以下是一个示例解决方案，使用Python实现前缀树（也称为字典树）和按顺序打印所有单词的功能：

class TrieNode:
    def __init__(self):
        self.children = {}
        self.is_word = False


class Trie:
    def __init__(self):
        self.root = TrieNode()

    def insert(self, word):
        node = self.root
        for char in word:
            if char not in node.children:
                node.children[char] = TrieNode()
            node = node.children[char]
        node.is_word = True

    def search(self, word):
        node = self.root
        for char in word:
            if char not in node.children:
                return False
            node = node.children[char]
        return node.is_word

    def starts_with(self, prefix):
        node = self.root
        for char in prefix:
            if char not in node.children:
                return []
            node = node.children[char]
        return self._dfs(node, prefix)

    def _dfs(self, node, prefix):
        result = []
        if node.is_word:
            result.append(prefix)
        for char in node.children:
            result += self._dfs(node.children[char], prefix + char)
        return result


# 创建一个前缀树
trie = Trie()

# 插入单词到前缀树中
trie.insert("apple")
trie.insert("banana")
trie.insert("bear")
trie.insert("cat")
trie.insert("dog")

# 按顺序打印前缀树中的所有单词
result = trie.starts_with("")
print(result)

运行上述代码将打印输出：['apple', 'banana', 'bear', 'cat', 'dog']，即按顺序打印了前缀树中的所有单词。