feat: 第一次作业

8 months ago · 8665c3f7b5
commit 8665c3f7b5
37 changed files with 1482 additions and 0 deletions
--- a/.gitignore
+++ b/.gitignore
@ -0,0 +1,105 @@
+# If you prefer the allow list template instead of the deny list, see community template:
+# https://github.com/github/gitignore/blob/main/community/Golang/Go.AllowList.gitignore
+#
+# Binaries for programs and plugins
+*.exe
+*.exe~
+*.dll
+*.so
+*.dylib
+
+# Test binary, built with `go test -c`
+*.test
+
+# Output of the go coverage tool, specifically when used with LiteIDE
+*.out
+
+# Dependency directories (remove the comment below to include it)
+# vendor/
+
+# Go workspace file
+go.work
+
+# Covers JetBrains IDEs: IntelliJ, RubyMine, PhpStorm, AppCode, PyCharm, CLion, Android Studio, WebStorm and Rider
+# Reference: https://intellij-support.jetbrains.com/hc/en-us/articles/206544839
+
+.idea
+
+# User-specific stuff
+.idea/**/workspace.xml
+.idea/**/tasks.xml
+.idea/**/usage.statistics.xml
+.idea/**/dictionaries
+.idea/**/shelf
+
+# AWS User-specific
+.idea/**/aws.xml
+
+# Generated files
+.idea/**/contentModel.xml
+
+# Sensitive or high-churn files
+.idea/**/dataSources/
+.idea/**/dataSources.ids
+.idea/**/dataSources.local.xml
+.idea/**/sqlDataSources.xml
+.idea/**/dynamic.xml
+.idea/**/uiDesigner.xml
+.idea/**/dbnavigator.xml
+
+# Gradle
+.idea/**/gradle.xml
+.idea/**/libraries
+
+# Gradle and Maven with auto-import
+# When using Gradle or Maven with auto-import, you should exclude module files,
+# since they will be recreated, and may cause churn.  Uncomment if using
+# auto-import.
+.idea/artifacts
+.idea/compiler.xml
+.idea/jarRepositories.xml
+.idea/modules.xml
+.idea/*.iml
+.idea/modules
+*.iml
+*.ipr
+
+# CMake
+cmake-build-*/
+
+# Mongo Explorer plugin
+.idea/**/mongoSettings.xml
+
+# File-based project format
+*.iws
+
+# IntelliJ
+out/
+
+# mpeltonen/sbt-idea plugin
+.idea_modules/
+
+# JIRA plugin
+atlassian-ide-plugin.xml
+
+# Cursive Clojure plugin
+.idea/replstate.xml
+
+# SonarLint plugin
+.idea/sonarlint/
+
+# Crashlytics plugin (for Android Studio and IntelliJ)
+com_crashlytics_export_strings.xml
+crashlytics.properties
+crashlytics-build.properties
+fabric.properties
+
+# Editor-based Rest Client
+.idea/httpRequests
+
+# Android studio 3.1+ serialized cache file
+.idea/caches/build_file_checksums.ser
+
+*.log
+
+/config.yml
--- a/README.md
+++ b/README.md
@ -0,0 +1,32 @@
+# Lavos
+
+算法设计与分析例题/作业代码合集，使用go编写实现
+
+## 目录结构
+
+包代码目录格式为，`cap{x}`，对应的是第x章的例题和作业代码，其中每个例题/作业代码文件均命名为`ex{x}.go`以及`work{x}.go`。
+
+如第三章例6，位于`cap3/ex6.go`中，第四章作业5，位于`cap4/ex5.go`中。
+
+## 运行/测试
+
+要运行测试，需要go开发环境。[Go installation instructions: https://go.dev/doc/install](https://go.dev/doc/install)
+
+完成后，运行
+```shell
+go test lavos/cap3
+```
+
+即可运行该章节下所有的例题和作业的test用例，例题和作业的test代码位于`example_test.go`和`work_test.go`中。
+
+如果需要单独测试某一个题目，运行
+```shell
+go test lavos/cap3 -v '-test.run' 'Ex6$'
+go test lavos/cap3 -v '-test.run' 'Work1$'
+```
+即可运行对应的题目，如示例中将会运行第三章例题6的test和作业1
+
+## 其他细节
+
+由于习惯原因，我并不是很喜欢在算法代码中进行具体的输出操作，或者直接将输出输入放置于算法代码中，而是使用了类似于leetcode中的核心代码模式，因此`ex{x}.go`和`work{x}.go`中的代码模式均为核心代码，不负责输出输入，
+如有需要输出的算法，通过callback实现，传入能够实现输出的callback函数，在核心中调用callback来实现输出，核心代码不关心也不区负责输出输入，输出输入由test负责实现。
--- a/cap3/ex1.go
+++ b/cap3/ex1.go
@ -0,0 +1,17 @@
+package cap3
+
+// Ex1 例题1
+// 求1/1! - 1/3! + 1/5! - 1/7! + ... + (-1)^(n+1)/(2n-1)!
+func Ex1(n int) float64 {
+    sum, fab := 0.0, uint64(1)
+    for i := 1; i <= n; i++ {
+        fab *= 2*uint64(i) + 1
+        if i%2 == 0 {
+            sum += -1.0 / float64(fab)
+        } else {
+            sum += 1.0 / float64(fab)
+        }
+    }
+
+    return sum
+}
--- a/cap3/ex10.go
+++ b/cap3/ex10.go
@ -0,0 +1,29 @@
+package cap3
+
+// Ex10 从0~n的整数中取r个不同的数做一组，求所有可能的组合
+func Ex10(n, r int, callback func(nums []int)) int {
+    if r > n {
+        return 0
+    }
+
+    count := 0
+    combine := make([]int, r)
+
+    var findCombine func(m, k int)
+    findCombine = func(n, k int) {
+        // 从n开始往下遍历组合
+        for i := n; i >= k; i-- {
+            combine[k-1] = i
+            if k > 1 {
+                // k-1和n-1，继续深入遍历，处理子问题
+                findCombine(i-1, k-1)
+            } else {
+                count++
+                callback(combine)
+            }
+        }
+    }
+
+    findCombine(n, r)
+    return count
+}
--- a/cap3/ex11.go
+++ b/cap3/ex11.go
@ -0,0 +1,23 @@
+package cap3
+
+type Candidate int // 候选人
+type Vote int      // 票数
+
+// Ex11 投票统计，有调整，这里不使用数组存储结果，使用hashmap表存结果
+func Ex11(votes []Candidate, numOfCandidate int) map[Candidate]Vote {
+    result := map[Candidate]Vote{}
+    for _, candidate := range votes {
+        // 无效的投票
+        if candidate <= 0 || int(candidate) > numOfCandidate {
+            continue
+        }
+
+        if _, exists := result[candidate]; !exists {
+            result[candidate] = 1
+        } else {
+            result[candidate]++
+        }
+    }
+
+    return result
+}
--- a/cap3/ex12.go
+++ b/cap3/ex12.go
@ -0,0 +1,21 @@
+package cap3
+
+type HeightGrade int
+
+// Ex12 身高统计，这里也是用的hashmap存结果
+func Ex12(heights []int) []int {
+    result := make([]int, 8)
+    for _, height := range heights {
+        // 身高映射，上下限调整
+        mapping := height/5 - 29
+        if mapping < 0 {
+            mapping = 0
+        } else if mapping > 7 {
+            mapping = 7
+        }
+
+        result[mapping]++
+    }
+
+    return result
+}
--- a/cap3/ex13.go
+++ b/cap3/ex13.go
@ -0,0 +1,26 @@
+package cap3
+
+type Subject int
+type Student int
+
+func Ex14(subjectPassedStudentMap map[Subject]Student) []Student {
+    result := make([]Student, 0)
+
+    // 学生及格科目数记录
+    studentRecord := map[Student]int{}
+    for _, student := range subjectPassedStudentMap {
+        // 对当前学生及格科目计数
+        if _, exists := studentRecord[student]; !exists {
+            studentRecord[student] = 1
+        } else {
+            studentRecord[student]++
+        }
+
+        // 学生及格科目数已达到传入的科目数，即为全科及格
+        if studentRecord[student] == len(subjectPassedStudentMap) {
+            result = append(result, student)
+        }
+    }
+
+    return result
+}
--- a/cap3/ex14.go
+++ b/cap3/ex14.go
@ -0,0 +1,25 @@
+package cap3
+
+var _numberTexts = []string{
+    "zero", "one", "two", "three", "four",
+    "five", "six", "seven", "eight", "nine",
+}
+
+// Ex14NumInput 输入数字，输出英文
+func Ex14NumInput(num uint64, callback func(str string)) {
+    digits := make([]uint8, 0, 20)
+    for i := num; i >= 1; i /= 10 {
+        digits = append(digits, uint8(i%10))
+    }
+
+    for i := len(digits) - 1; i >= 0; i-- {
+        callback(_numberTexts[digits[i]])
+    }
+}
+
+// Ex14StrInput 输入数字字符串，输出英文
+func Ex14StrInput(num string, callback func(str string)) {
+    for _, char := range num {
+        callback(_numberTexts[char-48])
+    }
+}
--- a/cap3/ex15.go
+++ b/cap3/ex15.go
@ -0,0 +1,24 @@
+package cap3
+
+var (
+    cashes = []int{50, 20, 10, 5, 2, 1}
+)
+
+// Ex15 最少的纸币找零钱
+func Ex15(amount, paid int) map[int]int {
+    result := map[int]int{}
+
+    // 还要找的钱
+    change := paid - amount
+    for i, cash := range cashes {
+        // 当前面额需要找的张数，整除后结果为0说明当前面额不足以找零
+        cashNum := change / cash
+        if cashNum != 0 {
+            result[i] = cashNum
+            // 当前面额找完后更新剩余未找余额
+            change = change - cashNum*cash
+        }
+    }
+
+    return result
+}
--- a/cap3/ex16.go
+++ b/cap3/ex16.go
@ -0,0 +1,22 @@
+package cap3
+
+// Ex16 求x，其平方为一个各位数字互不相同的九位数
+func Ex16(callback func(x, x2 int)) {
+Next:
+    for x := 10000; x < 32000; x++ {
+        numCntMap := map[int]bool{}
+
+        x2 := x * x
+        for i := x2; i >= 1; i /= 10 {
+            digit := i % 10
+            // 当前数字已经出现过，直接跳过，找下一个x，如果没出现过，则做标记后看下一位数字情况
+            if _, exists := numCntMap[digit]; exists {
+                continue Next
+            }
+
+            numCntMap[digit] = true
+        }
+
+        callback(x, x2)
+    }
+}
--- a/cap3/ex17.go
+++ b/cap3/ex17.go
@ -0,0 +1,53 @@
+package cap3
+
+// _node 链表节点，单向循环链表
+type _node struct {
+    Value int
+    Next  *_node
+}
+
+// 初始化长度为n的环
+func _initCircle(n int) *_node {
+    head := &_node{0, nil}
+    current := head
+    for i := 1; i < n; i++ {
+        newNode := &_node{i, nil}
+        current.Next = newNode
+        current = newNode
+    }
+
+    // 头尾相连成环
+    current.Next = head
+    return head
+}
+
+// Ex17Normal 小朋友游戏(约瑟夫问题)，一般解法（非数学解法），n: 总人数（节点数），k：出队报数
+func Ex17Normal(n, k int) int {
+    circle := _initCircle(n)
+    current := circle
+    for current.Next != current {
+        for i := 1; i < k-1; i++ {
+            current = current.Next
+        }
+
+        // 报到k-1时移除下一个节点
+        next := current.Next
+        current.Next = next.Next
+        current = current.Next
+
+        // 避免内存泄露
+        next.Next = nil
+    }
+
+    return current.Value
+}
+
+// Ex17Math 小朋友游戏(约瑟夫问题)，公式递推解法，n: 总人数（节点数），k：出队报数
+func Ex17Math(n, k int) int {
+    idx := 0
+    for i := 2; i <= n; i++ {
+        idx = (idx + k) % i
+    }
+
+    return idx
+}
--- a/cap3/ex18.go
+++ b/cap3/ex18.go
@ -0,0 +1,107 @@
+package cap3
+
+import (
+    "strings"
+)
+
+// Ex18 超长整数乘法（都超长）
+func Ex18(a, b string) string {
+    result := make([]uint8, len(a)+len(b))
+    resultEndIdx := len(result) - 1
+    for i := 0; i < len(b); i++ {
+        carry := uint8(0)
+        aEnd, bEnd, resultIdx := len(a)-1, len(b)-1, 0
+        bDigit := b[bEnd-i] - 48
+        for j := 0; j < len(a); j++ {
+            // 字符转数字
+            aDigit := a[aEnd-j] - 48
+            // 当前位计算结果 = 当前结果 + aDigit*bDigit + 进位
+            resultIdx = resultEndIdx - (i + j)
+            num := result[resultIdx] + aDigit*bDigit + carry
+            // 当前位为计算结果的个位，进位为十位上的数字
+            result[resultIdx] = num % 10
+            carry = num / 10
+        }
+
+        // 如果还有进位，则对下一个结果位添加进位，此时不会再有进位
+        if carry != 0 {
+            resultIdx--
+            result[resultIdx] += carry
+        }
+    }
+
+    zeroPrefix := true
+    sb := strings.Builder{}
+    for _, num := range result {
+        if zeroPrefix && num == 0 {
+            continue
+        } else {
+            zeroPrefix = false
+        }
+
+        sb.WriteByte(num + 48)
+    }
+
+    return sb.String()
+}
+
+// Ex18type2 超长整数乘法（都超长），a和b都是大端序的数字数组/切片
+func Ex18type2(a, b []uint8) []uint8 {
+    result := make([]uint8, len(a)+len(b))
+    resultEndIdx := len(result) - 1
+    for i := 0; i < len(b); i++ {
+        carry := uint8(0)
+        aEnd, bEnd, resultIdx := len(a)-1, len(b)-1, 0
+        bDigit := b[bEnd-i]
+        for j := 0; j < len(a); j++ {
+            // 字符转数字
+            aDigit := a[aEnd-j]
+            // 当前位计算结果 = 当前结果 + aDigit*bDigit + 进位
+            resultIdx = resultEndIdx - (i + j)
+            num := result[resultIdx] + aDigit*bDigit + carry
+            // 当前位为计算结果的个位，进位为十位上的数字
+            result[resultIdx] = num % 10
+            carry = num / 10
+        }
+
+        // 如果还有进位，则对下一个结果位添加进位，此时不会再有进位
+        if carry != 0 {
+            resultIdx--
+            result[resultIdx] += carry
+        }
+    }
+
+    return result
+}
+
+// Ex18type3 超长整数乘法（都超长），a是大端序的数字数组/切片，b为uint64
+func Ex18type3(a []uint8, b uint64) []uint8 {
+    result := make([]uint8, len(a)+22)
+    resultEndIdx := len(result) - 1
+    bOffset := 0
+    for i := b; i >= 1; i /= 10 {
+        carry := uint8(0)
+        bDigit := uint8(i % 10)
+        aEnd, resultIdx := len(a)-1, 0
+        for j := 0; j < len(a); j++ {
+            // 字符转数字
+            aDigit := a[aEnd-j]
+            // 当前位计算结果 = 当前结果 + aDigit*bDigit + 进位
+            resultIdx = resultEndIdx - (bOffset + j)
+            num := result[resultIdx] + aDigit*bDigit + carry
+            // 当前位为计算结果的个位，进位为十位上的数字
+            result[resultIdx] = num % 10
+            carry = num / 10
+        }
+
+        // 如果还有进位，则对下一个结果位添加进位，此时不会再有进位
+        if carry != 0 {
+            resultIdx--
+            result[resultIdx] += carry
+        }
+
+        bOffset++
+    }
+
+    return result
+}
--- a/cap3/ex19.go
+++ b/cap3/ex19.go
@ -0,0 +1,137 @@
+package cap3
+
+import "strings"
+
+// Ex19 高精度阶乘
+func Ex19(n uint64) string {
+    result := []uint8{1}
+    for i := uint64(2); i <= n; i++ {
+        result = multiply(result, i)
+    }
+
+    return DigitSlice2String(result)
+}
+
+func multiply(a []uint8, b uint64) []uint8 {
+    result := make([]uint8, len(a)+22)
+    resultEndIdx := len(result) - 1
+    bOffset := 0
+    for i := b; i >= 1; i /= 10 {
+        carry := uint8(0)
+        bDigit := uint8(i % 10)
+        aEnd, resultIdx := len(a)-1, 0
+        for j := 0; j < len(a); j++ {
+            // 字符转数字
+            aDigit := a[aEnd-j]
+            // 当前位计算结果 = 当前结果 + aDigit*bDigit + 进位
+            resultIdx = resultEndIdx - (bOffset + j)
+            num := result[resultIdx] + aDigit*bDigit + carry
+            // 当前位为计算结果的个位，进位为十位上的数字
+            result[resultIdx] = num % 10
+            carry = num / 10
+        }
+
+        // 如果还有进位，则对下一个结果位添加进位，此时不会再有进位
+        if carry != 0 {
+            resultIdx--
+            result[resultIdx] += carry
+        }
+
+        bOffset++
+    }
+
+    return result
+}
+
+func multiply2(a []uint8, b uint64) []uint8 {
+    result := make([]uint8, len(a)+22)
+    resultEndIdx := len(result)*2 - 1
+    bOffset := 0
+    for i := b; i >= 1; i /= 10 {
+        carry := uint8(0)
+        bDigit := uint8(i % 10)
+        aEnd, resultIdx := len(a)*2-1, 0
+        for j := 0; j < len(a); j++ {
+            // 字符转数字
+            aDigit := uint8(0)
+            // 4,5 -> 37(0010,0101)
+            aIdx := aEnd - j
+            if aIdx%2 == 0 {
+                aDigit = a[aIdx/2] >> 4
+            } else {
+                aDigit = a[aIdx/2] & 0b00001111
+            }
+
+            // 当前位计算结果 = 当前结果 + aDigit*bDigit + 进位
+            resultIdx = resultEndIdx - (bOffset + j)
+            bitIdx := resultIdx / 2
+            if resultIdx%2 == 0 {
+                num := (result[bitIdx] >> 4) + aDigit*bDigit + carry
+                // 清位
+                // 4,5 -> 37(0010,0101) => 0,5 -> 5(0000,0101)
+                result[bitIdx] &= 0b00001111
+                // 位赋值
+                // 0,5 -> 5(0000,0101) => 5,5 -> 5(0101,0101)
+                // 5(0000,0101) << 4 => 80(0101,0000)
+                // 5(0000,0101) | 80(0101,0000) => 5,5 -> 5(0101,0101)
+                result[bitIdx] |= (num % 10) << 4
+                carry = num / 10
+            } else {
+                num := (result[bitIdx] & 0b00001111) + aDigit*bDigit + carry
+                // 清位
+                // 4,5 -> 37(0010,0101) => 4,0 -> 32(0010,0000)
+                result[bitIdx] &= 0b11110000
+                // 赋值
+                // 4,0 -> 32(0010,0000) => 4,5 -> 37(0010,0101)
+                // 32(0010,0000) | 5(0000,0101) => 4,5 -> 37(0010,0101)
+                result[bitIdx] |= num % 10
+                carry = num / 10
+            }
+        }
+
+        // 如果还有进位，则对下一个结果位添加进位，此时不会再有进位
+        if carry != 0 {
+            resultIdx--
+            bitIdx := resultIdx / 2
+            if resultIdx%2 == 0 {
+                // 4,5 -> 37(0010,0101) => 5,5 -> 37(0101,0101)
+                // 4+1 -> 5(0000,0101) << 4 => 80(0101,0000)
+                // 5(0000,0101) | 80(0101,0000) => 5,5 -> 5(0101,0101)
+                result[bitIdx] &= 0b00001111
+                num := (result[bitIdx] >> 4) + carry
+                result[bitIdx] |= num << 4
+            } else {
+                result[bitIdx] &= 0b11110000
+                num := (result[bitIdx] & 0b00001111) + carry
+                result[bitIdx] |= num
+            }
+        }
+
+        bOffset++
+    }
+
+    return result
+}
+
+// Ex19LowMem 低内存使用版，两位数字结果按位存在同一个uint8中，一个0~9数字只使用四字节，uint8可存两位，一个字节拆成两半用
+func Ex19LowMem(n uint64) string {
+    result := []uint8{1}
+    for i := uint64(2); i <= n; i++ {
+        result = multiply2(result, i)
+    }
+
+    zeroPrefix := true
+    sb := strings.Builder{}
+    for _, num := range result {
+        if zeroPrefix && num == 0 {
+            continue
+        } else {
+            zeroPrefix = false
+        }
+
+        sb.WriteByte((num >> 4) + 48)
+        sb.WriteByte((num & 0b00001111) + 48)
+    }
+
+    return sb.String()
+}
--- a/cap3/ex2.go
+++ b/cap3/ex2.go
@ -0,0 +1,26 @@
+package cap3
+
+// Ex2 例2 求1000以内的完数，返回一个map，key为完数，value为其因数的数组
+func Ex2() map[int][]int {
+    result := map[int][]int{}
+    for i := range 1000 {
+        if i < 2 {
+            continue
+        }
+
+        sum := 0
+        factors := make([]int, 0, 20)
+        for j := 1; j <= i/2; j++ {
+            if i%j == 0 {
+                factors = append(factors, j)
+                sum += j
+            }
+        }
+
+        if sum == i {
+            result[i] = factors
+        }
+    }
+
+    return result
+}
--- a/cap3/ex3.go
+++ b/cap3/ex3.go
@ -0,0 +1,29 @@
+package cap3
+
+// Ex3 求鞍点数，行上最小，列上最大
+func Ex3(matrix [][]int) (int, int, int) {
+    rowMinIdx := map[int]int{} // key: 行索引, value: 最小值所在列
+    colMaxIdx := map[int]int{} // key: 列索引, value: 最大值所在行
+    for rowIdx, row := range matrix {
+        rowMinIdx[rowIdx] = 0
+        for colIdx, currNum := range row {
+            if currNum < row[rowMinIdx[rowIdx]] {
+                rowMinIdx[rowIdx] = colIdx
+            }
+
+            if _, has := colMaxIdx[colIdx]; !has {
+                colMaxIdx[colIdx] = rowIdx
+            } else if currNum > matrix[colMaxIdx[colIdx]][colIdx] {
+                colMaxIdx[colIdx] = rowIdx
+            }
+        }
+    }
+
+    for rowIdx, colIdx := range rowMinIdx {
+        if rowIdx == colMaxIdx[colIdx] {
+            return rowIdx, colIdx, matrix[rowIdx][colIdx]
+        }
+    }
+
+    return -1, -1, 0
+}
--- a/cap3/ex4.go
+++ b/cap3/ex4.go
@ -0,0 +1 @@
+package cap3
--- a/cap3/ex5.go
+++ b/cap3/ex5.go
@ -0,0 +1,69 @@
+package cap3
+
+import "lavos/common"
+
+// Ex5 例题5 汉诺塔问题，输出移动的步骤，可指定算法类型，每做出一步移动操作都将会调用callback
+func Ex5(beadNum int, algoType AlgoType, callback func(from string, to string)) {
+    switch algoType {
+    case AlgoTypeRecursion:
+        Ex5Recursive(beadNum, "A", "B", "C", callback)
+    default:
+        Ex5NonRecursive(beadNum, "A", "B", "C", callback)
+    }
+}
+
+func Ex5Recursive(beadNum int, a, b, c string, callback func(from string, to string)) {
+    if beadNum == 1 {
+        // 如果只有一颗珠子，直接从 A 移动到 C，结束
+        callback(a, c)
+    } else {
+        // 第二步：将所有在 N 之上的珠子（即 N-1 颗珠子）从 A 移动到 B。此时 C 是中转站
+        Ex5Recursive(beadNum-1, a, c, b, callback)
+
+        // 第二步：将 A 的珠子移动到 C
+        callback(a, c)
+
+        // 第三步：将剩余的 N-1 颗珠子从 B 移动到 C。此时 A 是中转站
+        Ex5Recursive(beadNum-1, b, a, c, callback)
+    }
+}
+
+type _step struct {
+    n                 int
+    from, transit, to string
+}
+
+func Ex5NonRecursive(beadNum int, a, b, c string, callback func(from string, to string)) {
+    stack := common.NewStack[_step](beadNum * 5)
+    // 最终状态：a->c，b作为中转
+    stack.Push(&_step{
+        n:    beadNum,
+        from: a, transit: b, to: c,
+    })
+    for !stack.Empty() {
+        status := stack.Pop()
+        if status.n == 1 {
+            callback(status.from, status.to)
+        } else {
+            // 把子问题的三个基本步骤压入栈
+            stack.Push(&_step{
+                n:       status.n - 1,
+                from:    status.transit,
+                transit: status.from,
+                to:      status.to,
+            })
+            stack.Push(&_step{
+                n:       1,
+                from:    status.from,
+                transit: status.transit,
+                to:      status.to,
+            })
+            stack.Push(&_step{
+                n:       status.n - 1,
+                from:    status.from,
+                transit: status.to,
+                to:      status.transit,
+            })
+        }
+    }
+}
--- a/cap3/ex6.go
+++ b/cap3/ex6.go
@ -0,0 +1,103 @@
+package cap3
+
+// Ex6Output 例六的带输出结果
+func Ex6Output(num int, callback func(nums []int)) {
+    Ex6RecursionOutput(num, callback)
+}
+
+// Ex6NoneOutput 例六的不带输出结果版本，只求数量
+func Ex6NoneOutput(num int, algoType AlgoType, callback func(nums []int)) int {
+    switch algoType {
+    case AlgoTypeRecursion:
+        return Ex6Recursion(num)
+    default:
+        return Ex6NoneRecursion(num)
+    }
+}
+
+// Ex6Recursion 整数划分，递归写法，只计算结果，但对算法经过调整以适合输出
+func Ex6Recursion(num int) int {
+    count := 0
+    var divider func(num, m int)
+    divider = func(num, m int) {
+        // num == 0 来源会有两种：递归中num==m，以及传入的num本身就是0，此时可以作为一个划分
+        if num == 0 {
+            count++
+            return
+        }
+
+        // 最大划分大小m逐级-1求划分数
+        if m > 1 {
+            divider(num, m-1)
+        }
+
+        // m <= num，对剩余未加的数进行划分
+        if m <= num {
+            divider(num-m, m)
+        }
+    }
+
+    divider(num, num)
+    return count
+}
+
+// Ex6RecursionOutput 整数划分，由上面的递归写法修改而来，可求划分情况，对算法经过调整以适合输出
+func Ex6RecursionOutput(num int, callback func(dividedNums []int)) {
+    var divider func(num, m int, dividedNums []int, callback func(dividedNums []int))
+    divider = func(num, m int, dividedNums []int, callback func(dividedNums []int)) {
+        // num==0时，当前已划分完毕，回调输出
+        if num == 0 {
+            callback(dividedNums)
+            return
+        }
+
+        // 最大划分大小m逐级-1求划分数
+        if m > 1 {
+            divider(num, m-1, dividedNums, callback)
+        }
+
+        if m <= num {
+            // m <= num，对剩余未加的数进行划分，当前的m已经是划分中的一个成员，将其添加进dividedNums中
+            divider(num-m, m, append(dividedNums, m), callback)
+        }
+    }
+
+    divider(num, num, make([]int, 0, num), callback)
+}
+
+// Ex6NoneRecursion 整数划分，非递归写法，由递归法改写而来，模拟递归过程
+func Ex6NoneRecursion(num int) int {
+    divider := func(num, divideMax int) int {
+        // 初始化
+        result := make([][]int, num+1)
+        for i := 0; i < num+1; i++ {
+            result[i] = make([]int, num+1)
+        }
+        for i := 1; i <= num; i++ {
+            result[0][i] = 1
+        }
+
+        // i从1开始到num进行划分计算，
+        // 里层j从1开始到m（最大划分大小）开始计算子问题的划分
+        // 从1开始，自底向上计算
+        // 此处为非递归写法，当前的结果依赖上一个结果，因此需要先计算上一个结果，
+        // 因此整个问题过程需要从最小的问题开始计算
+        divideMax = min(num, divideMax)
+        for n := 1; n <= num; n++ {
+            for m := 1; m <= divideMax; m++ {
+                if n <= m {
+                    // 对应 Q(n,n) = 1 + Q(n, n-1) 的情况
+                    // n < m (n < m) 时均看作i == m (n == m)
+                    result[n][m] = 1 + result[n][n-1]
+                } else {
+                    // 对应 Q(n,m) = Q(n, m-1) + Q(n-m, m) 的情况
+                    result[n][m] = result[n][m-1] + result[n-m][m]
+                }
+            }
+        }
+
+        return result[num][divideMax]
+    }
+
+    return divider(num, num)
+}
--- a/cap3/ex7.go
+++ b/cap3/ex7.go
@ -0,0 +1,26 @@
+package cap3
+
+// Ex7 低位到高位输出正整数的数字
+func Ex7(num uint64, algoType AlgoType, callback func(digit uint8)) {
+    switch algoType {
+    case AlgoTypeRecursion:
+        Ex7Recursion(num, callback)
+    default:
+        Ex7NoneRecursion(num, callback)
+    }
+}
+
+func Ex7Recursion(num uint64, callback func(digit uint8)) {
+    if num < 10 {
+        callback(uint8(num))
+    } else {
+        callback(uint8(num % 10))
+        Ex7Recursion(num/10, callback)
+    }
+}
+
+func Ex7NoneRecursion(num uint64, callback func(digit uint8)) {
+    for i := num; i >= 1; i /= 10 {
+        callback(uint8(i % 10))
+    }
+}
--- a/cap3/ex8.go
+++ b/cap3/ex8.go
@ -0,0 +1,34 @@
+package cap3
+
+// Ex8 高位到低位输出正整数的数字
+func Ex8(num uint64, algoType AlgoType, callback func(digit uint8)) {
+    switch algoType {
+    case AlgoTypeRecursion:
+        Ex8Recursion(num, callback)
+    default:
+        Ex8NoneRecursion(num, callback)
+    }
+}
+
+// Ex8Recursion 高位到低位输出正整数的数字(递归)
+func Ex8Recursion(num uint64, callback func(digit uint8)) {
+    if num < 10 {
+        callback(uint8(num))
+    } else {
+        // 跟ex7的小区别
+        Ex8Recursion(num/10, callback)
+        callback(uint8(num % 10))
+    }
+}
+
+// Ex8NoneRecursion 高位到低位输出正整数的数字(非递归)
+func Ex8NoneRecursion(num uint64, callback func(digit uint8)) {
+    digits := make([]uint8, 0, 20)
+    for i := num; i >= 1; i /= 10 {
+        digits = append(digits, uint8(i%10))
+    }
+
+    for i := len(digits) - 1; i >= 0; i-- {
+        callback(digits[i])
+    }
+}
--- a/cap3/ex9.go
+++ b/cap3/ex9.go
@ -0,0 +1,28 @@
+package cap3
+
+// Ex9t1 整数拆解为2的幂之和(返回整数的二进制bit取值情况，bit的idx对应相应的幂)
+func Ex9t1(num int) []bool {
+    // 传进来的是int，一般是32bit，这里就用64来存bit，肯定够了
+    bits := make([]bool, 0, 64)
+    for i := 0; num != 0; i++ {
+        bits = append(bits, num%2 == 1)
+        num /= 2
+    }
+
+    return bits
+}
+
+// Ex9t2 整数拆解为2的幂之和(返回幂取值)
+func Ex9t2(num int) []uint8 {
+    // 传进来的是int，一般是32bit，这里就用64来存bit，肯定够了
+    bits := make([]uint8, 0, 64)
+    for i := uint8(0); num != 0; i++ {
+        if num%2 == 1 {
+            bits = append(bits, i)
+        }
+
+        num /= 2
+    }
+
+    return bits
+}
--- a/cap3/example.go
+++ b/cap3/example.go
@ -0,0 +1,26 @@
+package cap3
+
+import "strings"
+
+type AlgoType int
+
+const (
+    AlgoTypeRecursion AlgoType = iota
+    AlgoTypeNoneRecursion
+)
+
+func DigitSlice2String(nums []uint8) string {
+    zeroPrefix := true
+    sb := strings.Builder{}
+    for _, num := range nums {
+        if zeroPrefix && num == 0 {
+            continue
+        } else {
+            zeroPrefix = false
+        }
+
+        sb.WriteByte(num + 48)
+    }
+
+    return sb.String()
+}
--- a/cap3/example_test.go
+++ b/cap3/example_test.go
@ -0,0 +1,217 @@
+package cap3
+
+import (
+    "fmt"
+    "strconv"
+    "testing"
+)
+
+func TestEx1(t *testing.T) {
+    fmt.Println(Ex1(1))
+    fmt.Println(Ex1(2))
+    fmt.Println(Ex1(3))
+    fmt.Println(Ex1(4))
+    fmt.Println(Ex1(5))
+    fmt.Println(Ex1(6))
+    fmt.Println(Ex1(7))
+    fmt.Println(Ex1(8))
+    fmt.Println(Ex1(9))
+}
+
+func TestEx2(t *testing.T) {
+    result := Ex2()
+    for num, factors := range result {
+        fmt.Printf("%d's factors are %+v\n", num, factors)
+    }
+}
+
+func TestEx3(t *testing.T) {
+    matrix := [][]int{
+        {1, 4, 5, 1},
+        {8, 9, 6, 7},
+        {1, 1, 4, 2},
+        {0, 8, 2, 9},
+    }
+
+    row, col, val := Ex3(matrix)
+    if row != -1 && col != -1 {
+        fmt.Printf("(%d,%d): %d\n", row, col, val)
+    }
+}
+
+func TestEx5(t *testing.T) {
+    beadsNum := 5
+    step := 0
+
+    fmt.Println("NoneRecursive: ")
+    Ex5(beadsNum, AlgoTypeNoneRecursion, func(from string, to string) {
+        step++
+        fmt.Printf("step %d: %s -> %s\n", step, from, to)
+    })
+
+    fmt.Println("----------------")
+
+    step = 0
+    fmt.Println("Recursive: ")
+    Ex5(beadsNum, AlgoTypeRecursion, func(from string, to string) {
+        step++
+        fmt.Printf("step %d: %s -> %s\n", step, from, to)
+    })
+}
+
+func TestEx6(t *testing.T) {
+    prev := 0
+    Ex6RecursionOutput(6, func(dividedNums []int) {
+        for i, num := range dividedNums {
+            if i == 0 {
+                if prev != num {
+                    prev = num
+                    fmt.Println()
+                }
+                fmt.Printf("%d", num)
+            } else {
+                fmt.Printf("+%d", num)
+            }
+        }
+
+        fmt.Print("\t\t\t")
+    })
+
+    fmt.Println()
+    fmt.Println("------------")
+
+    result := Ex6Recursion(6)
+    fmt.Println(result)
+
+    result = Ex6NoneRecursion(6)
+    fmt.Println(result)
+}
+
+func TestEx7(t *testing.T) {
+    num := uint64(123456)
+    Ex7(num, AlgoTypeNoneRecursion, func(digit uint8) {
+        fmt.Printf("%d ", digit)
+    })
+    fmt.Println()
+
+    Ex7(num, AlgoTypeRecursion, func(digit uint8) {
+        fmt.Printf("%d ", digit)
+    })
+    fmt.Println()
+}
+
+func TestEx8(t *testing.T) {
+    num := uint64(123456)
+    Ex8(num, AlgoTypeNoneRecursion, func(digit uint8) {
+        fmt.Printf("%d ", digit)
+    })
+    fmt.Println()
+
+    Ex8(num, AlgoTypeRecursion, func(digit uint8) {
+        fmt.Printf("%d ", digit)
+    })
+    fmt.Println()
+}
+
+func TestEx9(t *testing.T) {
+    bits := Ex9t1(137)
+    fmt.Printf("%d=", 137)
+    for i, bit := range bits {
+        if bit {
+            fmt.Printf("2^%d + ", i)
+        }
+    }
+
+    println()
+
+    pows := Ex9t2(137)
+    fmt.Printf("%d=", 137)
+    for _, pow := range pows {
+        fmt.Printf("2^%d + ", pow)
+    }
+
+    println()
+}
+
+func TestEx10(t *testing.T) {
+    Ex10(5, 3, func(nums []int) {
+        fmt.Printf("%+v\n", nums)
+    })
+}
+
+func TestEx14(t *testing.T) {
+    num := uint64(8734112)
+    Ex14StrInput(strconv.FormatUint(num, 10), func(str string) {
+        fmt.Printf("%s-", str)
+    })
+    fmt.Println()
+
+    Ex14NumInput(num, func(str string) {
+        fmt.Printf("%s-", str)
+    })
+    fmt.Println()
+}
+
+func TestEx15(t *testing.T) {
+    result := Ex15(60, 70)
+    for cash, cashNum := range result {
+        fmt.Printf("%d->%d, ", cashes[cash], cashNum)
+    }
+    fmt.Println()
+
+    result = Ex15(60, 100)
+    for cash, cashNum := range result {
+        fmt.Printf("%d->%d, ", cashes[cash], cashNum)
+    }
+    fmt.Println()
+
+    result = Ex15(60, 74)
+    for cash, cashNum := range result {
+        fmt.Printf("%d->%d, ", cashes[cash], cashNum)
+    }
+    fmt.Println()
+
+    result = Ex15(60, 130)
+    for cash, cashNum := range result {
+        fmt.Printf("%d->%d, ", cashes[cash], cashNum)
+    }
+
+    fmt.Println()
+}
+
+func TestEx16(t *testing.T) {
+    count := 0
+    Ex16(func(x, x2 int) {
+        count++
+        fmt.Printf("%d: %d, x^2=%d\n", count, x, x2)
+    })
+}
+
+func TestEx17(t *testing.T) {
+    n, k := 10, 2
+    result := Ex17Normal(n, k)
+    fmt.Println(result)
+
+    result = Ex17Math(n, k)
+    fmt.Println(result)
+}
+
+func TestEx18(t *testing.T) {
+    fmt.Println(Ex18("6451", "6637") == "42815287")
+    fmt.Println(Ex18("1111", "2") == "2222")
+
+    // 来个夸张点的
+    ans := "59431035264803873745814101793588195732295068254603339623610036212240642359886400430165726959529476600423448130231213495885200101414878403047792277609642"
+    fmt.Println(Ex18(
+        "953249582974085793083245237450927435989430572386540298743509843545728475284751234",
+        "62345723854798175908734905872984724974984398572942345324535728479275413") == ans,
+    )
+
+    result := Ex18type3([]uint8{6, 4, 5, 1}, 6637)
+    fmt.Println(DigitSlice2String(result) == "42815287")
+}
+
+func TestEx19(t *testing.T) {
+    fmt.Println(Ex19(10))
+    fmt.Println(Ex19(100))
+}
--- a/cap3/work.go
+++ b/cap3/work.go
@ -0,0 +1 @@
+package cap3
--- a/cap3/work1.go
+++ b/cap3/work1.go
@ -0,0 +1,27 @@
+package cap3
+
+// Work1 求 2 + 22 + 222 + 2222 + ...22...22(n个2)的精确值，返回大端序结果，高位在前存放结果
+// 按位直接计算结果，从最低位（结果索引的末尾）开始，
+// 每一位(索引i)的计算结果为2*(i+1)加上进位，该位的数字即为结果%10，进位即为结果/10取整。
+// 如n=10，则最低位(i=9)的计算结果为(9+1)*2 + 0 = 20，该位数字为result[i]=20%10=0，进位carry=20/10=2，
+// 下一位(i=8)计算结果为(8+1)*2 + 2 = 20，该位数字为result[i]=20%10=0，进位carry=20/10=2，
+// 下一位(i=7)计算结果为(7+1)*2 + 2 = 18，该位数字为result[i]=18%10=8，进位carry=18/10=1，
+// 以此类推
+func Work1(n int) []uint8 {
+    // 大端序，高位在前存放结果
+    result := make([]uint8, n)
+    carry := 0
+    for i := n - 1; i >= 0; i-- {
+        num := (i+1)*2 + carry
+        carry = num / 10
+        result[i] = uint8(num % 10)
+    }
+
+    if carry != 0 {
+        result = append(result, 0)
+        copy(result[1:], result[0:])
+        result[0] = uint8(carry)
+    }
+
+    return result
+}
--- a/cap3/work2.go
+++ b/cap3/work2.go
@ -0,0 +1,41 @@
+package cap3
+
+// Work2 返回给定数组的偏移布局矩阵
+func Work2(nums []int) [][]int {
+    n := len(nums)
+    result := make([][]int, n)
+    for i := 0; i < n; i++ {
+        result[i] = make([]int, n)
+    }
+
+    colStart := 0
+    for _, num := range nums {
+        for row, col := 0, colStart; row < n; row++ {
+            result[row][col%n] = num
+            col++
+        }
+
+        colStart++
+    }
+
+    return result
+}
+
+// Work2type2 返回给定数组的偏移布局矩阵，另一种写法
+func Work2type2(nums []int) [][]int {
+    n := len(nums)
+    result := make([][]int, n)
+    for i := 0; i < n; i++ {
+        result[i] = make([]int, n)
+    }
+
+    offset := 0
+    for row := 0; row < n; row++ {
+        for col := 0; col < n; col++ {
+            result[row][(offset+col)%n] = nums[col]
+        }
+        offset++
+    }
+
+    return result
+}
--- a/cap3/work3.go
+++ b/cap3/work3.go
@ -0,0 +1,44 @@
+package cap3
+
+// Work3 从外到里填充矩阵
+func Work3(n int) [][]int {
+    matrix := make([][]int, n)
+    for i := range matrix {
+        matrix[i] = make([]int, n)
+    }
+
+    // 逐层往里填充
+    num := 1
+    for layer := 0; layer < n/2; layer++ {
+        // 方阵上边
+        for i := layer; i < n-layer; i++ {
+            matrix[layer][i] = num
+            num++
+        }
+
+        // 方阵右边
+        for i := layer + 1; i < n-layer; i++ {
+            matrix[i][n-layer-1] = num
+            num++
+        }
+
+        // 方阵下边
+        for i := n - layer - 2; i >= layer; i-- {
+            matrix[n-layer-1][i] = num
+            num++
+        }
+
+        // 方阵左边
+        for i := n - layer - 2; i > layer; i-- {
+            matrix[i][layer] = num
+            num++
+        }
+    }
+
+    // 奇数阶中间位置需要手动设置
+    if n%2 != 0 {
+        matrix[n/2][n/2] = n * n
+    }
+
+    return matrix
+}
--- a/cap3/work4.go
+++ b/cap3/work4.go
@ -0,0 +1,20 @@
+package cap3
+
+func Work4(n int) [][]int {
+    matrix := make([][]int, n)
+    // 逐行长度递减的上三角矩阵
+    for i := range matrix {
+        matrix[i] = make([]int, n-i)
+    }
+
+    // 沿右上方向斜向上填充
+    num := 1
+    for i := 0; i < n; i++ {
+        for j := 0; j <= i; j++ {
+            matrix[i-j][j] = num
+            num++
+        }
+    }
+
+    return matrix
+}
--- a/cap3/work5.go
+++ b/cap3/work5.go
@ -0,0 +1,38 @@
+package cap3
+
+func Work5(n int) [][]int {
+    matrix := make([][]int, n)
+    for i := range matrix {
+        matrix[i] = make([]int, n)
+    }
+
+    // 逐层往里填充
+    for layer := 0; layer < n/2; layer++ {
+        // 方阵上边
+        for i := layer; i < n-layer; i++ {
+            matrix[layer][i] = layer + 1
+        }
+
+        // 方阵右边
+        for i := layer + 1; i < n-layer; i++ {
+            matrix[i][n-layer-1] = layer + 1
+        }
+
+        // 方阵下边
+        for i := n - layer - 2; i >= layer; i-- {
+            matrix[n-layer-1][i] = layer + 1
+        }
+
+        // 方阵左边
+        for i := n - layer - 2; i > layer; i-- {
+            matrix[i][layer] = layer + 1
+        }
+    }
+
+    // 奇数阶中间位置需要手动设置
+    if n%2 != 0 {
+        matrix[n/2][n/2] = n/2 + 1
+    }
+
+    return matrix
+}
--- a/cap3/work_test.go
+++ b/cap3/work_test.go
@ -0,0 +1,64 @@
+package cap3
+
+import (
+    "fmt"
+    "testing"
+)
+
+func TestWork1(t *testing.T) {
+    result := Work1(100)
+    for _, b := range result {
+        fmt.Print(b)
+    }
+
+    fmt.Println()
+}
+
+func _printMatrix(matrix [][]int) {
+    for _, row := range matrix {
+        for _, element := range row {
+            fmt.Printf("%d\t", element)
+        }
+        fmt.Println()
+    }
+}
+
+func TestWork2(t *testing.T) {
+    matrix := Work2([]int{5, 7, 4, 8, 9, 1})
+    _printMatrix(matrix)
+
+    println("----------------")
+
+    matrix = Work2type2([]int{5, 7, 4, 8, 9, 1})
+    _printMatrix(matrix)
+}
+
+func TestWork3(t *testing.T) {
+    matrix := Work3(7)
+    _printMatrix(matrix)
+
+    fmt.Println("----------------")
+
+    matrix = Work3(6)
+    _printMatrix(matrix)
+}
+
+func TestWork4(t *testing.T) {
+    matrix := Work4(5)
+    _printMatrix(matrix)
+}
+
+func TestWork5(t *testing.T) {
+    matrix := Work5(6)
+    _printMatrix(matrix)
+
+    fmt.Println("----------------")
+
+    matrix = Work5(5)
+    _printMatrix(matrix)
+
+    fmt.Println("----------------")
+
+    matrix = Work5(10)
+    _printMatrix(matrix)
+}
--- a/cap4/example.go
+++ b/cap4/example.go
@ -0,0 +1 @@
+package cap4
--- a/cap4/work.go
+++ b/cap4/work.go
@ -0,0 +1 @@
+package cap4
--- a/cap5/example.go
+++ b/cap5/example.go
@ -0,0 +1 @@
+package cap5
--- a/cap5/work.go
+++ b/cap5/work.go
@ -0,0 +1 @@
+package cap5
--- a/common/stack.go
+++ b/common/stack.go
@ -0,0 +1,55 @@
+package common
+
+type Stack[T any] struct {
+    data []*T
+}
+
+func NewStack[T any](size int) *Stack[T] {
+    stack := Stack[T]{}
+    if size != 0 {
+        stack.data = make([]*T, 0, size)
+    } else {
+        stack.data = make([]*T, 0, 16)
+    }
+
+    return &stack
+}
+
+func (s *Stack[T]) Push(element *T) *Stack[T] {
+    s.data = append(s.data, element)
+    return s
+}
+
+func (s *Stack[T]) Pop() *T {
+    if s.Size() == 0 {
+        return nil
+    }
+
+    element := s.Top()
+    s.data = s.data[:len(s.data)-1]
+    return element
+}
+
+func (s *Stack[T]) Top() *T {
+    if s.Size() == 0 {
+        return nil
+    }
+
+    return s.data[len(s.data)-1]
+}
+
+func (s *Stack[T]) Bottom() *T {
+    if s.Size() == 0 {
+        return nil
+    }
+
+    return s.data[0]
+}
+
+func (s *Stack[T]) Size() int {
+    return len(s.data)
+}
+
+func (s *Stack[T]) Empty() bool {
+    return s.Size() == 0
+}
--- a/go.mod
+++ b/go.mod
@ -0,0 +1,3 @@
+module lavos
+
+go 1.22
--- a/main.go
+++ b/main.go
@ -0,0 +1,5 @@
+package main
+
+func main() {
+
+}