組合回溯法

示例:1:

输入: candidates = [2, 3, 6, 7],target = 7,所求解集为: [[7], [2, 2, 3]]

示例2:

输入:candidates = [2, 3, 6, 7], depth=3,所求解集为:[[2,3,6],[2,3,7],[2,6,7],[3,6,7]]

示例3:

输入:candicates=[a,b,c,d],求全排列

思路:

构建一个树

     *

/  |   |   

2 3  6   7

|      

(2,3,6,7)  (2,3,6,7)

每一层为选择的数,层的元素为满足条件的candicates,每次递归为选择一个数. 利用先序遍历,入栈出站进行全遍历

根据条件决定终止条件。放入结果集,返回

如示例2:

def dfs(result,path,start,k,candicates):

  if depth ==3:

    result.append(path[:])

    return;

  for i in range(start,len(candicates)):

    path.append(candicate[i])

    dfs(result,path,i,k,candicates): # i 是含有重复的,i+1不含有重复的

    path.pop()

例code:

 示例2:

class Solution:
def sumisprime(self,A,k):
result = []
path = []
start = 0
if len(A)==0:
return []
self.dfs(result,path,start,A,k)
return result

def dfs(self,list, path, start, A, k):
if len(path)==k:
list.append(path[:])
return
for i in range(start,len(A)):
path.append(A[i])
self.dfs(list,path,i+1,A,k)
path.pop()

if __name__=='__main__':
solution=Solution()
print(solution.sumisprime([3,7,12,19],3))

示例1:(from leetcode力扣 https://leetcode-cn.com/problems/combination-sum/solution/hui-su-suan-fa-jian-zhi-python-dai-ma-java-dai-m-2/ )

from typing import List


class Solution:
def combinationSum(self, candidates: List[int], target: int) -> List[List[int]]:
  size = len(candidates)
  if size == 0:
    return []

# 剪枝的前提是数组元素排序
# 深度深的边不能比深度浅的边还小
# 要排序的理由:1、前面用过的数后面不能再用;2、下一层边上的数不能小于上一层边上的数。
  candidates.sort()
# 在遍历的过程中记录路径,一般而言它是一个栈
  path = []
  res = []
# 注意要传入 size ,在 range 中, size 取不到
  self.__dfs(candidates, 0, size, path, res, target)
  return res

def __dfs(self, candidates, begin, size, path, res, target):
# 先写递归终止的情况
if target == 0:
# Python 中可变对象是引用传递,因此需要将当前 path 里的值拷贝出来
# 或者使用 path.copy()
  res.append(path[:])

  for index in range(begin, size):
    residue = target - candidates[index]
// “剪枝”操作,不必递归到下一层,并且后面的分支也不必执行
    if residue < 0:
      break
  path.append(candidates[index])
# 因为下一层不能比上一层还小,起始索引还从 index 开始
  self.__dfs(candidates, index, size, path, res, residue)
  path.pop()


if __name__ == '__main__':
  candidates = [2, 3, 6, 7]
  target = 7
  solution = Solution()
  result = solution.combinationSum(candidates, target)
  print(result)。

原文地址:https://www.cnblogs.com/connie313/p/11877262.html