graphs part 1

Author: unknown

adjmatrix.py.py

@@ -0,0 +1,26 @@
+def printmatrix(matrix):
+    r,c = len(matrix),len(matrix[0])
+    for i in range(r):
+        for j in range(c):
+            print(matrix[i][j],end=" ")
+        print()
+        
+v,e = map(int,input().split())
+matrix = [[0]*v for i in range(v)]
+'''
+for i in range(e):
+    u,v = map(str,input().split())
+    u = ord(u) - ord('A')
+    v = ord(v)  - ord('A')
+    matrix[u][v] = 1 # True or False in case of edge
+    matrix[v][u] = 1
+'''
+for i in range(e):
+    u,v,w = map(str,input().split())
+    u = ord(u) - ord('A')
+    v = ord(v) - ord('A')
+    w = int(w)
+    matrix[u][v] = w # Weight / Cost in case of edge
+    
+
+printmatrix(matrix)

bfs.py.py

@@ -0,0 +1,47 @@
+from collections import deque
+from collections import defaultdict
+
+
+'''
+V E
+FOR EVERY EDGE
+U V
+7 9
+A B
+A C 
+A F
+C E
+C F
+C D
+D E 
+D G
+G F
+'''
+# T.C = O(V+)
+# S.C = O(V)
+def bfs(graph,start,visited,path):
+    queue = deque()
+    path.append(start)
+    queue.append(start)
+    visited[start] = True
+    while len(queue) != 0:
+        tmpnode = queue.popleft()
+        for neighbour in graph[tmpnode]:
+            if visited[neighbour] == False:
+                path.append(neighbour)
+                queue.append(neighbour)
+                visited[neighbour] = True
+    return path
+
+graph = defaultdict(list)
+v,e = map(int,input().split())
+for i in range(e):
+    u,v = map(str,input().split())
+    graph[u].append(v)
+    graph[v].append(u)
+
+start = 'A'
+path = []
+visited = defaultdict(bool)
+traversedpath = bfs(graph,start,visited,path)
+print(traversedpath)

dfs.py

@@ -0,0 +1,42 @@
+from collections import defaultdict
+
+'''
+V E
+FOR EVERY EDGE
+U V
+7 9
+A B
+A C 
+A F
+C E
+C F
+C D
+D E 
+D G
+G F
+
+'''
+# T.C = O(V+E)
+# S.C = O(V)
+def dfs(graph,start,visited,path):
+    path.append(start)
+    visited[start] = True
+    for neighbour in graph[start]: # O(V+E)
+        if visited[neighbour] == False: # O(1)
+            dfs(graph,neighbour,visited,path)
+    return path
+            
+    
+
+v,e = map(int,input().split())
+graph = defaultdict(list)
+for i in range(e):
+    u,v = map(str,input().split())
+    graph[u].append(v)
+    graph[v].append(u)
+
+path = []
+start = 'A'
+visited = defaultdict(bool)
+traversedpath = dfs(graph,start,visited,path)
+print(traversedpath)

primalitytest.py

@@ -23,7 +23,7 @@ def approach2(n):
         return True
     if n%2 == 0 or n%3 == 0:# O(1)
         return False
-    for i in range(5,int(sqrt(n))+1): # [1,root n]
+    for i in range(5,int(sqrt(n))+1,6): # [1,root n] prime numbers are in the form of 6k-1 or 6k+1
         if n%i == 0 or n%(i+2) == 0:
             return False
     return True