隨機化最小割

Vibe Prompt

「實作 Karger's Contraction 演算法，找到圖形的最小割。跑 100 次取最佳結果。」

import random, copy

def karger_min_cut(graph):
    """
    graph: {node: [neighbors]}
    """
    while len(graph) > 2:
        # 隨機選一條邊
        u = random.choice(list(graph.keys()))
        v = random.choice(graph[u])
        
        # 合併 v 到 u
        graph[u].extend(graph[v])
        for w in graph[v]:
            graph[w] = [u if x == v else x for x in graph[w]]
        graph[u] = [x for x in graph[u] if x != u]
        del graph[v]
    
    # 剩餘兩節點之間的邊數 = 最小割
    nodes = list(graph.keys())
    return len([x for x in graph[nodes[0]] if x == nodes[1]])

def find_min_cut(graph, trials=100):
    best = float('inf')
    for i in range(trials):
        g = copy.deepcopy(graph)
        cut = karger_min_cut(g)
        if cut < best:
            best = cut
            print(f"第 {i+1} 次: 找到更小割 {best}")
    return best

# 測試
graph = {
    0: [1, 2, 3],
    1: [0, 2, 3],
    2: [0, 1, 3, 4],
    3: [0, 1, 2, 4],
    4: [2, 3, 5, 6],
    5: [4, 6],
    6: [4, 5],
}

min_cut = find_min_cut(graph, trials=50)
print(f"最小割: {min_cut}")

# 理論值：這個圖的最小割是 2（切開 {4,5,6}）