old_contents: # Time:  O(n^m)
  # Space: O(m)
  #
  # Given a set of candidate numbers (C) 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.
  # Elements in a combination (a1, a2, ... , ak) must be in non-descending order. (ie, a1 <= a2 <= ... <= ak).
  # 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] 
  #
  
  class Solution:
      # @param candidates, a list of integers
      # @param target, integer
      # @return a list of lists of integers
      def combinationSum(self, candidates, target):
          result = []
          self.combinationSumDFS(sorted(candidates), result, 0, [], target)
          return result
      
      def combinationSumDFS(self, candidates, result, start, intermediate, target):
          if target == 0:
              result.append(intermediate)
          while start < len(candidates) and candidates[start] <= target:
              self.combinationSumDFS(candidates, result, start, intermediate + [candidates[start]], target - candidates[start])
              start += 1
  
  if __name__ == "__main__":
      candidates, target = [2, 3, 6, 7], 7
      result = Solution().combinationSum(candidates, target)     
      print result       
  
new_contents: # Time:  O(n^m)
  # Space: O(m)
  #
  # Given a set of candidate numbers (C) 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.
  # Elements in a combination (a1, a2, ... , ak) must be in non-descending order. (ie, a1 <= a2 <= ... <= ak).
  # 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] 
  #
  
  class Solution:
      # @param candidates, a list of integers
      # @param target, integer
      # @return a list of lists of integers
      def combinationSum(self, candidates, target):
          result = []
          self.combinationSumRecu(sorted(candidates), result, 0, [], target)
          return result
      
      def combinationSumRecu(self, candidates, result, start, intermediate, target):
          if target == 0:
              result.append(intermediate)
          while start < len(candidates) and candidates[start] <= target:
              self.combinationSumRecu(candidates, result, start, intermediate + [candidates[start]], target - candidates[start])
              start += 1
  
  if __name__ == "__main__":
      candidates, target = [2, 3, 6, 7], 7
      result = Solution().combinationSum(candidates, target)     
      print result       
  
subject: Update combination-sum.py