''' The sum-of-subsetsproblem states that a set of non-negative integers, and a value M, determine all possible subsets of the given set whose summation sum equal to given M. Summation of the chosen numbers must be equal to given number M and one number can be used only once. ''' def generate_sum_of_subsets_soln(nums, max_sum): result = [] path = [] num_index = 0 remaining_nums_sum = sum(nums) create_state_space_tree(nums, max_sum, num_index, path,result, remaining_nums_sum) return result def create_state_space_tree(nums,max_sum,num_index,path,result, remaining_nums_sum): ''' Creates a state space tree to iterate through each branch using DFS. It terminates the branching of a node when any of the two conditions given below satisfy. This algorithm follows depth-fist-search and backtracks when the node is not branchable. ''' if sum(path) > max_sum or (remaining_nums_sum + sum(path)) < max_sum: return if sum(path) == max_sum: result.append(path) return for num_index in range(num_index,len(nums)): create_state_space_tree(nums, max_sum, num_index + 1, path + [nums[num_index]], result, remaining_nums_sum - nums[num_index]) ''' remove the comment to take an input from the user print("Enter the elements") nums = list(map(int, input().split())) print("Enter max_sum sum") max_sum = int(input()) ''' nums = [3, 34, 4, 12, 5, 2] max_sum = 9 result = generate_sum_of_subsets_soln(nums,max_sum) print(*result)