diff --git a/codes/swift/Package.swift b/codes/swift/Package.swift index d76498f3..19a8ae47 100644 --- a/codes/swift/Package.swift +++ b/codes/swift/Package.swift @@ -68,6 +68,9 @@ let package = Package( .executable(name: "preorder_traversal_iii_template", targets: ["preorder_traversal_iii_template"]), .executable(name: "permutations_i", targets: ["permutations_i"]), .executable(name: "permutations_ii", targets: ["permutations_ii"]), + .executable(name: "subset_sum_i_naive", targets: ["subset_sum_i_naive"]), + .executable(name: "subset_sum_i", targets: ["subset_sum_i"]), + .executable(name: "subset_sum_ii", targets: ["subset_sum_ii"]), .executable(name: "n_queens", targets: ["n_queens"]), ], targets: [ @@ -137,6 +140,9 @@ let package = Package( .executableTarget(name: "preorder_traversal_iii_template", dependencies: ["utils"], path: "chapter_backtracking", sources: ["preorder_traversal_iii_template.swift"]), .executableTarget(name: "permutations_i", path: "chapter_backtracking", sources: ["permutations_i.swift"]), .executableTarget(name: "permutations_ii", path: "chapter_backtracking", sources: ["permutations_ii.swift"]), + .executableTarget(name: "subset_sum_i_naive", path: "chapter_backtracking", sources: ["subset_sum_i_naive.swift"]), + .executableTarget(name: "subset_sum_i", path: "chapter_backtracking", sources: ["subset_sum_i.swift"]), + .executableTarget(name: "subset_sum_ii", path: "chapter_backtracking", sources: ["subset_sum_ii.swift"]), .executableTarget(name: "n_queens", path: "chapter_backtracking", sources: ["n_queens.swift"]), ] ) diff --git a/codes/swift/chapter_backtracking/subset_sum_i.swift b/codes/swift/chapter_backtracking/subset_sum_i.swift new file mode 100644 index 00000000..470d06cf --- /dev/null +++ b/codes/swift/chapter_backtracking/subset_sum_i.swift @@ -0,0 +1,53 @@ +/** + * File: subset_sum_i.swift + * Created Time: 2023-07-02 + * Author: nuomi1 (nuomi1@qq.com) + */ + +/* 回溯算法:子集和 I */ +func backtrack(state: inout [Int], target: Int, choices: [Int], start: Int, res: inout [[Int]]) { + // 子集和等于 target 时,记录解 + if target == 0 { + res.append(state) + return + } + // 遍历所有选择 + // 剪枝二:从 start 开始遍历,避免生成重复子集 + for i in stride(from: start, to: choices.count, by: 1) { + // 剪枝一:若子集和超过 target ,则直接结束循环 + // 这是因为数组已排序,后边元素更大,子集和一定超过 target + if target - choices[i] < 0 { + break + } + // 尝试:做出选择,更新 target, start + state.append(choices[i]) + // 进行下一轮选择 + backtrack(state: &state, target: target - choices[i], choices: choices, start: i, res: &res) + // 回退:撤销选择,恢复到之前的状态 + state.removeLast() + } +} + +/* 求解子集和 I */ +func subsetSumI(nums: [Int], target: Int) -> [[Int]] { + var state: [Int] = [] // 状态(子集) + let nums = nums.sorted() // 对 nums 进行排序 + let start = 0 // 遍历起始点 + var res: [[Int]] = [] // 结果列表(子集列表) + backtrack(state: &state, target: target, choices: nums, start: start, res: &res) + return res +} + +@main +enum SubsetSumI { + /* Driver Code */ + static func main() { + let nums = [3, 4, 5] + let target = 9 + + let res = subsetSumI(nums: nums, target: target) + + print("输入数组 nums = \(nums), target = \(target)") + print("所有和等于 \(target) 的子集 res = \(res)") + } +} diff --git a/codes/swift/chapter_backtracking/subset_sum_i_naive.swift b/codes/swift/chapter_backtracking/subset_sum_i_naive.swift new file mode 100644 index 00000000..b40b793c --- /dev/null +++ b/codes/swift/chapter_backtracking/subset_sum_i_naive.swift @@ -0,0 +1,51 @@ +/** + * File: subset_sum_i_naive.swift + * Created Time: 2023-07-02 + * Author: nuomi1 (nuomi1@qq.com) + */ + +/* 回溯算法:子集和 I */ +func backtrack(state: inout [Int], target: Int, total: Int, choices: [Int], res: inout [[Int]]) { + // 子集和等于 target 时,记录解 + if total == target { + res.append(state) + return + } + // 遍历所有选择 + for i in stride(from: 0, to: choices.count, by: 1) { + // 剪枝:若子集和超过 target ,则跳过该选择 + if total + choices[i] > target { + continue + } + // 尝试:做出选择,更新元素和 total + state.append(choices[i]) + // 进行下一轮选择 + backtrack(state: &state, target: target, total: total + choices[i], choices: choices, res: &res) + // 回退:撤销选择,恢复到之前的状态 + state.removeLast() + } +} + +/* 求解子集和 I(包含重复子集) */ +func subsetSumINaive(nums: [Int], target: Int) -> [[Int]] { + var state: [Int] = [] // 状态(子集) + let total = 0 // 子集和 + var res: [[Int]] = [] // 结果列表(子集列表) + backtrack(state: &state, target: target, total: total, choices: nums, res: &res) + return res +} + +@main +enum SubsetSumINaive { + /* Driver Code */ + static func main() { + let nums = [3, 4, 5] + let target = 9 + + let res = subsetSumINaive(nums: nums, target: target) + + print("输入数组 nums = \(nums), target = \(target)") + print("所有和等于 \(target) 的子集 res = \(res)") + print("请注意,该方法输出的结果包含重复集合") + } +} diff --git a/codes/swift/chapter_backtracking/subset_sum_ii.swift b/codes/swift/chapter_backtracking/subset_sum_ii.swift new file mode 100644 index 00000000..f3e494cf --- /dev/null +++ b/codes/swift/chapter_backtracking/subset_sum_ii.swift @@ -0,0 +1,58 @@ +/** + * File: subset_sum_ii.swift + * Created Time: 2023-07-02 + * Author: nuomi1 (nuomi1@qq.com) + */ + +/* 回溯算法:子集和 II */ +func backtrack(state: inout [Int], target: Int, choices: [Int], start: Int, res: inout [[Int]]) { + // 子集和等于 target 时,记录解 + if target == 0 { + res.append(state) + return + } + // 遍历所有选择 + // 剪枝二:从 start 开始遍历,避免生成重复子集 + // 剪枝三:从 start 开始遍历,避免重复选择同一元素 + for i in stride(from: start, to: choices.count, by: 1) { + // 剪枝一:若子集和超过 target ,则直接结束循环 + // 这是因为数组已排序,后边元素更大,子集和一定超过 target + if target - choices[i] < 0 { + break + } + // 剪枝四:如果该元素与左边元素相等,说明该搜索分支重复,直接跳过 + if i > start, choices[i] == choices[i - 1] { + continue + } + // 尝试:做出选择,更新 target, start + state.append(choices[i]) + // 进行下一轮选择 + backtrack(state: &state, target: target - choices[i], choices: choices, start: i + 1, res: &res) + // 回退:撤销选择,恢复到之前的状态 + state.removeLast() + } +} + +/* 求解子集和 II */ +func subsetSumII(nums: [Int], target: Int) -> [[Int]] { + var state: [Int] = [] // 状态(子集) + let nums = nums.sorted() // 对 nums 进行排序 + let start = 0 // 遍历起始点 + var res: [[Int]] = [] // 结果列表(子集列表) + 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("输入数组 nums = \(nums), target = \(target)") + print("所有和等于 \(target) 的子集 res = \(res)") + } +}