|
|
|
|
|
/**
|
|
|
|
|
|
* File: subset_sum_ii.swift
|
|
|
|
|
|
* Created Time: 2023-07-02
|
|
|
|
|
|
* Author: nuomi1 (nuomi1@qq.com)
|
|
|
|
|
|
*/
|
|
|
|
|
|
|
|
|
|
|
|
/* 回溯演算法：子集和 II */
|
|
|
|
|
|
func backtrack(state: inout [Int], target: Int, choices: [Int], start: Int, res: inout [[Int]]) {
|
|
|
|
|
|
// 子集和等於 target 時，記錄解
|
|
|
|
|
|
if target == 0 {
|
|
|
|
|
|
res.append(state)
|
|
|
|
|
|
return
|
|
|
|
|
|
}
|
|
|
|
|
|
// 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 choices.indices.dropFirst(start) {
|
|
|
|
|
|
// 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
|
|
|
|
|
|
if target - choices[i] < 0 {
|
|
|
|
|
|
break
|
|
|
|
|
|
}
|
|
|
|
|
|
// 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
|
|
|
|
|
|
if i > start, choices[i] == choices[i - 1] {
|
|
|
|
|
|
continue
|
|
|
|
|
|
}
|
|
|
|
|
|
// 嘗試：做出選擇，更新 target, start
|
|
|
|
|
|
state.append(choices[i])
|
|
|
|
|
|
// 進行下一輪選擇
|
|
|
|
|
|
backtrack(state: &state, target: target - choices[i], choices: choices, start: i + 1, res: &res)
|
|
|
|
|
|
// 回退：撤銷選擇，恢復到之前的狀態
|
|
|
|
|
|
state.removeLast()
|
|
|
|
|
|
}
|
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
|
|
/* 求解子集和 II */
|
|
|
|
|
|
func subsetSumII(nums: [Int], target: Int) -> [[Int]] {
|
|
|
|
|
|
var state: [Int] = [] // 狀態（子集）
|
|
|
|
|
|
let nums = nums.sorted() // 對 nums 進行排序
|
|
|
|
|
|
let start = 0 // 走訪起始點
|
|
|
|
|
|
var res: [[Int]] = [] // 結果串列（子集串列）
|
|
|
|
|
|
backtrack(state: &state, target: target, choices: nums, start: start, res: &res)
|
|
|
|
|
|
return res
|
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
|
|
@main
|
|
|
|
|
|
enum SubsetSumII {
|
|
|
|
|
|
/* Driver Code */
|
|
|
|
|
|
static func main() {
|
|
|
|
|
|
let nums = [4, 4, 5]
|
|
|
|
|
|
let target = 9
|
|
|
|
|
|
|
|
|
|
|
|
let res = subsetSumII(nums: nums, target: target)
|
|
|
|
|
|
|
|
|
|
|
|
print("輸入陣列 nums = \(nums), target = \(target)")
|
|
|
|
|
|
print("所有和等於 \(target) 的子集 res = \(res)")
|
|
|
|
|
|
}
|
|
|
|
|
|
}
|
