Create floyd_warshall.py

graphs/floyd_warshall.py

@@ -0,0 +1,58 @@
+"""
+Author:- Sanjay Muthu <https://github.com/XenoBytesX>
+
+The Algorithm:
+    The Floyd Warshall algorithm is a All Pairs Shortest Path algorithm (APSP)
+    which finds the shortest path between all the pairs of nodes.
+
+Complexity:
+    Time Complexity:- O(n^3)
+    Space Complexity:- O(n^2)
+
+Wiki page:- <https://en.wikipedia.org/wiki/Floyd%E2%80%93Warshall_algorithm>
+"""
+
+def floyd_warshall(graph, n):
+    """
+    Returns the shortest distance between all pairs of nodes
+
+    >>> INF = 999999
+    >>> G = []
+    >>> G.append([0, 2, INF, INF, INF, 3])
+    >>> G.append([2, 0, 2, INF, INF, INF])
+    >>> G.append([INF, 2, 0, 1, INF, INF])
+    >>> G.append([INF, INF, 1, 0, 1, INF])
+    >>> G.append([INF, INF, INF, 1, 0, 5])
+    >>> G.append([3, INF, INF, INF, 5, 0])
+    >>> floyd_warshall(G, 6)
+    [\
+[0, 2, 4, 5, 6, 3], \
+[2, 0, 2, 3, 4, 5], \
+[4, 2, 0, 1, 2, 7], \
+[5, 3, 1, 0, 1, 6], \
+[6, 4, 2, 1, 0, 5], \
+[3, 5, 7, 6, 5, 0]\
+]
+    """
+    # The graph is a Adjancecy matrix (see <https://en.wikipedia.org/wiki/Adjacency_matrix>)
+    distance: list[list] = graph
+    for k in range(n):
+        for i in range(n):
+            for j in range(n):
+                distance[i][j] = min(distance[i][j], distance[i][k] + distance[k][j])
+    return distance
+
+if __name__ == '__main__':
+    """
+    Layout of G:-
+           2           2           1           1           5
+    (1) <-----> (2) <-----> (3) <-----> (4) <-----> (5) <-----> (6)
+    /\\                                                         /\\
+    ||                                                          ||
+    --------------------------------------------------------------
+                              3
+    """
+
+    import doctest
+
+    doctest.testmod()