It is often handy to store a binary tree in a file. Assume each node in the binary tree contains a character string. Assume also that all operations you need on strings are provided. For example, you...

It is often handy to store a binary tree in a file. Assume each node in the binary tree contains a character string. Assume also that all operations you need on strings are provided. For example, you do not need to design algorithms to test if a string equals ".", to write a string into a file, or to read a string from a file. To create the file in preorder file format do a preorder traversal of the tree, when a node is visited put the character string in the file followed by a newline and when a null is visited put a dot, ".", followed by a newline. For example, the tree                                                           a                             /   \                            b     c                           /    /   \                          d    e     f is stored as the file "a b d . . . c e . . f . ." where spaces indicate newlines. Design an algorithm which outputs the preorder file format of a binary tree given a pointer to the root of a binary tree. Assume the binary tree has nodes with fields "data", "left_child", and "right_child". Design an algorithm which takes a preorder file format of a binary tree and produces the binary tree. Hint: an effective approach is to design a recursive function that processes a sequence of lines in a file and returns a binary tree.