Welcome to your C programming journey into the world of Shortest Path Algorithms! In this lesson, we'll explore various techniques to find the shortest path between nodes in a graph, which is a fundamental concept in computer science with numerous real-world applications.
Shortest Path Algorithms help find the shortest path between nodes in a graph, given some specific criteria. This is crucial for navigation systems, social networks, and more.
Let's start with Breadth-First Search (BFS), a simple algorithm to traverse and search trees or graphs. BFS visits all vertices of a graph before backtracking.
#include <stdio.h>
#include <limits.h>
#include <stdbool.h>
#define V 9
int minDistance(int dist[], bool sptSet[]) {
int min = INT_MAX, minIndex;
for (int v = 0; v < V; v++)
if (sptSet[v] == false && dist[v] <= min)
min = dist[v], minIndex = v;
return minIndex;
}
void printSolution(int dist[], int n) {
printf("Vertex Distance from Source\n");
for (int i = 0; i < V; i++)
printf("%d \t %d\n", i, dist[i]);
}
void BFS(int graph[V][V], int src) {
int dist[V];
bool sptSet[V];
for (int i = 0; i < V; i++)
dist[i] = INT_MAX, sptSet[i] = false;
dist[src] = 0;
sptSet[src] = true;
for (int count = 0; count < V - 1; count++) {
int u = minDistance(dist, sptSet);
sptSet[u] = true;
for (int v = 0; v < V; v++)
if (!sptSet[v] && graph[u][v] && dist[u] != INT_MAX
&& dist[u] + graph[u][v] < dist[v])
dist[v] = dist[u] + graph[u][v];
}
printSolution(dist, V);
}
int main() {
int graph[V][V] = {{0, 4, 0, 0, 0, 0, 0, 8, 0},
{4, 0, 8, 0, 0, 0, 0, 0, 0},
{0, 8, 0, 7, 0, 4, 0, 0, 2},
{0, 0, 7, 0, 9, 14, 0, 0, 0},
{0, 0, 0, 9, 0, 10, 0, 0, 0},
{0, 0, 4, 14, 10, 0, 2, 0, 0},
{0, 0, 0, 0, 0, 2, 0, 1, 6},
{8, 0, 0, 0, 0, 0, 1, 0, 7},
{0, 0, 2, 0, 0, 0, 6, 7, 0}};
BFS(graph, 0);
return 0;
}š” Pro Tip: The given example uses an adjacency matrix to represent the graph, and the source vertex is 0.
Dijkstra's Algorithm is used to find the shortest path between nodes in a graph with non-negative edge weights.
#include <stdio.h>
#include <limits.h>
#include <stdbool.h>
#define V 9
int minDistance(int dist[], bool sptSet[]) {
int min = INT_MAX, minIndex;
for (int v = 0; v < V; v++)
if (sptSet[v] == false && dist[v] <= min)
min = dist[v], minIndex = v;
return minIndex;
}
void printSolution(int dist[], int n) {
printf("Vertex Distance from Source\n");
for (int i = 0; i < V; i++)
printf("%d \t %d\n", i, dist[i]);
}
void dijkstra(int graph[V][V], int src) {
int dist[V];
bool sptSet[V];
for (int i = 0; i < V; i++) {
dist[i] = INT_MAX;
sptSet[i] = false;
}
dist[src] = 0;
for (int count = 0; count < V - 1; count++) {
int u = minDistance(dist, sptSet);
sptSet[u] = true;
for (int v = 0; v < V; v++)
if (!sptSet[v] && graph[u][v] && dist[u] != INT_MAX
&& dist[u] + graph[u][v] < dist[v])
dist[v] = dist[u] + graph[u][v];
}
printSolution(dist, V);
}
int main() {
int graph[V][V] = {{0, 4, 0, 0, 0, 0, 0, 8, 0},
{4, 0, 8, 0, 0, 0, 0, 0, 0},
{0, 8, 0, 7, 0, 4, 0, 0, 2},
{0, 0, 7, 0, 9, 14, 0, 0, 0},
{0, 0, 0, 9, 0, 10, 0, 0, 0},
{0, 0, 4, 14, 10, 0, 2, 0, 0},
{0, 0, 0, 0, 0, 2, 0, 1, 6},
{8, 0, 0, 0, 0, 0, 1, 0, 7},
{0, 0, 2, 0, 0, 0, 6, 7, 0}};
dijkstra(graph, 0);
return 0;
}š” Pro Tip: The main difference between BFS and Dijkstra's Algorithm is that Dijkstra's Algorithm can handle graphs with negative edge weights, whereas BFS can only handle graphs with non-negative edge weights.
What is the main difference between BFS and Dijkstra's Algorithm?