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feat: add solutions to lc problem: No.1104
No.1104.Path In Zigzag Labelled Binary Tree
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‎solution/1100-1199/1104.Path In Zigzag Labelled Binary Tree/README.md

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<!-- 这里可写通用的实现逻辑 -->
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**方法一：数学**
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对于一棵完全二叉树，第 $i$ 行的节点个数为 $2^{i-1}$，第 $i$ 行的节点编号范围为 $[2^{i-1}, 2^i - 1]$。而题目中对于奇数行，按从左到右的顺序进行标记，对于偶数行，按从右到左的顺序进行标记。所以对于第 $i$ 行的节点 $label$，它的互补节点编号为 $2^{i-1} + 2^i - 1 - label$。所以节点 $label$ 的实际父节点编号为 $(2^{i-1} + 2^i - 1 - label) / 2$。我们可以通过不断地求互补节点编号和父节点编号，直到到达根节点，即可得到从根节点到节点 $label$ 的路径。
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最后，我们需要将路径反转，因为题目要求路径是从根节点到节点 $label$ 的路径。
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时间复杂度 $O(\log n)$，其中 $n$ 为节点 $label$ 的编号。忽略答案的空间消耗，空间复杂度 $O(1)$。
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<!-- tabs:start -->
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### **Python3**
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<!-- 这里可写当前语言的特殊实现逻辑 -->
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```python
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class Solution:
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def pathInZigZagTree(self, label: int) -> List[int]:
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x = i = 1
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while (x << 1) <= label:
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x <<= 1
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i += 1
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ans = [0] * i
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while i:
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ans[i - 1] = label
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label = ((1 << (i - 1)) + (1 << i) - 1 - label) >> 1
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i -= 1
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return ans
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```
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### **Java**
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<!-- 这里可写当前语言的特殊实现逻辑 -->
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```java
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class Solution {
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public List<Integer> pathInZigZagTree(int label) {
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int x = 1, i = 1;
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while ((x << 1) <= label) {
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x <<= 1;
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++i;
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}
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List<Integer> ans = new ArrayList<>();
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for (; i > 0; --i) {
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ans.add(label);
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label = ((1 << (i - 1)) + (1 << i) - 1 - label) >> 1;
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}
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Collections.reverse(ans);
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return ans;
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}
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}
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```
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### **C++**
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```cpp
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class Solution {
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public:
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vector<int> pathInZigZagTree(int label) {
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int x = 1, i = 1;
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while ((x << 1) <= label) {
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x <<= 1;
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++i;
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}
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vector<int> ans;
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for (; i > 0; --i) {
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ans.push_back(label);
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label = ((1 << (i - 1)) + (1 << i) - 1 - label) >> 1;
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}
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reverse(ans.begin(), ans.end());
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return ans;
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}
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};
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```
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### **Go**
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```go
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func pathInZigZagTree(label int) (ans []int) {
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x, i := 1, 1
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for x<<1 <= label {
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x <<= 1
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i++
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}
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for ; i > 0; i-- {
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ans = append(ans, label)
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label = ((1 << (i - 1)) + (1 << i) - 1 - label) >> 1
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}
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for i, j := 0, len(ans)-1; i < j; i, j = i+1, j-1 {
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ans[i], ans[j] = ans[j], ans[i]
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}
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return
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}
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```
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### **...**

‎solution/1100-1199/1104.Path In Zigzag Labelled Binary Tree/README_EN.md

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### **Python3**
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```python
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class Solution:
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def pathInZigZagTree(self, label: int) -> List[int]:
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x = i = 1
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while (x << 1) <= label:
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x <<= 1
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i += 1
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ans = [0] * i
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while i:
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ans[i - 1] = label
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label = ((1 << (i - 1)) + (1 << i) - 1 - label) >> 1
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i -= 1
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return ans
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```
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### **Java**
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```java
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class Solution {
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public List<Integer> pathInZigZagTree(int label) {
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int x = 1, i = 1;
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while ((x << 1) <= label) {
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x <<= 1;
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++i;
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}
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List<Integer> ans = new ArrayList<>();
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for (; i > 0; --i) {
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ans.add(label);
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label = ((1 << (i - 1)) + (1 << i) - 1 - label) >> 1;
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}
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Collections.reverse(ans);
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return ans;
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}
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}
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```
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### **C++**
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```cpp
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class Solution {
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public:
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vector<int> pathInZigZagTree(int label) {
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int x = 1, i = 1;
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while ((x << 1) <= label) {
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x <<= 1;
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++i;
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}
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vector<int> ans;
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for (; i > 0; --i) {
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ans.push_back(label);
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label = ((1 << (i - 1)) + (1 << i) - 1 - label) >> 1;
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}
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reverse(ans.begin(), ans.end());
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return ans;
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}
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};
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```
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### **Go**
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```go
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func pathInZigZagTree(label int) (ans []int) {
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x, i := 1, 1
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for x<<1 <= label {
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x <<= 1
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i++
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}
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for ; i > 0; i-- {
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ans = append(ans, label)
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label = ((1 << (i - 1)) + (1 << i) - 1 - label) >> 1
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}
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for i, j := 0, len(ans)-1; i < j; i, j = i+1, j-1 {
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ans[i], ans[j] = ans[j], ans[i]
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}
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return
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}
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```
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### **...**

‎solution/1100-1199/1104.Path In Zigzag Labelled Binary Tree/Solution.cpp

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class Solution {
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public:
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vector<int> pathInZigZagTree(int label) {
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int x = 1, i = 1;
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while ((x << 1) <= label) {
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x <<= 1;
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++i;
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}
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vector<int> ans;
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for (; i > 0; --i) {
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ans.push_back(label);
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label = ((1 << (i - 1)) + (1 << i) - 1 - label) >> 1;
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}
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reverse(ans.begin(), ans.end());
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return ans;
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}
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};

‎solution/1100-1199/1104.Path In Zigzag Labelled Binary Tree/Solution.go

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func pathInZigZagTree(label int) (ans []int) {
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x, i := 1, 1
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for x<<1 <= label {
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x <<= 1
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i++
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}
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for ; i > 0; i-- {
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ans = append(ans, label)
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label = ((1 << (i - 1)) + (1 << i) - 1 - label) >> 1
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}
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for i, j := 0, len(ans)-1; i < j; i, j = i+1, j-1 {
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ans[i], ans[j] = ans[j], ans[i]
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}
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return
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}

‎solution/1100-1199/1104.Path In Zigzag Labelled Binary Tree/Solution.java

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class Solution {
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public List<Integer> pathInZigZagTree(int label) {
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List<Integer> res = new ArrayList<>();
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int n = Integer.highestOneBit(label);
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while (label > 0) {
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res.add(label);
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int pos = ((n << 1) - 1 - label) >> 1;
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label = (n >> 1) + pos;
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n >>= 1;
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int x = 1, i = 1;
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while ((x << 1) <= label) {
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x <<= 1;
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++i;
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}
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Collections.reverse(res);
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return res;
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List<Integer> ans = new ArrayList<>();
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for (; i > 0; --i) {
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ans.add(label);
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label = ((1 << (i - 1)) + (1 << i) - 1 - label) >> 1;
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}
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Collections.reverse(ans);
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return ans;
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}
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}
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}

‎solution/1100-1199/1104.Path In Zigzag Labelled Binary Tree/Solution.py

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class Solution:
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def pathInZigZagTree(self, label: int) -> List[int]:
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x = i = 1
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while (x << 1) <= label:
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x <<= 1
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i += 1
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ans = [0] * i
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while i:
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ans[i - 1] = label
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label = ((1 << (i - 1)) + (1 << i) - 1 - label) >> 1
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i -= 1
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return ans

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