fX

Author: limingzhong

advanced_algorithm/backtrack.md

@@ -20,6 +20,12 @@ func backtrack(选择列表,路径):
 
 核心就是从选择列表里做一个选择，然后一直递归往下搜索答案，如果遇到路径不通，就返回来撤销这次选择。
 
+## 参考阅读
+[回溯算法解题套路框架](https://labuladong.gitbook.io/algo/suan-fa-si-wei-xi-lie/hui-su-suan-fa-xiang-jie-xiu-ding-ban)
+[回溯算法团灭子集、排列、组合问题](https://labuladong.gitbook.io/algo/suan-fa-si-wei-xi-lie/zi-ji-pai-lie-zu-he)
+[回溯算法最佳实践：解数独](https://labuladong.gitbook.io/algo/suan-fa-si-wei-xi-lie/sudoku)
+[回溯算法最佳实践：括号生成](https://labuladong.gitbook.io/algo/suan-fa-si-wei-xi-lie/he-fa-kuo-hao-sheng-cheng)
+
 ## 示例
 
 ### [subsets](https://leetcode-cn.com/problems/subsets/)

src/nums/backtrack.go

@@ -0,0 +1,225 @@
+package nums
+
+import (
+	"sort"
+	"strings"
+)
+
+// 递归解法
+func SubSets(nums []int) [][]int {
+	if len(nums) == 0 {
+		return [][]int{{}}
+	}
+
+	cur := nums[len(nums)-1]
+	res := SubSets(nums[:len(nums)-1])
+	l := len(res)
+	for i := 0; i < l; i++ {
+		res = append(res, append(res[i], cur))
+	}
+	return res
+}
+
+// 回溯解法
+func SubSetsV2(nums []int) [][]int {
+	var (
+		backtrack func(nums []int, track []int, res *[][]int)
+
+		res   = make([][]int, 0)
+		track = make([]int, 0)
+	)
+
+	backtrack = func(nums []int, track []int, res *[][]int) {
+		tmp := make([]int, len(track))
+		copy(tmp, track)
+		*res = append(*res, tmp)
+
+		for i := 0; i < len(nums); i++ {
+			track = append(track, nums[i])
+			backtrack(nums[i+1:], track, res)
+			track = track[:len(track)-1]
+		}
+	}
+
+	backtrack(nums, track, &res)
+
+	return res
+}
+
+// 回溯法 有重复数字的序列
+func SubsetsDup(nums []int) [][]int {
+	var (
+		backtrack func(nums []int, track []int, res *[][]int)
+
+		res   = make([][]int, 0)
+		track = make([]int, 0)
+	)
+
+	backtrack = func(nums []int, track []int, res *[][]int) {
+		tmp := make([]int, len(track))
+		copy(tmp, track)
+		*res = append(*res, tmp)
+
+		for i := 0; i < len(nums); i++ {
+			// 去重 同一树层去重
+			if i > 0 && nums[i] == nums[i-1] {
+				continue
+			}
+
+			track = append(track, nums[i])
+			backtrack(nums[i+1:], track, res)
+			track = track[:len(track)-1]
+		}
+	}
+
+	sort.Ints(nums)
+	backtrack(nums, track, &res)
+
+	return res
+}
+
+// 回溯法 组合问题
+func Combine(n, k int) [][]int {
+	var (
+		backtrack func(n, pos, k int, track []int, res *[][]int)
+
+		res   = make([][]int, 0)
+		track = make([]int, 0)
+	)
+
+	backtrack = func(n, pos, k int, track []int, res *[][]int) {
+		if len(track) == k {
+			ans := make([]int, k)
+			copy(ans, track)
+			*res = append(*res, ans)
+			return
+		}
+
+		for i := pos; i <= n; i++ {
+			track = append(track, i)
+			backtrack(n, i+1, k, track, res)
+			track = track[:len(track)-1]
+		}
+	}
+
+	backtrack(n, 1, k, track, &res)
+
+	return res
+}
+
+// 非重复序列
+func Permutation(nums []int) [][]int {
+	var (
+		backtrack func(nums []int, visited []bool, track []int, res *[][]int)
+
+		res     = make([][]int, 0)
+		visited = make([]bool, len(nums))
+		track   = make([]int, 0)
+	)
+
+	backtrack = func(nums []int, visited []bool, track []int, res *[][]int) {
+		if len(track) == len(nums) {
+			ans := make([]int, len(nums))
+			copy(ans, track)
+			*res = append(*res, ans)
+			return
+		}
+
+		for i := 0; i < len(nums); i++ {
+			if visited[i] {
+				continue
+			}
+			visited[i] = true
+			track = append(track, nums[i])
+			backtrack(nums, visited, track, res)
+			track = track[:len(track)-1]
+			visited[i] = false
+		}
+	}
+
+	backtrack(nums, visited, track, &res)
+
+	return res
+}
+
+// 有重复数字的序列
+func PermutationV2(nums []int) [][]int {
+	var (
+		backtrack func(nums []int, visited []bool, track []int, res *[][]int)
+
+		res     = make([][]int, 0)
+		visited = make([]bool, len(nums))
+		track   = make([]int, 0)
+	)
+
+	backtrack = func(nums []int, visited []bool, track []int, res *[][]int) {
+		if len(track) == len(nums) {
+			ans := make([]int, len(nums))
+			copy(ans, track)
+			*res = append(*res, ans)
+			return
+		}
+
+		for i := 0; i < len(nums); i++ {
+			if visited[i] {
+				continue
+			}
+
+			// 去重 同一树层去重 visited[i-1] == false
+			if i > 0 && nums[i] == nums[i-1] && !visited[i-1] {
+				continue
+			}
+
+			//// 去重 同一树枝去重 visited[i-1] == false
+			//if i >0 && nums[i] == nums[i-1] && visited[i-1] {
+			//	continue
+			//}
+
+			visited[i] = true
+			track = append(track, nums[i])
+			backtrack(nums, visited, track, res)
+			track = track[:len(track)-1]
+			visited[i] = false
+		}
+	}
+
+	sort.Ints(nums)
+	backtrack(nums, visited, track, &res)
+
+	return res
+}
+
+func RestoreIpAddresses(s string) []string {
+	var (
+		res   = make([]string, 0)
+		track = make([]string, 0)
+	)
+	backtrack(s, len(s), 0, 0, track, &res)
+	return res
+}
+
+func backtrack(s string, total, lastIndex int, segLen int, track []string, res *[]string) {
+
+	// 每段ip最多3位，
+	if total-lastIndex-segLen > (4-len(track))*3 || total-lastIndex-segLen < 4-len(track) {
+		return
+	}
+
+	if len(track) == 4 {
+		ts := ""
+		for i := 0; i < len(track); i++ {
+			ts += track[i] + "."
+		}
+		*res = append(*res, strings.TrimSuffix(ts, "."))
+		return
+	}
+
+	for i := 1; i <= 3; i++ {
+		if s[lastIndex:lastIndex+i] > "255" || (i > 1 && s[lastIndex] == '0') {
+			continue
+		}
+		track = append(track, s[lastIndex:lastIndex+i])
+		backtrack(s, len(s), lastIndex+i, i, track, res)
+		track = track[:len(track)-1]
+	}
+}

src/nums/backtrack_test.go

@@ -0,0 +1,25 @@
+package nums
+
+import (
+	"fmt"
+	"testing"
+)
+
+func TestSubSets(t *testing.T) {
+	fmt.Println(SubSets([]int{1, 2, 3}))
+	fmt.Println(SubSetsV2([]int{1, 2, 3}))
+	fmt.Println(SubsetsDup([]int{1, 2, 2}))
+}
+
+func TestCombine(t *testing.T) {
+	fmt.Println(Combine(4, 2))
+}
+
+func TestPermutation(t *testing.T) {
+	fmt.Println(Permutation([]int{1, 2, 3}))
+	fmt.Println(PermutationV2([]int{1, 2, 2}))
+}
+
+func TestRestoreIpAddresses(t *testing.T) {
+	fmt.Println(RestoreIpAddresses("25525511135"))
+}