Add IPM-based maximum flow solver (Chen et al. 2022)

[kenkoooo]

Summary

• Implement an interior point method (IPM) based maximum flow algorithm inspired by Chen, Kyng, Liu, Peng, Gutenberg, Sachdeva (2022) "Maximum Flow and Minimum-Cost Flow in Almost-Linear Time"
• Reduces max flow to min-cost circulation, then solves with a primal-dual IPM using weighted Laplacian Newton steps
• Modular design with 7 components, each independently unit-tested (23 tests total including GRL_6_A integration)

Algorithm components

1. solve_laplacian — Gaussian elimination for weighted Laplacian systems
2. prune_dead_ends — Iterative removal of edges to/from dead-end nodes
3. compute_excess — Flow conservation violation at each node
4. compute_step_size — Line search keeping flow strictly interior
5. initialize_flow — Weighted projection of cap/2 onto conservation constraints
6. ipm_step — Newton step via KKT conditions of barrier-penalized circulation
7. max_flow — Integration: reduction → pruning → initialization → IPM loop → rounding

Test plan

• Unit tests for Laplacian solver (path, triangle, weighted, single node)
• Unit tests for dead-end pruning (cycle, dead-end, cascading, all dead)
• Unit tests for excess computation
• Unit tests for step size bounds
• Unit tests for flow initialization (conservation + interiority)
• Unit tests for IPM step (feasibility, positive alpha, convergence)
• Integration tests (simple, no path, single edge)
• GRL_6_A: all 40 test cases pass

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