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hello-algo/zh-hant/codes/ruby/chapter_backtracking/subset_sum_ii.rb

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1.5 KiB

=begin
File: subset_sum_ii.rb
Created Time: 2024-05-22
Author: Xuan Khoa Tu Nguyen (ngxktuzkai2000@gmail.com)
=end
### 回溯演算法:子集和 II ###
def backtrack(state, target, choices, start, res)
# 子集和等於 target 時,記錄解
if target.zero?
res << state.dup
return
end
# 走訪所有選擇
# 剪枝二:從 start 開始走訪,避免生成重複子集
# 剪枝三:從 start 開始走訪,避免重複選擇同一元素
for i in start...choices.length
# 剪枝一:若子集和超過 target ,則直接結束迴圈
# 這是因為陣列已排序,後邊元素更大,子集和一定超過 target
break if target - choices[i] < 0
# 剪枝四:如果該元素與左邊元素相等,說明該搜尋分支重複,直接跳過
next if i > start && choices[i] == choices[i - 1]
# 嘗試:做出選擇,更新 target, start
state << choices[i]
# 進行下一輪選擇
backtrack(state, target - choices[i], choices, i + 1, res)
# 回退:撤銷選擇,恢復到之前的狀態
state.pop
end
end
### 求解子集和 II ###
def subset_sum_ii(nums, target)
state = [] # 狀態(子集)
nums.sort! # 對 nums 進行排序
start = 0 # 走訪起始點
res = [] # 結果串列(子集串列)
backtrack(state, target, nums, start, res)
res
end
### Driver Code ###
if __FILE__ == $0
nums = [4, 4, 5]
target = 9
res = subset_sum_ii(nums, target)
puts "輸入陣列 nums = #{nums}, target = #{target}"
puts "所有和等於 #{target} 的子集 res = #{res}"
end