题目要求
Serialization is the process of converting a data structure or object into a sequence of bits so that it can be stored in a file or memory buffer, or transmitted across a network connection link to be reconstructed later in the same or another computer environment.
Design an algorithm to serialize and deserialize a binary search tree. There is no restriction on how your serialization/deserialization algorithm should work. You just need to ensure that a binary search tree can be serialized to a string and this string can be deserialized to the original tree structure.
The encoded string should be as compact as possible.
Note: Do not use class member/global/static variables to store states. Your serialize and deserialize algorithms should be stateless.将二叉搜索树序列化和反序列化，序列化是指将树用字符串的形式表示，反序列化是指将字符串形式的树还原成原来的样子。
思路和代码
对于树的序列化，可以直接联想到对树的遍历。树的遍历包括前序遍历，中序遍历，后序遍历和水平遍历，并且可知前序遍历和中序遍历，或中序遍历和后序遍历可以构成一棵唯一的树。除此以外，因为这是一棵二叉搜索树，可知该树的中序遍历就是所有元素的从小到大的排列。
举个例子，假如一棵树的结构如下：
3
/ \
2 4
\
1该树的前序遍历结果为3,2,1,4，中序遍历为1,2,3,4。再仔细分析前序遍历的结果，结合二叉搜索树可知，比中间节点小的值一定位于左子树，反之一定位于右子树，即可以对前序遍历进行分割3,|2,1,|4。也就是说，我们可以只利用前序遍历，就可以区分出二叉搜索树的左子树和右子树。
代码如下：
public String serialize(TreeNode root) {
StringBuilder sb = new StringBuilder();
preorder(root, sb);
return sb.toString();
}
public void preorder(TreeNode root, StringBuilder result) {
if(root != null) {
result.append(root.val);
result.append(":");
preorder(root.left, result);
preorder(root.right, result);
}
}
// Decodes your encoded data to tree.
public TreeNode deserialize(String data) {
if(data==null || data.isEmpty()) return null;
String[] preorder = data.split(":");
String[] inorder = Arrays.copyOf(preorder, preorder.length);
Arrays.sort(inorder, new Comparator(){
@Override
public int compare(String o1, String o2) {
Integer i1 = Integer.valueOf(o1);
Integer i2 = Integer.valueOf(o2);
return i1.compareTo(i2);
}
});
return build(inorder, preorder, 0, 0, inorder.length);
}
public TreeNode build(String[] inorder, String[] preorder, int inorderStart, int preorderStart, int length) {
if(length <= 0) return null;
TreeNode root = new TreeNode(Integer.valueOf(preorder[preorderStart]));
for(int i = inorderStart ; i < inorderStart+length ; i++) {
if(inorder[i].equals(preorder[preorderStart])) {
root.left = build(inorder, preorder, inorderStart, preorderStart+1, i-inorderStart);
root.right = build(inorder, preorder, i+1, preorderStart+i-inorderStart+1, inorderStart+length-i-1);
break;
}
}
return root;
} 这里的代码是直接使用排序生成了二叉搜索树的中序遍历的结果，并利用先序遍历和中序遍历构造了一棵二叉搜索树。假如二叉搜索树的节点较多，该算法将会占用大量的额外空间。可以只用先序遍历作为构造树的输入，代码如下：
public TreeNode deserialize(String data) {
if (data==null) return null;
String[] strs = data.split(":");
Queue q = new LinkedList<>();
for (String e : strs) {
q.offer(Integer.parseInt(e));
}
return getNode(q);
}
private TreeNode getNode(Queue q) {
if (q.isEmpty()) return null;
TreeNode root = new TreeNode(q.poll());//root (5)
Queue samllerQueue = new LinkedList<>();
while (!q.isEmpty() && q.peek() < root.val) {
samllerQueue.offer(q.poll());
}
root.left = getNode(samllerQueue);
root.right = getNode(q);
return root;
}