有没有一种快速算法可以将一个集合的所有分区生成大小为2的子集(和一个大小为1的子集)？

def generate_partitions(arr):
    def backtrack(start, path):
        if len(path) == len(arr):
            result.append(path[:])
            return
        for i in range(start, len(arr)):
            if i > start and arr[i] == arr[i - 1]:
                continue
            path.append([arr[i]])
            backtrack(i + 1, path)
            path.pop()

    result = []
    arr.sort()
    backtrack(0, [])
    partitions = []
    for partition in result:
        for i in range(len(partition)):
            sub_partition = partition[:i] + partition[i + 1:]
            for j in range(len(sub_partition)):
                new_partition = sub_partition[:j] + [[sub_partition[j][0], partition[i][0]]] + sub_partition[j + 1:]
                partitions.append(new_partition)
    return partitions

# 示例
arr = [1, 2, 3]
partitions = generate_partitions(arr)
for partition in partitions:
    print(partition)