combination-sum.py

# -*- coding:utf-8 -*-


# Given a set of candidate numbers (candidates) (without duplicates) and a target number (target), find all unique combinations in candidates where the candidate numbers sums to target.
#
# The same repeated number may be chosen from candidates unlimited number of times.
#
# Note:
#
#
# 	All numbers (including target) will be positive integers.
# 	The solution set must not contain duplicate combinations.
#
#
# Example 1:
#
#
# Input: candidates = [2,3,6,7], target = 7,
# A solution set is:
# [
#   [7],
#   [2,2,3]
# ]
#
#
# Example 2:
#
#
# Input: candidates = [2,3,5], target = 8,
# A solution set is:
# [
#   [2,2,2,2],
#   [2,3,3],
#   [3,5]
# ]
#
#


class Solution(object):
    def combinationSum(self, candidates, target):
        """
        :type candidates: List[int]
        :type target: int
        :rtype: List[List[int]]
        """
        res = []
        candidates.sort()
        self.dfs(candidates, target, 0, [], res)
        return res
    
    def dfs(self, nums, target, index, path, res):
        if target < 0:
            return  # backtracking
        if target == 0:
            res.append(path)
            return 
        for i in xrange(index, len(nums)):
            self.dfs(nums, target-nums[i], i, path+[nums[i]], res)