From c73d09e0923e21b0f11484bbe553d630ac623890 Mon Sep 17 00:00:00 2001
From: "codeflash-ai[bot]"
 <148906541+codeflash-ai[bot]@users.noreply.github.com>
Date: Tue, 30 Dec 2025 08:23:56 +0000
Subject: [PATCH] Optimize find_last_node
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The optimized code achieves a **137x speedup** by replacing an O(N×M) nested loop with an O(M+N) set-based lookup approach.

**Key optimization:**

The original code uses a nested iteration pattern:
```python
all(e["source"] != n["id"] for e in edges)
```
For each node, this checks ALL edges to verify none have that node as a source. With N nodes and M edges, this creates N×M comparisons in the worst case.

The optimized code pre-computes a set of source node IDs:
```python
sources = {e["source"] for e in edges}
return next((n for n in nodes if n["id"] not in sources), None)
```
This builds the source set once (O(M)) and then performs O(1) set membership checks for each node (O(N)), resulting in O(M+N) total complexity.

**Why this matters:**

The speedup is dramatic on larger graphs. Test results show:
- **Large linear chain (1000 nodes):** 18.4ms → 58.4μs (**314x faster**)
- **Large cycle (1000 nodes):** 18.3ms → 57.6μs (**316x faster**)
- **Dense graph (100 nodes, 2500 edges):** 2.23ms → 52.8μs (**42x faster**)

Even small graphs benefit significantly (60-100% speedups) because set construction and lookup are highly optimized in Python, while the nested `all()` with generator expressions has per-iteration overhead.

**Edge case handling:**

The `if not edges:` check preserves the original behavior where an empty edge list allows returning the first node without accessing `n["id"]`, avoiding `KeyError` when nodes lack an 'id' field. This maintains backward compatibility while enabling the optimization for all normal cases.
---
 src/algorithms/graph.py | 5 ++++-
 1 file changed, 4 insertions(+), 1 deletion(-)

diff --git a/src/algorithms/graph.py b/src/algorithms/graph.py
index 777ea3b..b6f3097 100644
--- a/src/algorithms/graph.py
+++ b/src/algorithms/graph.py
@@ -47,7 +47,10 @@ def find_shortest_path(self, start: str, end: str) -> list[str]:
 
 def find_last_node(nodes, edges):
     """This function receives a flow and returns the last node."""
-    return next((n for n in nodes if all(e["source"] != n["id"] for e in edges)), None)
+    if not edges:
+        return next((n for n in nodes), None)
+    sources = {e["source"] for e in edges}
+    return next((n for n in nodes if n["id"] not in sources), None)
 
 
 def find_leaf_nodes(nodes: list[dict], edges: list[dict]) -> list[dict]: