementation  
+- **Optional target node parameter** for partial shortest-path computation  
+
+These features make the C++ backend robust for a wide range of applications  from general-purpose graph analytics to low-level algorithm benchmarking.
+
+---
+
+### 4. Testing and Validation
+
+This update includes extensive test coverage to ensure correctness and cross-backend consistency.  
+Highlights:
+
+- Added dedicated C++ backend tests for DFS and Bellman-Ford  
+- Verified behavior for graphs with both positive and negative weights  
+- Included cycle detection validation in Bellman-Ford  
+- Confirmed callback handling in DFS for custom operations  
+
+All tests across Python and C++ backends pass successfully, ensuring stable integration with the existing codebase.
+
+---
+
+### 5. The Road Ahead
+
+With DFS and Bellman-Ford now integrated, the focus shifts toward:
+
+- **Adding more C++ backend algorithms** — including SCC’s and max flow algorithms  
+- **Backend benchmarking suite** — to quantify speedups across graph sizes and structures