⚡️ Speed up method PathFinder.find_shortest_path by 246%

The optimized code achieves a 245% speedup through two key algorithmic improvements:

**1. Replaced list-based queue with deque for O(1) operations**
The original code used `queue.pop(0)` on a list, which is O(n) because it shifts all remaining elements. The line profiler shows this operation taking 15.4% of total time (2.327ms out of 15.129ms). The optimized version uses `collections.deque` with `popleft()`, which is O(1). This change alone eliminates the most expensive operation in the BFS traversal.

**2. Eliminated path copying with parent tracking**
The original code maintained complete paths by copying and extending them (`new_path = list(path)` + `new_path.append(neighbor)`), taking 19.7% of total time (12.6% + 7.1%). With thousands of nodes visited, this creates substantial memory allocation overhead. The optimized version stores only parent pointers in a dictionary and reconstructs the path once at the end, reducing both time and space complexity.

**Performance characteristics by test case type:**
- **Large linear graphs (1000+ nodes)**: Show the most dramatic improvement (400-433% faster) because they maximize the impact of both optimizations - many queue operations and long paths to copy
- **Small graphs (2-5 nodes)**: Actually perform 17-50% slower due to the overhead of importing deque and managing the parent dictionary, but the absolute difference is negligible (microseconds)
- **Dense/branching graphs**: Show moderate improvements (10-96% faster) as they benefit from reduced queue overhead but have shorter average path lengths
- **Disconnected graphs**: Benefit significantly (286% faster) when no path exists, as the BFS explores many nodes before terminating

The optimization transforms the algorithm from O(V²) time complexity (due to path copying) to O(V + E), making it scale much better for larger graphs while maintaining identical BFS shortest-path semantics.

Author: codeflash-ai[bot]

src/dsa/various.py

@@ -1,4 +1,5 @@
 import re
+from collections import deque
 
 
 class Graph:
@@ -96,21 +97,25 @@ def find_shortest_path(self, start: str, end: str) -> list[str]:
         if start not in self.graph or end not in self.graph:
             return []
 
-        queue = [[start]]
+        queue = deque([start])
         visited = set([start])
+        parent = {start: None}
 
         while queue:
-            path = queue.pop(0)
-            node = path[-1]
+            node = queue.popleft()
 
             if node == end:
-                return path
+                # Reconstruct path backwards
+                path = []
+                while node is not None:
+                    path.append(node)
+                    node = parent[node]
+                return path[::-1]
 
             for neighbor in self.graph.get(node, []):
                 if neighbor not in visited:
                     visited.add(neighbor)
-                    new_path = list(path)
-                    new_path.append(neighbor)
-                    queue.append(new_path)
+                    parent[neighbor] = node
+                    queue.append(neighbor)
 
         return []  # No path found