Merge pull request #629 from PranathiNagisetti/floyd_warshall_algo

Add Floyd-Warshall algorithm to Python graph algorithms

Author: Karanjot786

Python/algorithms/graph_algorithms/floyd_Warshall_algorithm.py

@@ -0,0 +1,54 @@
+""""
+Purpose: Finds the shortest paths between all pairs of vertices in a weighted graph (can handle negative weights but no negative cycles)."""
+# Floyd-Warshall Algorithm in Python
+# Function to implement Floyd-Warshall Algorithm
+def floyd_warshall(graph):
+    """
+    graph: 2D list of edge weights (adjacency matrix)
+           graph[i][j] = weight of edge from i to j, or float('inf') if no edge
+    Returns: 2D list with shortest distances between all pairs
+    """
+    # Number of vertices
+    V = len(graph)
+    
+    # Initialize distance matrix same as graph
+    dist = [list(row) for row in graph]  # deep copy
+
+    # Add all vertices one by one as intermediate vertices
+    for k in range(V):
+        for i in range(V):
+            for j in range(V):
+                # Update dist[i][j] if going through k is shorter
+                if dist[i][k] + dist[k][j] < dist[i][j]:
+                    dist[i][j] = dist[i][k] + dist[k][j]
+    
+    return dist
+
+# Utility function to print the distance matrix
+def print_matrix(dist):
+    V = len(dist)
+    print("Shortest distances between every pair of vertices:")
+    for i in range(V):
+        for j in range(V):
+            if dist[i][j] == float('inf'):
+                print("INF", end="\t")
+            else:
+                print(dist[i][j], end="\t")
+        print()
+
+# Main function
+if __name__ == "__main__":
+    # Example graph represented as adjacency matrix
+    INF = float('inf')
+    graph = [
+        [0, 3, INF, 5],
+        [2, 0, INF, 4],
+        [INF, 1, 0, INF],
+        [INF, INF, 2, 0]
+    ]
+
+    # Compute shortest paths
+    shortest_distances = floyd_warshall(graph)
+    
+    # Print the result
+    print_matrix(shortest_distances)