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floyd_warshall_algorithm.cpp
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floyd_warshall_algorithm.cpp
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#include <iostream>
#include <limits.h> // For INT_MAX, to represent infinity
using namespace std;
const int V = 4; // Number of vertices (nodes) in the graph
#define INF INT_MAX // Infinity, for places where no path exists
// The heart of the Floyd-Warshall algorithm: It updates the distances between all pairs of nodes
void floydWarshall(int graph[V][V]) {
// Step 1: Create a distance matrix to store the shortest distances between all pairs
int dist[V][V];
// Step 2: Initialize the distance matrix with the given graph values (initial distances)
for (int i = 0; i < V; i++) {
for (int j = 0; j < V; j++) {
dist[i][j] = graph[i][j]; // Initially, shortest paths are the direct paths (or INF if no path)
}
}
// Step 3: Start the main algorithm
for (int k = 0; k < V; k++) { // 'k' is the intermediate node we're testing
for (int i = 0; i < V; i++) { // For each pair of nodes (i, j)...
for (int j = 0; j < V; j++) {
// Only update if there's a path through 'k'
if (dist[i][k] != INF && dist[k][j] != INF && dist[i][k] + dist[k][j] < dist[i][j]) {
dist[i][j] = dist[i][k] + dist[k][j]; // Found a shorter path, update it!
}
}
}
}
// Step 4: Output the results
cout << "The shortest distances between every pair of vertices are as follows:\n";
for (int i = 0; i < V; i++) {
for (int j = 0; j < V; j++) {
if (dist[i][j] == INF) {
cout << "INF "; // No path exists
} else {
cout << dist[i][j] << " "; // Shortest path between i and j
}
}
cout << endl;
}
}
int main() {
// Example graph: adjacency matrix representation
int graph[V][V] = {
{0, 3, INF, 5},
{2, 0, INF, 4},
{INF, 1, 0, INF},
{INF, INF, 2, 0}
};
// Call the function to find the shortest paths
floydWarshall(graph);
return 0;
}