Breadth-First Search (BFS) is a strategic traversal technique in graph theory that prioritizes neighboring vertices before moving deeper. This systematic method ensures vertices are visited in a layer-by-layer manner, spiraling outward from the starting vertex.
Implementing BFS in C
In the C language, with its expansive libraries, BFS can be implemented efficiently. Our primary function, breadth_first_search(), needs the graph’s edges, vertex count, and a callback for each vertex visitation.
Practical Code Example
To demonstrate BFS in action, let’s explore a simple coded example:
| #include <stdio.h>#include <stdlib.h> typedef struct { unsigned int start; unsigned int end;} Edge; void BFS(const Edge *edges, unsigned int n_edges, unsigned int n_vertices, void (*visitFunc)(unsigned int)) { unsigned int *visited = calloc(n_vertices, sizeof(unsigned int)); unsigned int *queue = malloc(n_vertices * sizeof(unsigned int)); unsigned int front = 0, rear = 0; visited[0] = 1; queue[rear++] = 0; while (front != rear) { unsigned int current = queue[front++]; visitFunc(current); for (unsigned int i = 0; i < n_edges; i++) { if (edges[i].start == current && !visited[edges[i].end]) { visited[edges[i].end] = 1; queue[rear++] = edges[i].end; } if (edges[i].end == current && !visited[edges[i].start]) { visited[edges[i].start] = 1; queue[rear++] = edges[i].start; } } } free(visited); free(queue);} void printVertex(unsigned int vertex) { printf(“Visited vertex: %u\n”, vertex);} int main() { Edge edges[] = { {0, 1}, {0, 2}, {1, 3}, {2, 3}, {3, 4}, {2, 4}, {4, 5} }; unsigned int n_edges = sizeof(edges) / sizeof(edges[0]); BFS(edges, n_edges, 6, printVertex); return 0;} |
Output Analysis
Expected traversal results:
Commence at vertex 0
Progress sequentially through vertices 1 to 12
| Visited vertex: 0Visited vertex: 1Visited vertex: 2Visited vertex: 3Visited vertex: 4Visited vertex: 5 |
Comparison Table: BFS vs. Other Graph Algorithms
| Attribute | BFS | Other Algorithms |
|---|---|---|
| Depth Handling | Radially, Layer-by-Layer | Specific |
| Memory Use | Queue-based | Varies |
| Complexity | O(V+E) for Adjacency List | Depends |
| Application | Shortest Paths in Unweighted Graphs | Specific |
Understanding vector::emplace_back
Introduced in C++11, the vector::emplace_back method revolutionized the way objects are added to the end of a vector. Instead of creating an object and then copying or moving it into the vector (often a two-step process), emplace_back constructs the object directly in the vector’s memory, eliminating redundant operations.
Consider a scenario with a complex object:
| std::vector<MyClass> vec;vec.push_back(MyClass(arg1, arg2)); // Might involve extra copy/move operations |
Using emplace_back:
| vec.emplace_back(arg1, arg2); // Directly constructs the object inside the vector |
This enhancement is more than syntactic sugar; it offers performance benefits, especially when dealing with objects that are expensive to copy or move. In BFS or any graph algorithm where you might want to store vertices or edges in a vector, leveraging emplace_back can lead to more efficient and faster code.
Conclusion
BFS’s capability is evident in its exhaustive and systematic vertex visitation. The layer-by-layer approach ensures comprehensive coverage, with C language highlighting its true efficiency. Practical code examples further underscore its versatility and potential applications in diverse scenarios.