138 lines
3.5 KiB
C++
138 lines
3.5 KiB
C++
/**
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* File: array_binary_tree.cpp
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* Created Time: 2023-07-19
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* Author: krahets (krahets@163.com)
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*/
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#include "../utils/common.hpp"
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/* 数组表示下的二叉树类 */
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class ArrayBinaryTree {
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public:
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/* 构造方法 */
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ArrayBinaryTree(vector<int> arr) {
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tree = arr;
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}
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/* 列表容量 */
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int size() {
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return tree.size();
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}
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/* 获取索引为 i 节点的值 */
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int val(int i) {
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// 若索引越界，则返回 INT_MAX ，代表空位
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if (i < 0 || i >= size())
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return INT_MAX;
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return tree[i];
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}
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/* 获取索引为 i 节点的左子节点的索引 */
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int left(int i) {
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return 2 * i + 1;
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}
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/* 获取索引为 i 节点的右子节点的索引 */
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int right(int i) {
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return 2 * i + 2;
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}
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/* 获取索引为 i 节点的父节点的索引 */
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int parent(int i) {
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return (i - 1) / 2;
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}
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/* 层序遍历 */
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vector<int> levelOrder() {
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vector<int> res;
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// 直接遍历数组
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for (int i = 0; i < size(); i++) {
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if (val(i) != INT_MAX)
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res.push_back(val(i));
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}
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return res;
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}
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/* 前序遍历 */
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vector<int> preOrder() {
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vector<int> res;
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dfs(0, "pre", res);
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return res;
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}
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/* 中序遍历 */
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vector<int> inOrder() {
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vector<int> res;
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dfs(0, "in", res);
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return res;
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}
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/* 后序遍历 */
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vector<int> postOrder() {
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vector<int> res;
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dfs(0, "post", res);
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return res;
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}
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private:
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vector<int> tree;
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/* 深度优先遍历 */
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void dfs(int i, string order, vector<int> &res) {
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// 若为空位，则返回
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if (val(i) == INT_MAX)
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return;
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// 前序遍历
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if (order == "pre")
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res.push_back(val(i));
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dfs(left(i), order, res);
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// 中序遍历
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if (order == "in")
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res.push_back(val(i));
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dfs(right(i), order, res);
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// 后序遍历
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if (order == "post")
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res.push_back(val(i));
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}
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};
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/* Driver Code */
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int main() {
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// 初始化二叉树
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// 使用 INT_MAX 代表空位 nullptr
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vector<int> arr = {1, 2, 3, 4, INT_MAX, 6, 7, 8, 9, INT_MAX, INT_MAX, 12, INT_MAX, INT_MAX, 15};
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TreeNode *root = vectorToTree(arr);
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cout << "\n初始化二叉树\n";
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cout << "二叉树的数组表示：\n";
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printVector(arr);
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cout << "二叉树的链表表示：\n";
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printTree(root);
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// 数组表示下的二叉树类
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ArrayBinaryTree abt(arr);
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// 访问节点
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int i = 1;
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int l = abt.left(i), r = abt.right(i), p = abt.parent(i);
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cout << "\n当前节点的索引为 " << i << "，值为 " << abt.val(i) << "\n";
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cout << "其左子节点的索引为 " << l << "，值为 " << (l != INT_MAX ? to_string(abt.val(l)) : "nullptr") << "\n";
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cout << "其右子节点的索引为 " << r << "，值为 " << (r != INT_MAX ? to_string(abt.val(r)) : "nullptr") << "\n";
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cout << "其父节点的索引为 " << p << "，值为 " << (p != INT_MAX ? to_string(abt.val(p)) : "nullptr") << "\n";
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// 遍历树
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vector<int> res = abt.levelOrder();
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cout << "\n层序遍历为： ";
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printVector(res);
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res = abt.preOrder();
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cout << "前序遍历为： ";
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printVector(res);
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res = abt.inOrder();
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cout << "中序遍历为： ";
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printVector(res);
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res = abt.postOrder();
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cout << "后序遍历为： ";
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printVector(res);
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return 0;
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}
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