mirror of
https://github.com/TheAlgorithms/Python.git
synced 2024-10-06 21:59:30 +00:00
831558d38d
* Adding nqueens.py for backtracking * Adding sum_of_subsets.py for backtracking * Update nqueens.py * Rename nqueens.py to n_queens.py * Deleting /other/n_queens.py
45 lines
1.4 KiB
Python
45 lines
1.4 KiB
Python
'''
|
|
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) |