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feat: add solutions to lc problem: No.0254
No.0254.Factor Combinations
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‎solution/0200-0299/0254.Factor Combinations/README.md

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<!-- 这里可写通用的实现逻辑 -->
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**方法一：回溯**
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我们设计函数 $dfs(n, i)$，其中 $n$ 表示当前待分解的数，$i$ 表示当前分解的数的最大因子，函数的作用是将 $n$ 分解为若干个因子，其中每个因子都不小于 $i$，并将所有分解结果保存到 $ans$ 中。
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在函数 $dfs(n, i)$ 中，我们从 $i$ 开始枚举 $n$ 的因子 $j$，如果 $j$ 是 $n$ 的因子，那么我们将 $j$ 加入当前分解结果，然后继续分解 $n / j$，即调用函数 $dfs(n / j, j)$。
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时间复杂度 $O(\sqrt{n})$。
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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 getFactors(self, n: int) -> List[List[int]]:
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def dfs(n, i):
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if t:
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ans.append(t + [n])
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j = i
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while j * j <= n:
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if n % j == 0:
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t.append(j)
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dfs(n // j, j)
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t.pop()
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j += 1
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t = []
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ans = []
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dfs(n, 2)
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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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private List<Integer> t = new ArrayList<>();
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private List<List<Integer>> ans = new ArrayList<>();
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public List<List<Integer>> getFactors(int n) {
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dfs(n, 2);
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return ans;
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}
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private void dfs(int n, int i) {
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if (!t.isEmpty()) {
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List<Integer> cp = new ArrayList<>(t);
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cp.add(n);
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ans.add(cp);
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}
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for (int j = i; j <= n / j; ++j) {
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if (n % j == 0) {
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t.add(j);
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dfs(n / j, j);
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t.remove(t.size() - 1);
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}
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}
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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<vector<int>> getFactors(int n) {
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vector<int> t;
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vector<vector<int>> ans;
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function<void(int, int)> dfs = [&](int n, int i) {
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if (t.size()) {
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vector<int> cp = t;
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cp.emplace_back(n);
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ans.emplace_back(cp);
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}
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for (int j = i; j <= n / j; ++j) {
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if (n % j == 0) {
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t.emplace_back(j);
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dfs(n / j, j);
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t.pop_back();
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}
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}
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};
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dfs(n, 2);
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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 getFactors(n int) [][]int {
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t := []int{}
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ans := [][]int{}
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var dfs func(n, i int)
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dfs = func(n, i int) {
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if len(t) > 0 {
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cp := make([]int, len(t))
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copy(cp, t)
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cp = append(cp, n)
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ans = append(ans, cp)
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}
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for j := i; j <= n/j; j++ {
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if n%j == 0 {
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t = append(t, j)
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dfs(n/j, j)
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t = t[:len(t)-1]
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}
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}
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}
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dfs(n, 2)
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return ans
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}
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```
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### **...**

‎solution/0200-0299/0254.Factor Combinations/README_EN.md

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### **Python3**
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```python
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class Solution:
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def getFactors(self, n: int) -> List[List[int]]:
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def dfs(n, i):
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if t:
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ans.append(t + [n])
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j = i
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while j * j <= n:
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if n % j == 0:
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t.append(j)
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dfs(n // j, j)
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t.pop()
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j += 1
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t = []
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ans = []
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dfs(n, 2)
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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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private List<Integer> t = new ArrayList<>();
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private List<List<Integer>> ans = new ArrayList<>();
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public List<List<Integer>> getFactors(int n) {
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dfs(n, 2);
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return ans;
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}
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private void dfs(int n, int i) {
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if (!t.isEmpty()) {
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List<Integer> cp = new ArrayList<>(t);
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cp.add(n);
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ans.add(cp);
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}
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for (int j = i; j <= n / j; ++j) {
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if (n % j == 0) {
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t.add(j);
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dfs(n / j, j);
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t.remove(t.size() - 1);
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}
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}
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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<vector<int>> getFactors(int n) {
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vector<int> t;
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vector<vector<int>> ans;
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function<void(int, int)> dfs = [&](int n, int i) {
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if (t.size()) {
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vector<int> cp = t;
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cp.emplace_back(n);
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ans.emplace_back(cp);
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}
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for (int j = i; j <= n / j; ++j) {
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if (n % j == 0) {
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t.emplace_back(j);
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dfs(n / j, j);
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t.pop_back();
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}
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}
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};
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dfs(n, 2);
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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 getFactors(n int) [][]int {
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t := []int{}
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ans := [][]int{}
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var dfs func(n, i int)
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dfs = func(n, i int) {
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if len(t) > 0 {
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cp := make([]int, len(t))
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copy(cp, t)
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cp = append(cp, n)
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ans = append(ans, cp)
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}
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for j := i; j <= n/j; j++ {
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if n%j == 0 {
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t = append(t, j)
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dfs(n/j, j)
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t = t[:len(t)-1]
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}
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}
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}
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dfs(n, 2)
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return ans
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}
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```
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### **...**

‎solution/0200-0299/0254.Factor Combinations/Solution.cpp

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class Solution {
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public:
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vector<vector<int>> getFactors(int n) {
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vector<int> t;
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vector<vector<int>> ans;
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function<void(int, int)> dfs = [&](int n, int i) {
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if (t.size()) {
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vector<int> cp = t;
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cp.emplace_back(n);
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ans.emplace_back(cp);
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}
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for (int j = i; j <= n / j; ++j) {
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if (n % j == 0) {
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t.emplace_back(j);
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dfs(n / j, j);
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t.pop_back();
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}
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}
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};
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dfs(n, 2);
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return ans;
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}
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};

‎solution/0200-0299/0254.Factor Combinations/Solution.go

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func getFactors(n int) [][]int {
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t := []int{}
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ans := [][]int{}
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var dfs func(n, i int)
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dfs = func(n, i int) {
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if len(t) > 0 {
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cp := make([]int, len(t))
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copy(cp, t)
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cp = append(cp, n)
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ans = append(ans, cp)
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}
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for j := i; j <= n/j; j++ {
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if n%j == 0 {
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t = append(t, j)
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dfs(n/j, j)
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t = t[:len(t)-1]
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}
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}
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}
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dfs(n, 2)
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return ans
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}

‎solution/0200-0299/0254.Factor Combinations/Solution.java

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class Solution {
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private List<Integer> t = new ArrayList<>();
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private List<List<Integer>> ans = new ArrayList<>();
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public List<List<Integer>> getFactors(int n) {
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dfs(n, 2);
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return ans;
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}
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private void dfs(int n, int i) {
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if (!t.isEmpty()) {
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List<Integer> cp = new ArrayList<>(t);
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cp.add(n);
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ans.add(cp);
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}
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for (int j = i; j <= n / j; ++j) {
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if (n % j == 0) {
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t.add(j);
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dfs(n / j, j);
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t.remove(t.size() - 1);
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}
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}
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}
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}

‎solution/0200-0299/0254.Factor Combinations/Solution.py

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class Solution:
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def getFactors(self, n: int) -> List[List[int]]:
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def dfs(n, i):
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if t:
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ans.append(t + [n])
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j = i
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while j * j <= n:
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if n % j == 0:
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t.append(j)
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dfs(n // j, j)
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t.pop()
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j += 1
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t = []
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ans = []
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dfs(n, 2)
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return ans

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