mirror of
https://github.com/krahets/hello-algo.git
synced 2026-11-10 16:00:36 +08:00
14c314c08c
* Retranslate the complete English edition from Simplified Chinese * Polish three English explanations after reader-focused review
53 lines
1.8 KiB
Python
53 lines
1.8 KiB
Python
"""
|
|
File: subset_sum_ii.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: subset sum II"""
|
|
# Record a solution when the remaining target is zero
|
|
if target == 0:
|
|
res.append(list(state))
|
|
return
|
|
# Iterate over all choices
|
|
# Pruning 2: iterate from start to avoid generating duplicate subsets
|
|
# Pruning 3: start after the previously chosen index to avoid choosing the same element again
|
|
for i in range(start, len(choices)):
|
|
# Pruning 1: exit the loop if this choice exceeds the remaining target
|
|
# The array is sorted, so later elements are at least as large and also exceed the remaining target
|
|
if target - choices[i] < 0:
|
|
break
|
|
# Pruning 4: if this element equals its left neighbor at the same search depth, the branch is a duplicate; skip it
|
|
if i > start and choices[i] == choices[i - 1]:
|
|
continue
|
|
# Try: make a choice and update target and start
|
|
state.append(choices[i])
|
|
# Proceed to the next choice
|
|
backtrack(state, target - choices[i], choices, i + 1, res)
|
|
# Backtrack: undo the choice and restore the previous state
|
|
state.pop()
|
|
|
|
|
|
def subset_sum_ii(nums: list[int], target: int) -> list[list[int]]:
|
|
"""Solve subset sum II"""
|
|
state = [] # State (subset)
|
|
nums.sort() # Sort nums
|
|
start = 0 # Starting index for iteration
|
|
res = [] # Result list (list of subsets)
|
|
backtrack(state, target, nums, start, res)
|
|
return res
|
|
|
|
|
|
"""Driver code"""
|
|
if __name__ == "__main__":
|
|
nums = [4, 4, 5]
|
|
target = 9
|
|
res = subset_sum_ii(nums, target)
|
|
|
|
print(f"Input array nums = {nums}, target = {target}")
|
|
print(f"All subsets with sum {target}: res = {res}")
|