Depth-first Search (DFS) Python

Graphs/DFS/README.md

@@ -0,0 +1,40 @@
+## Overview:
+Two techniques are frequently used for graph traversal: These techniques are called **depth-first search (DFS)** and **breadth-first search (BFS)**, although we will just talk about DFS. DFS involves diving deep into the graph and then backtrack when it reaches the bottom.
+
+## What is Depth First Search in Python?
+In DFS, *we continue to traverse downwards through linked nodes until we reach the end*, then retrace our steps to check which connected nodes we haven't visited and repeat the process. In depth-first search, we dive deep into the graph and then backtrack when we reach the bottom.
+
+## Algorithm of DFS in Python
+Every time we reach a new node, we will take the following steps:
+1. We add the node to the top of the stack.
+2. Marked it as visited.
+3. We check if this node has any adjacent nodes:
+ 1. If it has adjacent nodes, then we ensure that they have not been visited already, and then visited it.
+ 2. We removed it from the stack if it had no adjacent nodes.
+
+## Time & Space Complexity
+* **Time Complexity:**
+Time complexity of DFS is `O(V+|E|)`, where V is the number of vertices and E is the number of edges.
+* **Space Complexity:**
+The space complexity of the DFS algorithm is `O(V)`, where V is the number of vertices.
+
+## Input & Output:
+<img src="../DFS/Images/dfs.jpg"> 
+
+### Input:
+
+```python
+graph = {
+ 0: [2],
+ 1: [2, 3],
+ 2: [0, 1, 4],
+ 3: [1, 4],
+ 4: [2, 3]
+ }
+ ```
+
+ ### Output:
+ ```python
+ Depth-first search: [0, 2, 1, 3, 4]
+ ```
+ <img width=50% src="../DFS/Images/output.jpg"> 

Graphs/DFS/dfs.py

@@ -0,0 +1,25 @@
+def dfs(node, graph, visited, component):
+ component.append(node) # Store answer
+ visited[node] = True # Mark visited
+
+ # Traverse to each adjacent node of a node
+ for child in graph[node]:
+ if not visited[child]: # Check whether the node is visited or not
+ dfs(child, graph, visited, component)
+
+
+if __name__ == "__main__":
+
+ # Graph of nodes
+ graph = {
+ 0: [2],
+ 1: [2, 3],
+ 2: [0, 1, 4],
+ 3: [1, 4],
+ 4: [2, 3]
+ }
+ node = 0 # Starting node
+ visited = [False]*len(graph)
+ component = []
+ dfs(node, graph, visited, component) # Traverse to each node of a graph
+ print(f"Following is the Depth-first search: {component}") # Print the answer