在Python中使用SAT求解查找通过图中各折点的路径

import pycosat

def find_path(graph, start, end):
    # 创建变量
    variables = []
    for node in graph:
        variables.append([])
        for i in range(len(graph)):
            variables[-1].append(f"P_{node}_{i}")
    
    # 添加路径约束
    clauses = []
    for node in graph:
        for i in range(len(graph)):
            clause = []
            for j in range(len(graph)):
                if i == j:
                    clause.append(variables[node][j])
                else:
                    clause.append(f"-{variables[node][j]}")
            clauses.append(clause)
    
    # 添加起点和终点约束
    start_clause = [variables[start][0]]
    end_clause = [variables[end][len(graph)-1]]
    clauses.append(start_clause)
    clauses.append(end_clause)
    
    # 添加路径连续性约束
    for node in graph:
        for i in range(len(graph)-1):
            clause = [f"-{variables[node][i]}", variables[node][i+1]]
            clauses.append(clause)
    
    # 添加路径长度约束
    length_clause = []
    for node in graph:
        for i in range(len(graph)):
            length_clause.append(variables[node][i])
    clauses.append(length_clause)
    
    # 求解布尔公式
    solution = pycosat.solve(clauses)
    
    if solution != "UNSAT":
        path = []
        for node in graph:
            for i in range(len(graph)):
                if variables[node][i] in solution:
                    path.append(node)
                    break
        return path
    
    return None

# 示例图
graph = {
    "A": ["B", "C"],
    "B": ["C", "D"],
    "C": ["D"],
    "D": ["E"],
    "E": []
}

start_node = "A"
end_node = "E"
path = find_path(graph, start_node, end_node)

if path:
    print(f"找到路径：{path}")
else:
    print("未找到路径")