combination_sum.py

"""
Given a set of candidate numbers (C) (without duplicates) and a target number
(T), find all unique combinations in C where the candidate numbers sums to T.

The same repeated number may be chosen from C unlimited number of times.

Note:
All numbers (including target) will be positive integers.
The solution set must not contain duplicate combinations.
For example, given candidate set [2, 3, 6, 7] and target 7,
A solution set is:
[
  [7],
  [2, 2, 3]
]
"""


def combination_sum(candidates, target):

    def dfs(nums, target, index, path, res):
        if target < 0:
            return  # backtracking
        if target == 0:
            res.append(path)
            return
        for i in range(index, len(nums)):
            dfs(nums, target-nums[i], i, path+[nums[i]], res)

    res = []
    candidates.sort()
    dfs(candidates, target, 0, [], res)
    return res