You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
49 lines
1.6 KiB
49 lines
1.6 KiB
"""
|
|
File: subset_sum_i.py
|
|
Created Time: 2023-06-17
|
|
Author: krahets (krahets@163.com)
|
|
"""
|
|
|
|
|
|
def backtrack(
|
|
state: list[int], target: int, choices: list[int], start: int, res: list[list[int]]
|
|
):
|
|
"""Backtracking algorithm: Subset Sum I"""
|
|
# When the subset sum equals target, record the solution
|
|
if target == 0:
|
|
res.append(list(state))
|
|
return
|
|
# Traverse all choices
|
|
# Pruning two: start traversing from start to avoid generating duplicate subsets
|
|
for i in range(start, len(choices)):
|
|
# Pruning one: if the subset sum exceeds target, end the loop immediately
|
|
# This is because the array is sorted, and later elements are larger, so the subset sum will definitely exceed target
|
|
if target - choices[i] < 0:
|
|
break
|
|
# Attempt: make a choice, update target, start
|
|
state.append(choices[i])
|
|
# Proceed to the next round of selection
|
|
backtrack(state, target - choices[i], choices, i, res)
|
|
# Retract: undo the choice, restore to the previous state
|
|
state.pop()
|
|
|
|
|
|
def subset_sum_i(nums: list[int], target: int) -> list[list[int]]:
|
|
"""Solve Subset Sum I"""
|
|
state = [] # State (subset)
|
|
nums.sort() # Sort nums
|
|
start = 0 # Start point for traversal
|
|
res = [] # Result list (subset list)
|
|
backtrack(state, target, nums, start, res)
|
|
return res
|
|
|
|
|
|
"""Driver Code"""
|
|
if __name__ == "__main__":
|
|
nums = [3, 4, 5]
|
|
target = 9
|
|
res = subset_sum_i(nums, target)
|
|
|
|
print(f"Input array nums = {nums}, target = {target}")
|
|
print(f"All subsets equal to {target} res = {res}")
|