Question
Given a directed graph with n nodes (0..n-1) and edges [u, v, cap, cost] (per-unit cost, non-negative capacity), find the maximum flow from source s to sink t and, among all max flows, the minimum total cost. Return a two-element list [max_flow, min_cost]. Costs are non-negative integers. If t is unreachable return [0, 0]. Assume 1 <= n <= 200 with small capacities so successive shortest augmenting paths finish under 5s.
min_cost_max_flow(n: int, edges: list[list[int]], s: int, t: int) → list[int][4,[[0,1,2,1],[0,2,1,2],[1,3,1,1],[2,3,2,1],[1,2,1,1]],0,3]out[3,8]State your approach and its time/space complexity out loud before you optimize. Handle the edge cases (empty input, duplicates, overflow), and say why you chose this over the brute force. Green tests are the floor, not the grade.
Vibe coding: describe the solution in plain language (or narrate it) and the coach grades your approach. Generating runnable code from your description is coming next.