如何在给定的二叉树中找到最大大小为 K 的所有有根子树？

Question

如题。 如何有效地生成与原始二叉树共享同一根的所有子树？

Answer 1

这与生成所有大小为 k 的未标记二叉树非常相似，其算法如下所示：

trees(k):
    if k is zero:
        yield the null tree
    else:
        for i from 0 to k-1:
            for l in trees(i):
                for r in trees(k-i):
                    yield the tree whose root has left subtree l
                        and right subtree r

你应该能够在你最喜欢的编程语言中找到一个具体的实现。

为了解决这个问题，我们修改了这段代码，将给定的树与递归分开。

subtrees(T, k):
    if k is zero:
        yield the null tree
    else if T is not null:
        let L be the left subtree of T's root
        let R be the right subtree of T's root
        for i from 0 to k-1:
            for l in subtrees(L, i):
                for r in subtrees(R, k-i):
                    yield the tree whose root has the same value as T's,
                        with left subtree l and right subtree r