Add Floyd-Warshall algorithm under graphs

graphs/floyd_warshall.py

@@ -0,0 +1,42 @@
+"""
+Floyd-Warshall Algorithm
+Solves the all-pairs shortest path problem for a weighted graph.
+"""
+
+def floyd_warshall(dist):
+    """
+    Updates the distance matrix to contain the shortest distances
+    between all pairs of vertices.
+
+    Args:
+        dist: 2D list, adjacency matrix where dist[i][j] is the weight
+              from vertex i to vertex j (use a large number for infinity)
+    """
+    V = len(dist)
+
+    # Consider each vertex as an intermediate point
+    for k in range(V):
+        for i in range(V):
+            for j in range(V):
+                # Update dist[i][j] if a shorter path is found through k
+                if dist[i][k] != INF and dist[k][j] != INF:
+                    dist[i][j] = min(dist[i][j], dist[i][k] + dist[k][j])
+
+
+if __name__ == "__main__":
+    INF = 100000000  # Representation of "infinity"
+
+    # New example adjacency matrix
+    dist = [
+        [0, 3, INF, 7, INF],
+        [8, 0, 2, INF, INF],
+        [5, INF, 0, 1, INF],
+        [2, INF, INF, 0, 1],
+        [INF, INF, INF, INF, 0]
+    ]
+
+    floyd_warshall(dist)
+
+    print("Shortest distances between all pairs of vertices:")
+    for row in dist:
+        print(row)