From 43bd0d975719d1348888d285b7a7358930c5c8ef Mon Sep 17 00:00:00 2001
From: "codeflash-ai[bot]"
 <148906541+codeflash-ai[bot]@users.noreply.github.com>
Date: Sat, 27 Dec 2025 00:21:17 +0000
Subject: [PATCH] Optimize find_last_node
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The optimized code achieves a **228x speedup** (from 78.6ms to 344μs) by eliminating a quadratic nested loop pattern.

**Key optimization:**
- **Original approach**: For each node, iterates through *all* edges to check if the node's ID appears as a source — O(N×M) complexity where N is the number of nodes and M is the number of edges.
- **Optimized approach**: Pre-builds a set of all source IDs in one pass, then performs O(1) membership checks for each node — O(N+M) complexity.

**Why this matters:**
Python's `set` lookup using hash tables is extremely fast (O(1) average case), while the original `all()` with a generator expression must scan through every edge for each node. The performance gap widens dramatically as the graph grows:
- **Large chain graph (1000 nodes)**: 18.5ms → 56.8μs (324x faster)
- **Large cycle graph (1000 nodes)**: 18.4ms → 55.1μs (333x faster)

**Test case performance patterns:**
- Small graphs (2-3 nodes): 30-91% faster — modest gains due to overhead of set creation
- Medium graphs (10-100 nodes): Consistent 50-80% improvements
- Large graphs (1000+ nodes): 300-330x speedups — the optimization truly shines here
- Empty/single node cases: Slight overhead (~10% slower) due to set creation, but negligible in absolute terms (nanoseconds)

**Impact considerations:**
The optimization is most beneficial when:
1. The function is called repeatedly in workflows involving large graphs
2. Graph processing happens in performance-critical paths (data pipelines, real-time graph analysis)
3. The edge count is substantial relative to node count

The tradeoff is minimal: a tiny overhead for empty graphs (which complete in <1μs anyway) in exchange for massive gains on any non-trivial graph structure.
---
 src/algorithms/graph.py | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/src/algorithms/graph.py b/src/algorithms/graph.py
index 777ea3b..156485a 100644
--- a/src/algorithms/graph.py
+++ b/src/algorithms/graph.py
@@ -47,7 +47,8 @@ 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)
+    source_ids = {e["source"] for e in edges}
+    return next((n for n in nodes if n["id"] not in source_ids), None)
 
 
 def find_leaf_nodes(nodes: list[dict], edges: list[dict]) -> list[dict]: