|
|
/**
|
|
|
* File: array_binary_tree.js
|
|
|
* Created Time: 2023-08-06
|
|
|
* Author: yuan0221 (yl1452491917@gmail.com)
|
|
|
*/
|
|
|
|
|
|
const { arrToTree } = require('../modules/TreeNode');
|
|
|
const { printTree } = require('../modules/PrintUtil');
|
|
|
|
|
|
/* 陣列表示下的二元樹類別 */
|
|
|
class ArrayBinaryTree {
|
|
|
#tree;
|
|
|
|
|
|
/* 建構子 */
|
|
|
constructor(arr) {
|
|
|
this.#tree = arr;
|
|
|
}
|
|
|
|
|
|
/* 串列容量 */
|
|
|
size() {
|
|
|
return this.#tree.length;
|
|
|
}
|
|
|
|
|
|
/* 獲取索引為 i 節點的值 */
|
|
|
val(i) {
|
|
|
// 若索引越界，則返回 null ，代表空位
|
|
|
if (i < 0 || i >= this.size()) return null;
|
|
|
return this.#tree[i];
|
|
|
}
|
|
|
|
|
|
/* 獲取索引為 i 節點的左子節點的索引 */
|
|
|
left(i) {
|
|
|
return 2 * i + 1;
|
|
|
}
|
|
|
|
|
|
/* 獲取索引為 i 節點的右子節點的索引 */
|
|
|
right(i) {
|
|
|
return 2 * i + 2;
|
|
|
}
|
|
|
|
|
|
/* 獲取索引為 i 節點的父節點的索引 */
|
|
|
parent(i) {
|
|
|
return Math.floor((i - 1) / 2); // 向下整除
|
|
|
}
|
|
|
|
|
|
/* 層序走訪 */
|
|
|
levelOrder() {
|
|
|
let res = [];
|
|
|
// 直接走訪陣列
|
|
|
for (let i = 0; i < this.size(); i++) {
|
|
|
if (this.val(i) !== null) res.push(this.val(i));
|
|
|
}
|
|
|
return res;
|
|
|
}
|
|
|
|
|
|
/* 深度優先走訪 */
|
|
|
#dfs(i, order, res) {
|
|
|
// 若為空位，則返回
|
|
|
if (this.val(i) === null) return;
|
|
|
// 前序走訪
|
|
|
if (order === 'pre') res.push(this.val(i));
|
|
|
this.#dfs(this.left(i), order, res);
|
|
|
// 中序走訪
|
|
|
if (order === 'in') res.push(this.val(i));
|
|
|
this.#dfs(this.right(i), order, res);
|
|
|
// 後序走訪
|
|
|
if (order === 'post') res.push(this.val(i));
|
|
|
}
|
|
|
|
|
|
/* 前序走訪 */
|
|
|
preOrder() {
|
|
|
const res = [];
|
|
|
this.#dfs(0, 'pre', res);
|
|
|
return res;
|
|
|
}
|
|
|
|
|
|
/* 中序走訪 */
|
|
|
inOrder() {
|
|
|
const res = [];
|
|
|
this.#dfs(0, 'in', res);
|
|
|
return res;
|
|
|
}
|
|
|
|
|
|
/* 後序走訪 */
|
|
|
postOrder() {
|
|
|
const res = [];
|
|
|
this.#dfs(0, 'post', res);
|
|
|
return res;
|
|
|
}
|
|
|
}
|
|
|
|
|
|
/* Driver Code */
|
|
|
// 初始化二元樹
|
|
|
// 這裡藉助了一個從陣列直接生成二元樹的函式
|
|
|
const arr = Array.of(
|
|
|
1,
|
|
|
2,
|
|
|
3,
|
|
|
4,
|
|
|
null,
|
|
|
6,
|
|
|
7,
|
|
|
8,
|
|
|
9,
|
|
|
null,
|
|
|
null,
|
|
|
12,
|
|
|
null,
|
|
|
null,
|
|
|
15
|
|
|
);
|
|
|
|
|
|
const root = arrToTree(arr);
|
|
|
console.log('\n初始化二元樹\n');
|
|
|
console.log('二元樹的陣列表示：');
|
|
|
console.log(arr);
|
|
|
console.log('二元樹的鏈結串列表示：');
|
|
|
printTree(root);
|
|
|
|
|
|
// 陣列表示下的二元樹類別
|
|
|
const abt = new ArrayBinaryTree(arr);
|
|
|
|
|
|
// 訪問節點
|
|
|
const i = 1;
|
|
|
const l = abt.left(i);
|
|
|
const r = abt.right(i);
|
|
|
const p = abt.parent(i);
|
|
|
console.log('\n當前節點的索引為 ' + i + ' ，值為 ' + abt.val(i));
|
|
|
console.log(
|
|
|
'其左子節點的索引為 ' + l + ' ，值為 ' + (l === null ? 'null' : abt.val(l))
|
|
|
);
|
|
|
console.log(
|
|
|
'其右子節點的索引為 ' + r + ' ，值為 ' + (r === null ? 'null' : abt.val(r))
|
|
|
);
|
|
|
console.log(
|
|
|
'其父節點的索引為 ' + p + ' ，值為 ' + (p === null ? 'null' : abt.val(p))
|
|
|
);
|
|
|
|
|
|
// 走訪樹
|
|
|
let res = abt.levelOrder();
|
|
|
console.log('\n層序走訪為：' + res);
|
|
|
res = abt.preOrder();
|
|
|
console.log('前序走訪為：' + res);
|
|
|
res = abt.inOrder();
|
|
|
console.log('中序走訪為：' + res);
|
|
|
res = abt.postOrder();
|
|
|
console.log('後序走訪為：' + res);
|
