'''
39. Combination Sum
https://leetcode.com/problems/combination-sum/
Given an array of distinct integers candidates and a target integer target,
return a list of all unique combinations of candidates
where the chosen numbers sum to target.
You may return the combinations in any order.
The same number may be chosen from candidates an unlimited number of times.
Two combinations are unique if the frequency of at least one of
the chosen numbers is different.
It is guaranteed that the number of unique combinations that
sum up to target is less than 150 combinations for the given input.
Example 1:
Input: candidates = [2,3,6,7], target = 7
Output: [[2,2,3],[7]]
Explanation:
2 and 3 are candidates, and 2 + 2 + 3 = 7. Note that 2 can be used multiple times.
7 is a candidate, and 7 = 7.
These are the only two combinations.
Example 2:
Input: candidates = [2,3,5], target = 8
Output: [[2,2,2,2],[2,3,3],[3,5]]
Example 3:
Input: candidates = [2], target = 1
Output: []
'''
def combination_sum(candidates: List[int], target: int) -> List[List[int]]:
@cache
def comb(k: int, target: int) -> List[List[int]]:
if k == 0:
if target == 0:
return [[]]
return []
res = list(comb(k-1, target))
if candidates[k-1] <= target:
res.extend(c + [candidates[k-1]] for c in comb(k, target-candidates[k-1]))
return res
return comb(len(candidates), target)
def combination_sum(candidates: List[int], target: int) -> List[List[int]]:
@cache
def comb(k: int, target: int, tail: Tuple[int]) -> Tuple[Tuple[int]]:
if k == 0:
if target == 0:
return (tail,)
return tuple()
res = comb(k-1, target, tail)
if candidates[k-1] <= target:
res += comb(k, target-candidates[k-1], tail + (candidates[k-1],))
return res
return comb(len(candidates), target, tuple())
def combination_sum(candidates: List[int], target: int) -> List[List[int]]:
res = []
@cache
def comb(k: int, target: int, tail: Tuple[int]):
if k == 0:
if target == 0:
res.append(tail)
return
comb(k-1, target, tail)
if candidates[k-1] <= target:
comb(k, target-candidates[k-1], tail + (candidates[k-1],))
comb(len(candidates), target, tuple())
return res
def combination_sum(candidates: List[int], target: int) -> List[List[int]]:
res = []
def comb(k: int, target: int, tail: Tuple[int]):
if k == 0:
if target == 0:
res.append(tail)
return
comb(k-1, target, tail)
times = 1
while times*candidates[k-1] <= target:
comb(k-1, target - times*candidates[k-1], tail + times*(candidates[k-1],))
times += 1
comb(len(candidates), target, tuple())
return res
def combination_sum(candidates: List[int], target: int) -> List[List[int]]:
res = []
def comb(k: int, target: int, tail: List[int]):
if k == 0:
if target == 0:
res.append(tail)
return
comb(k-1, target, tail)
tail = tail[:]
while candidates[k-1] <= target:
tail.append(candidates[k-1])
target -= candidates[k-1]
comb(k-1, target, tail)
comb(len(candidates), target, [])
return res
