Commit 3ca33ab
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Optimize find_last_node
The optimization transforms an O(n*m) algorithm into an O(n+m) algorithm by eliminating redundant edge scanning.
**Key Changes:**
- **Pre-computed source set**: Creates a set `sources = {e["source"] for e in edges}` containing all source node IDs from edges
- **O(1) membership testing**: Replaces `all(e["source"] != n["id"] for e in edges)` with `n["id"] not in sources`
**Why This Is Faster:**
The original code performs a linear scan through all edges for every node being checked. With n nodes and m edges, this creates O(n*m) time complexity. For each node, it checks every edge to ensure that node isn't a source anywhere.
The optimized version builds the source set once in O(m) time, then performs O(1) hash table lookups for each node, resulting in O(n+m) total complexity.
**Performance Impact:**
The 245x speedup (from 101ms to 410μs) demonstrates the dramatic improvement, especially evident in large-scale test cases:
- `test_large_linear_chain` (1000 nodes): Benefits significantly as it avoids 1000×999 = 999,000 edge comparisons
- `test_large_fan_in` (1000 nodes): Similarly optimized from quadratic to linear scanning
- Small graphs see less dramatic but still substantial improvements
**Test Case Performance:**
The optimization is most beneficial for graphs with many edges relative to nodes, where the original's repeated edge scanning becomes a bottleneck. Even simple cases like `test_three_nodes_linear` benefit from avoiding redundant edge iterations.1 parent e776522 commit 3ca33ab
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