diff --git a/chapter_backtracking/subset_sum_problem.md b/chapter_backtracking/subset_sum_problem.md index 19182895e..b8b0645ce 100644 --- a/chapter_backtracking/subset_sum_problem.md +++ b/chapter_backtracking/subset_sum_problem.md @@ -125,15 +125,35 @@ comments: true === "Go" ```go title="subset_sum_i_naive.go" - [class]{}-[func]{backtrackINaive} + /* 回溯算法:子集和 I */ + func backtrackSubsetSumINaive(total, target int, state, choices *[]int, res *[][]int) { + // 子集和等于 target 时,记录解 + if target == total { + newState := append([]int{}, *state...) + *res = append(*res, newState) + return + } + // 遍历所有选择 + for i := 0; i < len(*choices); i++ { + // 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(*state, (*choices)[i]) + // 进行下一轮选择 + backtrackSubsetSumINaive(total+(*choices)[i], target, state, choices, res) + // 回退:撤销选择,恢复到之前的状态 + *state = (*state)[:len(*state)-1] + } + } /* 求解子集和 I(包含重复子集) */ func subsetSumINaive(nums []int, target int) [][]int { - s := subset{} state := make([]int, 0) // 状态(子集) total := 0 // 子集和 res := make([][]int, 0) // 结果列表(子集列表) - s.backtrack(total, target, &state, &nums, &res) + backtrackSubsetSumINaive(total, target, &state, &nums, &res) return res } ``` @@ -364,16 +384,38 @@ comments: true === "Go" ```go title="subset_sum_i.go" - [class]{}-[func]{backtrackI} + /* 回溯算法:子集和 I */ + func backtrackSubsetSumI(start, target int, state, choices *[]int, res *[][]int) { + // 子集和等于 target 时,记录解 + if target == 0 { + newState := append([]int{}, *state...) + *res = append(*res, newState) + 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 := start; i < len(*choices); i++ { + // 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(*state, (*choices)[i]) + // 进行下一轮选择 + backtrackSubsetSumI(i, target-(*choices)[i], state, choices, res) + // 回退:撤销选择,恢复到之前的状态 + *state = (*state)[:len(*state)-1] + } + } /* 求解子集和 I */ func subsetSumI(nums []int, target int) [][]int { - s := subsetI{} state := make([]int, 0) // 状态(子集) sort.Ints(nums) // 对 nums 进行排序 start := 0 // 遍历起始点 res := make([][]int, 0) // 结果列表(子集列表) - s.backtrack(start, target, &state, &nums, &res) + backtrackSubsetSumI(start, target, &state, &nums, &res) return res } ``` @@ -614,16 +656,43 @@ comments: true === "Go" ```go title="subset_sum_ii.go" - [class]{}-[func]{backtrackII} + /* 回溯算法:子集和 II */ + func backtrackSubsetSumII(start, target int, state, choices *[]int, res *[][]int) { + // 子集和等于 target 时,记录解 + if target == 0 { + newState := append([]int{}, *state...) + *res = append(*res, newState) + 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 := start; i < len(*choices); i++ { + // 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(*state, (*choices)[i]) + // 进行下一轮选择 + backtrackSubsetSumII(i+1, target-(*choices)[i], state, choices, res) + // 回退:撤销选择,恢复到之前的状态 + *state = (*state)[:len(*state)-1] + } + } /* 求解子集和 II */ func subsetSumII(nums []int, target int) [][]int { - s := subsetII{} state := make([]int, 0) // 状态(子集) sort.Ints(nums) // 对 nums 进行排序 start := 0 // 遍历起始点 res := make([][]int, 0) // 结果列表(子集列表) - s.backtrack(start, target, &state, &nums, &res) + backtrackSubsetSumII(start, target, &state, &nums, &res) return res } ```