Optimize heap operations in min-cost flow slope calculation - #30
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…omparison Encode (dist, vertex) as dist*n+v so heapq operates on plain integers instead of tuples, eliminating per-push/pop tuple allocation and element-wise comparison overhead.
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Summary
This PR optimizes the heap operations in the
slope()method of the min-cost flow algorithm by encoding node information directly into heap values instead of using tuples.Key Changes
self.n: Storeself.nin a local variablento reduce repeated attribute lookups(distance, node)with encoded integer values:sinstead of(0, s)dist[e["to"]] * n + e["to"]instead of(dist[e["to"]], e["to"])heapq.heappop(que) % ninstead ofheapq.heappop(que)[1]Implementation Details
The optimization encodes both distance and node information into a single integer by using the formula
distance * n + node_id. This allows the heap to naturally sort by distance (primary) and node ID (secondary) while reducing memory overhead and tuple allocation overhead. The node is recovered using modulo arithmetic during dequeue operations.https://claude.ai/code/session_011Ns3CZfpPTnJM3tDqCaDVt