Merge pull request #442 from Khushi-agarwal/Branch1

Warshall Algorithm in Python

Author: smv1999

Data Structures/Graphs/WarshallAlgorithm.py

@@ -0,0 +1,74 @@
+'''
+A program for warshall algorithm.It is a shortest path algorithm which is used to find the 
+distance from source node,which is the first node,to all the other nodes.
+If there is no direct distance between two vertices then it is considered as -1
+'''
+
+
+def warshall(g,ver):
+    dist = list(map(lambda i: list(map(lambda j: j, i)), g))
+    for i in range(0,ver):
+        for j in range(0,ver):
+            dist[i][j] = g[i][j]
+	#Finding the shortest distance if found
+    for k in range(0,ver):
+        for i in range(0,ver):
+            for j in range(0,ver):
+                if dist[i][k] + dist[k][j] < dist[i][j] and  dist[i][k]!=-1 and dist[k][j]!=-1:
+                    dist[i][j] = dist[i][k] + dist[k][j]
+	#Prnting the complete short distance matrix
+    print("The distance matrix is\n")
+    for i in range(0,ver):
+        for j in range(0,ver):
+            if dist[i][j]>=0:
+                print(dist[i][j],end=" ")
+            else:
+                print(-1,end=" ")
+        print("\n")
+#Driver's code
+def main():
+    print("Enter number of vertices\n")
+    ver=int(input())
+    graph=[]
+	#Creating the  graph
+    print("Enter the graph\n")
+    for i in range(ver):
+        a =[]
+        for j in range(ver):     
+            a.append(int(input()))
+        graph.append(a)
+    warshall(graph,ver)
+if __name__=="__main__":
+	main()
+
+
+
+'''
+Time Complexity:O(ver^3)
+Space Complexity:O(ver^2)
+Input/Output:
+Enter number of vertices 
+4
+Enter the graph
+0
+8
+-1
+1
+-1
+0
+1
+-1
+4
+-1
+0
+-1
+-1
+2
+9
+0
+The distance matrix is
+0 3 -1 1 
+-1 0 1 -1 
+4 -1 0 -1 
+-1 2 3 0 
+'''