Convert recursive DFS to iterative stack-based implementation

[shakayami]

Summary

Refactored the DFS function in the max flow algorithm from a recursive implementation to an iterative stack-based approach. This change improves robustness by eliminating potential stack overflow issues on deep graphs while maintaining the same algorithmic correctness.

Key Changes

• Converted recursive DFS to iterative implementation: Replaced the recursive dfs(v, up) function with an iterative version using an explicit stack data structure
• Updated function signature: Changed dfs(v, up) to dfs(s_, t_, up) to accept both source and target nodes, enabling the iterative approach
• Introduced path tracking: Added a path list to track (node, edge_index) pairs during traversal, allowing capacity updates to be applied after finding an augmenting path
• Refactored edge iteration logic: Moved the edge iteration into a while loop within the main stack processing loop, with explicit Iter[v] increment management
• Simplified capacity updates: Consolidated capacity updates into a single loop that processes the discovered path in reverse order

Implementation Details

• The iterative approach maintains a stack of (node, flow_into_node) tuples representing the current traversal state
• When the source node is reached, the algorithm updates all edge capacities along the discovered path in a single pass
• The level array invalidation (level[v] = self.n) is preserved to maintain the algorithm's efficiency properties
• The function returns 0 when no augmenting path is found, consistent with the original behavior

https://claude.ai/code/session_01JAwRWVg1ZbRWobeGyFuc6a