1、编程求一个二元关系的自反闭包、对称闭包和传递闭包。我要代码

在编程中，二元关系的自反闭包、对称闭包和传递闭包通常是图论中的概念，用于描述集合之间的连接模式。以下是这三个概念及其简单的Python代码示例，假设我们有一个名为`relation`的二元关系存储在列表的列表中：

def self_reflexive_closure(relation):
    new_relations = relation.copy()
    for i in range(len(new_relations)):
        new_relations[i].append((i, i))
    return new_relations

def symmetric_closure(relation):
    new_relations = [(a, b) if (b, a) not in relation else relation[(a, b)] for a in relation for b in relation]
    return new_relations

def transitive_closure(relation):
    closure = {}
    for pair in relation:
        a, b = pair
        if a not in closure:
            closure[a] = set([b])
        else:
            closure[a].add(b)
    
    while True:
        updated = False
        for key, values in closure.items():
            for value in values:
                if value in closure and key not in closure[value]:
                    closure[key].add(value)
                    updated = True
        if not updated:
            break
    
    result = []
    for key, values in closure.items():
        result.append((key, tuple(sorted(values))))
    return result

# 示例
relation_example = [
    (0, 1),
    (1, 2)
]

self_ref = self_reflexive_closure(relation_example)
symmetric_rel = symmetric_closure(relation_example)
transitive_rel = transitive_closure(relation_example)

print("自反闭包:", self_ref)
print("对称闭包:", symmetric_rel)
print("传递闭包:", transitive_rel)