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chapter_divide_and_conquer/build_binary_tree_problem.md
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@@ -72,70 +72,6 @@ status: new
为了提升查询 $m$ 的效率，我们借助一个哈希表 `hmap` 来存储数组 `inorder` 中元素到索引的映射。
=== "Java"
```java title="build_tree.java"
/* 构建二叉树：分治 */
TreeNode dfs(int[] preorder, int[] inorder, Map<Integer, Integer> hmap, int i, int l, int r) {
// 子树区间为空时终止
if (r - l < 0)
return null;
// 初始化根节点
TreeNode root = new TreeNode(preorder[i]);
// 查询 m ，从而划分左右子树
int m = hmap.get(preorder[i]);
// 子问题：构建左子树
root.left = dfs(preorder, inorder, hmap, i + 1, l, m - 1);
// 子问题：构建右子树
root.right = dfs(preorder, inorder, hmap, i + 1 + m - l, m + 1, r);
// 返回根节点
return root;
}
/* 构建二叉树 */
TreeNode buildTree(int[] preorder, int[] inorder) {
// 初始化哈希表，存储 inorder 元素到索引的映射
Map<Integer, Integer> hmap = new HashMap<>();
for (int i = 0; i < inorder.length; i++) {
hmap.put(inorder[i], i);
}
TreeNode root = dfs(preorder, inorder, hmap, 0, 0, inorder.length - 1);
return root;
}
```
=== "C++"
```cpp title="build_tree.cpp"
/* 构建二叉树：分治 */
TreeNode *dfs(vector<int> &preorder, vector<int> &inorder, unordered_map<int, int> &hmap, int i, int l, int r) {
// 子树区间为空时终止
if (r - l < 0)
return NULL;
// 初始化根节点
TreeNode *root = new TreeNode(preorder[i]);
// 查询 m ，从而划分左右子树
int m = hmap[preorder[i]];
// 子问题：构建左子树
root->left = dfs(preorder, inorder, hmap, i + 1, l, m - 1);
// 子问题：构建右子树
root->right = dfs(preorder, inorder, hmap, i + 1 + m - l, m + 1, r);
// 返回根节点
return root;
}
/* 构建二叉树 */
TreeNode *buildTree(vector<int> &preorder, vector<int> &inorder) {
// 初始化哈希表，存储 inorder 元素到索引的映射
unordered_map<int, int> hmap;
for (int i = 0; i < inorder.size(); i++) {
hmap[inorder[i]] = i;
}
TreeNode *root = dfs(preorder, inorder, hmap, 0, 0, inorder.size() - 1);
return root;
}
```
=== "Python"
```python title="build_tree.py"
@@ -170,6 +106,102 @@ status: new
return root
```
=== "C++"
```cpp title="build_tree.cpp"
/* 构建二叉树：分治 */
TreeNode *dfs(vector<int> &preorder, vector<int> &inorder, unordered_map<int, int> &hmap, int i, int l, int r) {
// 子树区间为空时终止
if (r - l < 0)
return NULL;
// 初始化根节点
TreeNode *root = new TreeNode(preorder[i]);
// 查询 m ，从而划分左右子树
int m = hmap[preorder[i]];
// 子问题：构建左子树
root->left = dfs(preorder, inorder, hmap, i + 1, l, m - 1);
// 子问题：构建右子树
root->right = dfs(preorder, inorder, hmap, i + 1 + m - l, m + 1, r);
// 返回根节点
return root;
}
/* 构建二叉树 */
TreeNode *buildTree(vector<int> &preorder, vector<int> &inorder) {
// 初始化哈希表，存储 inorder 元素到索引的映射
unordered_map<int, int> hmap;
for (int i = 0; i < inorder.size(); i++) {
hmap[inorder[i]] = i;
}
TreeNode *root = dfs(preorder, inorder, hmap, 0, 0, inorder.size() - 1);
return root;
}
```
=== "Java"
```java title="build_tree.java"
/* 构建二叉树：分治 */
TreeNode dfs(int[] preorder, int[] inorder, Map<Integer, Integer> hmap, int i, int l, int r) {
// 子树区间为空时终止
if (r - l < 0)
return null;
// 初始化根节点
TreeNode root = new TreeNode(preorder[i]);
// 查询 m ，从而划分左右子树
int m = hmap.get(preorder[i]);
// 子问题：构建左子树
root.left = dfs(preorder, inorder, hmap, i + 1, l, m - 1);
// 子问题：构建右子树
root.right = dfs(preorder, inorder, hmap, i + 1 + m - l, m + 1, r);
// 返回根节点
return root;
}
/* 构建二叉树 */
TreeNode buildTree(int[] preorder, int[] inorder) {
// 初始化哈希表，存储 inorder 元素到索引的映射
Map<Integer, Integer> hmap = new HashMap<>();
for (int i = 0; i < inorder.length; i++) {
hmap.put(inorder[i], i);
}
TreeNode root = dfs(preorder, inorder, hmap, 0, 0, inorder.length - 1);
return root;
}
```
=== "C#"
```csharp title="build_tree.cs"
/* 构建二叉树：分治 */
TreeNode dfs(int[] preorder, int[] inorder, Dictionary<int, int> hmap, int i, int l, int r) {
// 子树区间为空时终止
if (r - l < 0)
return null;
// 初始化根节点
TreeNode root = new TreeNode(preorder[i]);
// 查询 m ，从而划分左右子树
int m = hmap[preorder[i]];
// 子问题：构建左子树
root.left = dfs(preorder, inorder, hmap, i + 1, l, m - 1);
// 子问题：构建右子树
root.right = dfs(preorder, inorder, hmap, i + 1 + m - l, m + 1, r);
// 返回根节点
return root;
}
/* 构建二叉树 */
TreeNode buildTree(int[] preorder, int[] inorder) {
// 初始化哈希表，存储 inorder 元素到索引的映射
Dictionary<int, int> hmap = new Dictionary<int, int>();
for (int i = 0; i < inorder.Length; i++) {
hmap.TryAdd(inorder[i], i);
}
TreeNode root = dfs(preorder, inorder, hmap, 0, 0, inorder.Length - 1);
return root;
}
```
=== "Go"
```go title="build_tree.go"
@@ -204,6 +236,35 @@ status: new
}
```
=== "Swift"
```swift title="build_tree.swift"
/* 构建二叉树：分治 */
func dfs(preorder: [Int], inorder: [Int], hmap: [Int: Int], i: Int, l: Int, r: Int) -> TreeNode? {
// 子树区间为空时终止
if r - l < 0 {
return nil
}
// 初始化根节点
let root = TreeNode(x: preorder[i])
// 查询 m ，从而划分左右子树
let m = hmap[preorder[i]]!
// 子问题：构建左子树
root.left = dfs(preorder: preorder, inorder: inorder, hmap: hmap, i: i + 1, l: l, r: m - 1)
// 子问题：构建右子树
root.right = dfs(preorder: preorder, inorder: inorder, hmap: hmap, i: i + 1 + m - l, l: m + 1, r: r)
// 返回根节点
return root
}
/* 构建二叉树 */
func buildTree(preorder: [Int], inorder: [Int]) -> TreeNode? {
// 初始化哈希表，存储 inorder 元素到索引的映射
let hmap = inorder.enumerated().reduce(into: [:]) { $0[$1.element] = $1.offset }
return dfs(preorder: preorder, inorder: inorder, hmap: hmap, i: 0, l: 0, r: inorder.count - 1)
}
```
=== "JS"
```javascript title="build_tree.js"
@@ -273,83 +334,6 @@ status: new
}
```
=== "C"
```c title="build_tree.c"
[class]{}-[func]{dfs}
[class]{}-[func]{buildTree}
```
=== "C#"
```csharp title="build_tree.cs"
/* 构建二叉树：分治 */
TreeNode dfs(int[] preorder, int[] inorder, Dictionary<int, int> hmap, int i, int l, int r) {
// 子树区间为空时终止
if (r - l < 0)
return null;
// 初始化根节点
TreeNode root = new TreeNode(preorder[i]);
// 查询 m ，从而划分左右子树
int m = hmap[preorder[i]];
// 子问题：构建左子树
root.left = dfs(preorder, inorder, hmap, i + 1, l, m - 1);
// 子问题：构建右子树
root.right = dfs(preorder, inorder, hmap, i + 1 + m - l, m + 1, r);
// 返回根节点
return root;
}
/* 构建二叉树 */
TreeNode buildTree(int[] preorder, int[] inorder) {
// 初始化哈希表，存储 inorder 元素到索引的映射
Dictionary<int, int> hmap = new Dictionary<int, int>();
for (int i = 0; i < inorder.Length; i++) {
hmap.TryAdd(inorder[i], i);
}
TreeNode root = dfs(preorder, inorder, hmap, 0, 0, inorder.Length - 1);
return root;
}
```
=== "Swift"
```swift title="build_tree.swift"
/* 构建二叉树：分治 */
func dfs(preorder: [Int], inorder: [Int], hmap: [Int: Int], i: Int, l: Int, r: Int) -> TreeNode? {
// 子树区间为空时终止
if r - l < 0 {
return nil
}
// 初始化根节点
let root = TreeNode(x: preorder[i])
// 查询 m ，从而划分左右子树
let m = hmap[preorder[i]]!
// 子问题：构建左子树
root.left = dfs(preorder: preorder, inorder: inorder, hmap: hmap, i: i + 1, l: l, r: m - 1)
// 子问题：构建右子树
root.right = dfs(preorder: preorder, inorder: inorder, hmap: hmap, i: i + 1 + m - l, l: m + 1, r: r)
// 返回根节点
return root
}
/* 构建二叉树 */
func buildTree(preorder: [Int], inorder: [Int]) -> TreeNode? {
// 初始化哈希表，存储 inorder 元素到索引的映射
let hmap = inorder.enumerated().reduce(into: [:]) { $0[$1.element] = $1.offset }
return dfs(preorder: preorder, inorder: inorder, hmap: hmap, i: 0, l: 0, r: inorder.count - 1)
}
```
=== "Zig"
```zig title="build_tree.zig"
[class]{}-[func]{dfs}
[class]{}-[func]{buildTree}
```
=== "Dart"
```dart title="build_tree.dart"
@@ -421,6 +405,22 @@ status: new
}
```
=== "C"
```c title="build_tree.c"
[class]{}-[func]{dfs}
[class]{}-[func]{buildTree}
```
=== "Zig"
```zig title="build_tree.zig"
[class]{}-[func]{dfs}
[class]{}-[func]{buildTree}
```
图 12-8 展示了构建二叉树的递归过程，各个节点是在向下“递”的过程中建立的，而各条边（即引用）是在向上“归”的过程中建立的。
=== "<1>"