> For the complete documentation index, see [llms.txt](https://wenkangwei.gitbook.io/leetcode-notes/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://wenkangwei.gitbook.io/leetcode-notes/datastructure/dfs-bfs/factor-combination.md). # Factor Combination-质数分解 1**. Link** {% embed url="" %} **2. 题目** Given an integer number, return all possible combinations of the factors that can multiply to the target number. Example Give A = 24 since 24 = 2 x 2 x 2 x 3 \= 2 x 2 x 6 \= 2 x 3 x 4 \= 2 x 12 \= 3 x 8 \= 4 x 6 your solution should return { { 2, 2, 2, 3 }, { 2, 2, 6 }, { 2, 3, 4 }, { 2, 12 }, { 3, 8 }, { 4, 6 } } note: duplicate combination is not allowed. **3. 思路** ``` 1. bt input: action set: [2, 3,4 ... target], can not be 1 sols: final results, sol: current result, target, start: action start from 2 2. terminal state: when target ==1 no need to factorize. Append sol when sol len >1 3.for current target, action is between start to target-1, check if target can be divided by action if so append action and use dfs to next target/i, start = i (same factor may be used many times) ``` **4. Coding** ``` # class Solution(object): # def combinations(self, target): # """ # input: int target # return: int[][] # """ # # write your solution here # sol = [] # sols = [] # pos =2 # self.bt(sols, sol,target, pos) # #sols.sort() # return sols # def bt(self, sols, sol,target,pos): # if target ==1: # if len(sol)>1: # sols.append(sol[:]) # return # for i in range(pos, target+1): # if target%i ==0: # sol.append(i) # self.bt(sols, sol,target//i, i) # sol.pop(-1) class Solution(object): def combinations(self, target): """ input: int target return: int[][] """ #idea: DFS # 1. bt input: action set: [2, 3,4 ... target], can not be 1 # sols: final results, sol: current result, target, start: action start from 2 # 2. terminal state: when target ==1 no need to factorize. Append sol when sol len >1 # 3.for current target, action is between start to target-1, check if target can be divided by action # if so append action and use dfs to next target/i, start = i (same factor may be used many times) # #base case: target =1 if target ==1: return [[1]] sols = [] sol = [] start = 2 self.bt(sols, sol, start, target) return sols def bt(self, sols, sol, start, target): if target == 1: if len(sol) >1: sols.append(sol[:]) return for i in range(start, target+1): if target%i == 0: sol.append(i) self.bt(sols, sol, i, target//i) sol.pop(-1) ``` 如果只考虑所有质数，那就不用for loop直接看target能不能被start整除(之后start的倍数都会被直接跳过，因为target都已经不能被start整除那就更不可能被它的倍数整除)。如果可以就加上start，如果不行就跳过当前的start，进入下一个factor: start+1 ``` class Solution(object): def combinations(self, target): """ input: int target return: int[][] """ #idea: DFS # 1. bt input: action set: [2, 3,4 ... target], can not be 1 # sols: final results, sol: current result, target, start: action start from 2 # 2. terminal state: when target ==1 no need to factorize. Append sol when sol len >1 # 3.for current target, action is between start to target-1, check if target can be divided by action # if so append action and use dfs to next target/i, start = i (same factor may be used many times) # #base case: target =1 if target ==1: return [[1]] sols = [] sol = [] start = 2 self.bt(sols, sol, start, target) return sols def bt(self, sols, sol, start, target): if target == 1: if len(sol) >1: sols.append(sol[:]) return if target%start == 0: sol.append(start) self.bt(sols, sol, start, target//start) sol.pop(-1) else: self.bt(sols, sol, start+1, target) ``` --- # Agent Instructions This documentation is published with GitBook. GitBook is the documentation platform designed so that both humans and AI agents can read, navigate, and reason over technical content effectively. Learn more at gitbook.com. ## Querying This Documentation If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question. Perform an HTTP GET request on the current page URL with the `ask` query parameter, and the optional `goal` query parameter: ``` GET https://wenkangwei.gitbook.io/leetcode-notes/datastructure/dfs-bfs/factor-combination.md?ask=&goal= ``` `ask` is the immediate question: it should be specific, self-contained, and written in natural language. `goal` is optional and describes the broader end goal you are ultimately trying to accomplish on behalf of the user. GitBook uses it to tailor the answer towards what is most useful for that goal. The response will contain a direct answer to the question and relevant excerpts and sources from the documentation. Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.