From a5f49f916277161302453ad25ef240c4d3b352c8 Mon Sep 17 00:00:00 2001
From: "codeflash-ai[bot]"
 <148906541+codeflash-ai[bot]@users.noreply.github.com>
Date: Thu, 15 Jan 2026 03:37:39 +0000
Subject: [PATCH] Optimize find_last_node
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Brief: The optimized version replaces a repeated scan of the edges for every node with a single pass that collects all edge sources into a set, turning an O(N*M) check into O(N+M) work. It also adds a small fast-path for the empty-edges case to avoid unnecessary work and preserve the original function's behavior. These changes explain the ~168x measured speedup (52 ms → 307 μs).

What changed and why it’s faster
- Precompute sources set: The original code used
  next((n for n in nodes if all(e["source"] != n["id"] for e in edges)), None)
  which, for each node, iterates over edges (the all(...) generator). That is O(N * M) comparisons in the worst case (N = number of nodes, M = number of edges).
  The optimized code computes sources = {e["source"] for e in edges} once (O(M)) and then checks n["id"] not in sources for each node (O(1) average per membership test). Total complexity becomes O(M + N).
- Fast-path for empty edges: If edges is empty, the original all(...) check is vacuously true and returns the first node. The optimized code preserves that behavior with if not edges: return next(iter(nodes), None). This avoids building an unnecessary set and is faster for the common "no edges" case.
- Small memory/time tradeoff: We allocate a set of unique sources (size ≤ M). The small extra memory is offset by the large reduction in repeated iteration when M and N are non-trivial.

Evidence in the profiler
- Original line profiler shows all time was spent in the single generator/all(...) check (repeated traversal of edges per node).
- Optimized profiler shows time split between building the sources set and doing cheap membership tests. Building the set is linear in edges and then each node check is a single O(1) membership test — much cheaper than re-scanning edges each time.

Behavioral impact and correctness
- Semantics preserved:
  - Returns the first node that is not a source in any edge (same as original).
  - When edges is empty, returns the first node (preserved by the fast-path).
  - Malformed edges missing "source" still raise KeyError (behavior unchanged).
  - Duplicate ids and type-mismatch behavior remains identical.
- Performance tradeoffs:
  - For very small inputs (e.g., empty nodes or tiny lists), the micro-overhead of branching and set creation can be similar or slightly higher; tests show one tiny regression when nodes are empty (~15% slower in one case). This is expected and negligible in real workloads.
  - For moderate-to-large inputs (the heavy cases), the improvement is dramatic — tests like large_chain and large_unordered_edges show orders-of-magnitude speedups.

When this matters (based on tests)
- Best for workloads with many nodes and/or many edges (large_chain, large_unordered_edges): huge wins because you avoid repeated scanning of edges.
- Also benefits normal cases like duplicate ids, unordered edges, and typical graphs — basically any non-trivial graph.
- Minimal downside for trivial inputs.

Complexity summary
- Original: O(N * M) time, O(1) extra space.
- Optimized: O(N + M) time, O(M) extra space (for the set of sources).

In short: change from repeated edge scans to a single set-construction + O(1) membership checks explains the significant runtime improvement while preserving the original function’s behavior.
---
 src/algorithms/graph.py | 9 ++++++++-
 1 file changed, 8 insertions(+), 1 deletion(-)

diff --git a/src/algorithms/graph.py b/src/algorithms/graph.py
index e944b2d..b653c58 100644
--- a/src/algorithms/graph.py
+++ b/src/algorithms/graph.py
@@ -47,7 +47,14 @@ 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 edges is empty the original implementation effectively returns the
+    # first node; preserve that behavior.
+    if not edges:
+        return next(iter(nodes), None)
+
+    # Build a set of sources to avoid repeated iteration over edges
+    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]: