Merge pull request #208 from Iamtripathisatyam/main

Depth-first Search (DFS) Python

Author: prathimacode-hub

Graphs/DFS/Images/dfs.jpg

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+## 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/Images/output.jpg

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+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