1、什么是二叉树的序列化与反序列化
二叉树就是节点在内存区域中串联起来的，但是如果掉电，内存上的数据就没有了。为了保存这种结构，将二叉树用字符串的形式保存到硬盘中，这就是序列化；从字符串形式转换为二叉树，这就是反序列化。
唯一的字符串会对应唯一的结构，唯一的结构也会对应唯一的字符串，即字符串和二叉树是一一对应的。
【思路】首先认为 NULL 是不可忽略的，遇到 NULL 就用 # 或者其他字符代替。且每访问结束一个节点，用分隔符隔开。
2、先序方式序列化和反序列化
【例子】
上图红色数字就是先序遍历的顺序，所以得到的字符串就是 “1，1，#，1，#，#，#”。
之所以要用分隔符隔开，是为了防止二义性，比如如下两棵树：
【代码实现】
//先序序列化二叉树 void preS(TreeNode *root, queue&ans) { if (root == nullptr) ans.push("#"); else { //每个节点转成的字符串保存到队列中 ans.push(to_string(root->value)); preS(root->lchild, ans); preS(root->rchild, ans); } } queue preOrderSerial(TreeNode *root) { queue ans; preS(root, ans); return ans; } TreeNode *preb(queue &prelist) { string value = prelist.front(); prelist.pop(); //空树 if (value == "#") return nullptr; TreeNode *root = new TreeNode(stoi(value)); //每个节点字符串转成整数 root->lchild = preb(prelist); root->rchild = preb(prelist); return root; } //以先序序列化还原二叉树, 即反序列化 TreeNode *buildByPreQueue(queue &prelist) { if (prelist.size() == 0) return nullptr; return preb(prelist); }
3、后序方式序列化和反序列化
//后序序列化 void posS(TreeNode *root, queue&ans) { if (root == nullptr) ans.push("#"); else { posS(root->lchild, ans); posS(root->rchild, ans); ans.push(to_string(root->value)); } } queue posOrderSerial(TreeNode *root) { queue ans; posS(root, ans); return ans; } //后序反序列化 TreeNode *posB(stack &posstack) { string value = posstack.top(); posstack.pop(); if (value == "#") return nullptr; TreeNode *root = new TreeNode(stoi(value)); root->rchild = posB(posstack); root->lchild = posB(posstack); return root; } TreeNode *buildByPosQueue(queue &poslist) { if (poslist.size() == 0) return nullptr; stack sta; //栈中的顺序为：中右左 while (!poslist.empty()) { sta.push(poslist.front()); poslist.pop(); } return posB(sta); }
4、层序方式序列化和反序列化
//层序序列化 queuelevelSerial(TreeNode *root) { queue ans; if (root == nullptr) { ans.push("#"); } else { ans.push(to_string(root->value)); //准备队列，用于层序遍历 queue que; que.push(root); while (!que.empty()) { TreeNode *cur = que.front(); que.pop(); if (cur->lchild != nullptr) { ans.push(to_string(cur->lchild->value)); que.push(cur->lchild); } else { ans.push("#"); } if (cur->rchild != nullptr) { ans.push(to_string(cur->rchild->value)); que.push(cur->rchild); } else { ans.push("#"); } } } return ans; } //层序反序列化 TreeNode *generateTreeNode(string str) { if (str == "#") return nullptr; return new TreeNode(stoi(str)); } TreeNode *buildByLevelQueue(queue &levelList) { if (levelList.size() == 0) { return nullptr; } TreeNode *root = generateTreeNode(levelList.front()); levelList.pop(); queue que; if (root != nullptr) { que.push(root); } TreeNode *cur = nullptr; while (!que.empty()) { cur = que.front(); que.pop(); cur->lchild = generateTreeNode(levelList.front()); levelList.pop(); cur->rchild = generateTreeNode(levelList.front()); levelList.pop(); if (cur->lchild != nullptr) { que.push(cur->lchild); } if (cur->rchild != nullptr) { que.push(cur->rchild); } } return root; }
5、完整代码 C++ 版
/************************************************************************* > File Name: 029.二叉树的序列化与反序列化.cpp > Author: Maureen > Mail: [email protected] > Created Time: 一 6/20 17:40:56 2022 ************************************************************************/ #include#include #include #include #include using namespace std; /* * 二叉树可以通过先序、后序或者按层遍历的方式序列化和反序列化， * 以下代码全部实现了。 * 但是，二叉树无法通过中序遍历的方式实现序列化和反序列化 * 因为不同的两棵树，可能得到同样的中序序列，即便补了空位置也可能一样。 * 比如如下两棵树 * __2 * / * 1 * 和 * 1__ * \ * 2 * 补足空位置的中序遍历结果都是{ null, 1, null, 2, null} * * */ class TreeNode { public: int value; TreeNode *lchild; TreeNode *rchild; TreeNode(int data) : value(data) {} }; //先序序列化二叉树 void preS(TreeNode *root, queue &ans) { if (root == nullptr) ans.push("#"); else { //每个节点转成的字符串保存到队列中 ans.push(to_string(root->value)); preS(root->lchild, ans); preS(root->rchild, ans); } } queue preOrderSerial(TreeNode *root) { queue ans; preS(root, ans); return ans; } //以先序序列化还原二叉树, 即反序列化 TreeNode *preb(queue &prelist) { string value = prelist.front(); prelist.pop(); //空树 if (value == "#") return nullptr; TreeNode *root = new TreeNode(stoi(value)); //每个节点字符串转成整数 root->lchild = preb(prelist); root->rchild = preb(prelist); return root; } TreeNode *buildByPreQueue(queue &prelist) { if (prelist.size() == 0) return nullptr; return preb(prelist); } //后序序列化 void posS(TreeNode *root, queue &ans) { if (root == nullptr) ans.push("#"); else { posS(root->lchild, ans); posS(root->rchild, ans); ans.push(to_string(root->value)); } } queue posOrderSerial(TreeNode *root) { queue ans; posS(root, ans); return ans; } //后序反序列化 TreeNode *posB(stack &posstack) { string value = posstack.top(); posstack.pop(); if (value == "#") return nullptr; TreeNode *root = new TreeNode(stoi(value)); root->rchild = posB(posstack); root->lchild = posB(posstack); return root; } TreeNode *buildByPosQueue(queue &poslist) { if (poslist.size() == 0) return nullptr; stack sta; //栈中的顺序为：中右左 while (!poslist.empty()) { sta.push(poslist.front()); poslist.pop(); } return posB(sta); } //层序序列化 queue levelSerial(TreeNode *root) { queue ans; if (root == nullptr) { ans.push("#"); } else { ans.push(to_string(root->value)); //准备队列，用于层序遍历 queue que; que.push(root); while (!que.empty()) { TreeNode *cur = que.front(); que.pop(); if (cur->lchild != nullptr) { ans.push(to_string(cur->lchild->value)); que.push(cur->lchild); } else { ans.push("#"); } if (cur->rchild != nullptr) { ans.push(to_string(cur->rchild->value)); que.push(cur->rchild); } else { ans.push("#"); } } } return ans; } //层序反序列化 TreeNode *generateTreeNode(string str) { if (str == "#") return nullptr; return new TreeNode(stoi(str)); } TreeNode *buildByLevelQueue(queue &levelList) { if (levelList.size() == 0) { return nullptr; } TreeNode *root = generateTreeNode(levelList.front()); levelList.pop(); queue que; if (root != nullptr) { que.push(root); } TreeNode *cur = nullptr; while (!que.empty()) { cur = que.front(); que.pop(); cur->lchild = generateTreeNode(levelList.front()); levelList.pop(); cur->rchild = generateTreeNode(levelList.front()); levelList.pop(); if (cur->lchild != nullptr) { que.push(cur->lchild); } if (cur->rchild != nullptr) { que.push(cur->rchild); } } return root; } //for test TreeNode *generate(int level, int maxLevel, int maxValue) { if (level > maxLevel || rand() % 100 < 0.5) return nullptr; TreeNode *root = new TreeNode(rand() % maxValue); root->lchild = generate(level + 1, maxLevel, maxValue); root->rchild = generate(level + 1, maxLevel, maxValue); return root; } TreeNode *generateRandomBST(int maxLen, int maxVal) { return generate(1, maxLen, maxVal); } bool isSameValueStructure(TreeNode *root1, TreeNode *root2) { if (root1 == nullptr && root2 != nullptr) return false; if (root1 != nullptr && root2 == nullptr) return false; if (root1 == nullptr && root2 == nullptr) return true; if (root1->value != root2->value) return false; return isSameValueStructure(root1->lchild, root2->lchild) && isSameValueStructure(root1->rchild, root2->rchild); } string getSpace(int num) { string space = ""; for (int i = 0; i < num; i++) { space += " "; } return space; } void printInOrder(TreeNode *root, int height, string to, int len) { if (root == nullptr) return ; printInOrder(root->rchild, height + 1, "v", len); string val = to + to_string(root->value) + to; int lenM = val.length(); int lenL = (len - lenM) / 2; int lenR = len - lenM - lenL; val = getSpace(lenL) + val + getSpace(lenR); cout << getSpace(height * len) + val << endl; printInOrder(root->lchild, height + 1, "^", len); } void printTree(TreeNode *root) { cout << "Binary Tree:" << endl; printInOrder(root, 0, "H", 7); cout << endl; } int main() { srand(time(0)); int maxLevel = 5; int maxValue = 100; int testTime = 1000000; cout << "test begin" << endl; for (int i = 0; i < testTime + 1; i++) { TreeNode *root = generateRandomBST(maxLevel, maxValue); queue pre = preOrderSerial(root); queue post = posOrderSerial(root); queue level = levelSerial(root); TreeNode *preBuild = buildByPreQueue(pre); TreeNode *posBuild = buildByPosQueue(post); TreeNode *levelBuild = buildByLevelQueue(level); /*bool isPreBuildisSuccess = isSameValueStructure(root, preBuild); bool isPosBuildisSuccess = isSameValueStructure(root, posBuild); bool isLevelBuildSuccess = isSameValueStructure(root, levelBuild); cout << isPreBuildisSuccess << ", " << isPosBuildisSuccess << ", " << isLevelBuildSuccess << endl;*/ if (!isSameValueStructure(preBuild, posBuild) || !isSameValueStructure(posBuild, levelBuild)) { cout << "Oops!" << endl; break; } if (i && i % 100 == 0) cout << i << " cases passed!" << endl; } cout << "test finish!" << endl; return 0; }
Java 版
package class11;
import java.util.LinkedList;
import java.util.Queue;
import java.util.Stack;
public class Code02_SerializeAndReconstructTree {
/*
* 二叉树可以通过先序、后序或者按层遍历的方式序列化和反序列化，
* 以下代码全部实现了。
* 但是，二叉树无法通过中序遍历的方式实现序列化和反序列化
* 因为不同的两棵树，可能得到同样的中序序列，即便补了空位置也可能一样。
* 比如如下两棵树
* __2
* /
* 1
* 和
* 1__
* \
* 2
* 补足空位置的中序遍历结果都是{ null, 1, null, 2, null}
*
* */
public static class Node {
public int value;
public Node left;
public Node right;
public Node(int data) {
this.value = data;
}
}
public static Queue preSerial(Node head) {
Queue ans = new LinkedList<>();
pres(head, ans);
return ans;
}
public static void pres(Node head, Queue ans) {
if (head == null) {
ans.add(null);
} else {
ans.add(String.valueOf(head.value));
pres(head.left, ans);
pres(head.right, ans);
}
}
public static Queue inSerial(Node head) {
Queue ans = new LinkedList<>();
ins(head, ans);
return ans;
}
public static void ins(Node head, Queue ans) {
if (head == null) {
ans.add(null);
} else {
ins(head.left, ans);
ans.add(String.valueOf(head.value));
ins(head.right, ans);
}
}
public static Queue posSerial(Node head) {
Queue ans = new LinkedList<>();
poss(head, ans);
return ans;
}
public static void poss(Node head, Queue ans) {
if (head == null) {
ans.add(null);
} else {
poss(head.left, ans);
poss(head.right, ans);
ans.add(String.valueOf(head.value));
}
}
public static Node buildByPreQueue(Queue prelist) {
if (prelist == null || prelist.size() == 0) {
return null;
}
return preb(prelist);
}
public static Node preb(Queue prelist) {
String value = prelist.poll();
if (value == null) {
return null;
}
Node head = new Node(Integer.valueOf(value));
head.left = preb(prelist);
head.right = preb(prelist);
return head;
}
public static Node buildByPosQueue(Queue poslist) {
if (poslist == null || poslist.size() == 0) {
return null;
}
// 左右中 -> stack(中右左)
Stack stack = new Stack<>();
while (!poslist.isEmpty()) {
stack.push(poslist.poll());
}
return posb(stack);
}
public static Node posb(Stack posstack) {
String value = posstack.pop();
if (value == null) {
return null;
}
Node head = new Node(Integer.valueOf(value));
head.right = posb(posstack);
head.left = posb(posstack);
return head;
}
public static Queue levelSerial(Node head) {
Queue ans = new LinkedList<>();
if (head == null) {
ans.add(null);
} else {
ans.add(String.valueOf(head.value));
Queue queue = new LinkedList();
queue.add(head);
while (!queue.isEmpty()) {
head = queue.poll(); // head 父 子
if (head.left != null) {
ans.add(String.valueOf(head.left.value));
queue.add(head.left);
} else {
ans.add(null);
}
if (head.right != null) {
ans.add(String.valueOf(head.right.value));
queue.add(head.right);
} else {
ans.add(null);
}
}
}
return ans;
}
public static Node buildByLevelQueue(Queue levelList) {
if (levelList == null || levelList.size() == 0) {
return null;
}
Node head = generateNode(levelList.poll());
Queue queue = new LinkedList();
if (head != null) {
queue.add(head);
}
Node node = null;
while (!queue.isEmpty()) {
node = queue.poll();
node.left = generateNode(levelList.poll());
node.right = generateNode(levelList.poll());
if (node.left != null) {
queue.add(node.left);
}
if (node.right != null) {
queue.add(node.right);
}
}
return head;
}
public static Node generateNode(String val) {
if (val == null) {
return null;
}
return new Node(Integer.valueOf(val));
}
// for test
public static Node generateRandomBST(int maxLevel, int maxValue) {
return generate(1, maxLevel, maxValue);
}
// for test
public static Node generate(int level, int maxLevel, int maxValue) {
if (level > maxLevel || Math.random() < 0.5) {
return null;
}
Node head = new Node((int) (Math.random() * maxValue));
head.left = generate(level + 1, maxLevel, maxValue);
head.right = generate(level + 1, maxLevel, maxValue);
return head;
}
// for test
public static boolean isSameValueStructure(Node head1, Node head2) {
if (head1 == null && head2 != null) {
return false;
}
if (head1 != null && head2 == null) {
return false;
}
if (head1 == null && head2 == null) {
return true;
}
if (head1.value != head2.value) {
return false;
}
return isSameValueStructure(head1.left, head2.left) && isSameValueStructure(head1.right, head2.right);
}
// for test
public static void printTree(Node head) {
System.out.println("Binary Tree:");
printInOrder(head, 0, "H", 17);
System.out.println();
}
public static void printInOrder(Node head, int height, String to, int len) {
if (head == null) {
return;
}
printInOrder(head.right, height + 1, "v", len);
String val = to + head.value + to;
int lenM = val.length();
int lenL = (len - lenM) / 2;
int lenR = len - lenM - lenL;
val = getSpace(lenL) + val + getSpace(lenR);
System.out.println(getSpace(height * len) + val);
printInOrder(head.left, height + 1, "^", len);
}
public static String getSpace(int num) {
String space = " ";
StringBuffer buf = new StringBuffer("");
for (int i = 0; i < num; i++) {
buf.append(space);
}
return buf.toString();
}
public static void main(String[] args) {
int maxLevel = 5;
int maxValue = 100;
int testTimes = 1000000;
System.out.println("test begin");
for (int i = 0; i < testTimes; i++) {
Node head = generateRandomBST(maxLevel, maxValue);
Queue pre = preSerial(head);
Queue pos = posSerial(head);
Queue level = levelSerial(head);
Node preBuild = buildByPreQueue(pre);
Node posBuild = buildByPosQueue(pos);
Node levelBuild = buildByLevelQueue(level);
if (!isSameValueStructure(preBuild, posBuild) || !isSameValueStructure(posBuild, levelBuild)) {
System.out.println("Oops!");
}
}
System.out.println("test finish!");
}
}
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