Merge pull request larissalages#264 from UmaMaheswariGorusupudi/master

Added solution for a edges on graph problem in hacker earth

Author: larissalages

Hacker Earth/Algorithms/Graphs/Articulation points and bridges/edges on a path.py

@@ -0,0 +1,105 @@
+from collections import defaultdict
+from collections import deque
+
+
+#the solution is simple find the brige edges in the graph first 
+#find a path form a to b and check for the bridge edges in the and count them.
+
+
+#class for finding bridge edges
+class Graph:
+
+    #basic structure of graph
+    def __init__(self,vertices):
+        self.V = vertices
+        self.graph = defaultdict(list)
+        self.Time = 0
+        self.ans = []
+
+    #to add a edge
+    def addEdge(self,u,v):
+        self.graph[u].append(v)
+        self.graph[v].append(u)
+    
+    #helper function for finding bridge edges
+    def bridgeUtil(self,u,visited,parent,low,disc):
+
+        visited[u] = True
+        disc[u] = self.Time
+        low[u] = self.Time
+        self.Time +=1
+
+        for v in self.graph[u]:
+
+            if visited[v] == False:
+                parent[v] = u
+                self.bridgeUtil(v,visited,parent,low,disc)
+
+                low[u] = min(low[u],low[v])
+
+                if(low[v]>disc[u]):
+                    #finally found the bridge edge
+                    self.ans.append([u,v])
+                    #print(u,v)
+
+            elif v!=parent[u]:
+                low[u] = min(low[u],disc[v])
+ 
+    #function to call helper function with  initial inputs
+    def bridge(self):
+
+        visited = [False] * (self.V)
+        disc = [float("Inf")] * (self.V)
+        low = [float("Inf")] * (self.V)
+        parent = [-1] * (self.V)
+
+        for i in range(self.V):
+            if visited[i] == False:
+                self.bridgeUtil(i,visited,parent,low,disc)
+
+    #path function returns parent array 
+    #this function uses dfs for finding the path
+    #parent arr means for given edge V -- > u in arr[u] = v
+
+    def path(self,x,y):
+        q = deque()
+        visited = [False] * (self.V)
+        q.append(x)
+        parent = [-1] * (self.V)
+        while(len(q)>0):
+            u = q.popleft()
+            for v in self.graph[u]:
+                if(v == y):
+                    visited[v] = True
+                    parent[v] = u
+                    return parent
+                if(visited[v] == False):
+                    q.append(v)
+                    visited[v] = True
+                    parent[v] = u
+
+
+
+if __name__ == '__main__':
+    n,m = map(int,input().split())
+    a,b = map(int,input().split())
+    g1 = Graph(n)
+    count = 0
+    for i in range(m):
+        x,y = map(int,input().split())
+        g1.addEdge(x-1, y-1)
+    g1.bridge()
+    p = g1.path(a-1,b-1)
+    pa  =  []
+    u = b-1
+    
+    #checking for the bridge edegs in the path 
+    while(u != a-1):
+        pa.append([u,p[u]])
+        pa.append([p[u],u])
+        u = p[u]
+
+    for i in g1.ans:
+        if(i in pa):
+            count = count + 1
+    print(count)