Question
You are given a directed flow network on n nodes as edges [u, v, cap, cost] (capacity and per-unit cost are non-negative integers), a source s, a target t, and an integer K. Find the minimum total cost to send EXACTLY K units of flow from s to t, where each unit traversing an edge pays that edge's cost. Return the minimum cost, or -1 if it is impossible to route K units. Constraints: up to 50 nodes; small capacities and K (each <= a few hundred).
min_cost_flow(n: int, edges: list[list[int]], s: int, t: int, K: int) → int[4,[[0,1,2,1],[0,2,2,2],[1,3,2,1],[2,3,2,1]],0,3,3]out7State 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.