Update README.md

graphs/README.md

@@ -3,17 +3,23 @@
 <br>
 
 * graph is a non-linear data structure consisting of vertices and edges.
+  
 
 * graphs can be represented by adjacent matrices, adjacent lists, and hash table of hash tables.
+
   
 * in **undirected graphs**, the edges between any two vertices do not have a direction, indicating a two-way relationship.
+
   
 * in **directed graphs**, the edges between any two vertices are directional.
+
   
 * in **weighted graphs**, each edge has an associated weight. if the sum of the weights of all edges of a cycle is a negative values, it's a negative weight cycle.
+
   
 * the **degree of a vertex** is the number of edges connecting the vertex. in directed, graphs, if the **in-dregree** of a vertex is `d`, there are **d** directional edges incident to the vertex (and similarly, **out-degree** from the vertex).
 
+
 * with `|V|` the number of vertices and `|E|` is the number of edges, search in a graph (either bfs of dfs) is `O(|V| + |E|)`.
 
 <br>
@@ -62,6 +68,60 @@ def bfs(matrix):
 
 <br>
 
+* or as a class:
+
+<br>
+
+```python
+
+from collections import deque
+ 
+
+class Graph:
+
+    def __init__(self, edges, n):
+ 
+        self.adj_list = [[] for _ in range(n)]
+      
+        for (src, dest) in edges:
+            self.adj_list[src].append(dest)
+            self.adj_list[dest].append(src)
+ 
+ 
+def bfs(graph, v, discovered):
+ 
+    queue = deque(v)
+    discovered[v] = True
+ 
+    while queue:
+ 
+        v = queue.popleft()
+        print(v, end=' ')
+ 
+        for u in graph.adj_list[v]:
+            if not discovered[u]:
+                discovered[u] = True
+                queue.append(u)
+
+
+def recursive_bfs(graph, queue, discovered):
+ 
+    if not queue:
+        return
+ 
+    v = queue.popleft()
+    print(v, end=' ')
+ 
+    for u in graph.adj_list[v]:
+        if not discovered[u]:
+            discovered[u] = True
+            queue.append(u)
+ 
+    recursive_bfs(graph, queue, discovered)
+```
+
+<br>
+
 ----
 
 #### depth first search
@@ -95,4 +155,56 @@ def dfs(matrix):
     for j in range(cols):
       traverse(i, j)
 ```
+
+<br>
+
+* or as a class:
+
+<br>
+
+```python
+from collections import deque
+
+class Graph:
+
+    def __init__(self, edges, n):
+
+        self.adj_list = [[] for _ in range(n)]
+
+        for (src, dest) in edges:
+            self.adj_list[src].append(dest)
+            self.adj_list[dest].append(src)
+ 
+
+def dfs(graph, v, discovered):
+ 
+    discovered[v] = True           
+    print(v, end=' ')              
+ 
+    for u in graph.adj_list[v]:
+        if not discovered[u]:       #
+            dfs(graph, u, discovered)
+ 
+ 
+
+def iterative_dfs(graph, v, discovered):
+ 
+    stack = [v]
+ 
+    while stack:
+ 
+        v = stack.pop()
+ 
+        if discovered[v]:
+            continue
+ 
+        discovered[v] = True
+        print(v, end=' ')
+ 
+        adj_list = graph.adjList[v]
+        for i in reversed(range(len(adj_list))):
+            u = adj_list[i]
+            if not discovered[u]:
+                stack.append(u)
+```