diff --git a/.gitignore b/.gitignore index 22c46a4be..65f68683e 100644 --- a/.gitignore +++ b/.gitignore @@ -3,7 +3,7 @@ # Editor .vscode/ -.idea/ +**/.idea # mkdocs files .cache/ @@ -13,3 +13,4 @@ docs/overrides/ build/ site/ utils/ +**/cmake-build-debug diff --git a/codes/go/chapter_graph/graph_adjacency_list.go b/codes/go/chapter_graph/graph_adjacency_list.go index 0d5916e37..3d07649df 100644 --- a/codes/go/chapter_graph/graph_adjacency_list.go +++ b/codes/go/chapter_graph/graph_adjacency_list.go @@ -8,31 +8,20 @@ import ( "fmt" "strconv" "strings" + + . "github.com/krahets/hello-algo/pkg" ) -/* 顶点类 */ -type vertex struct { - val int -} - -/* 构造方法 */ -func newVertex(val int) vertex { - return vertex{ - val: val, - } -} - /* 基于邻接表实现的无向图类 */ type graphAdjList struct { - // 邻接表，使用哈希表来代替链表，以提升删除边、删除顶点的效率 - // 请注意，adjList 中的元素是 Vertex 对象 - adjList map[vertex]map[vertex]struct{} + // 邻接表，key: 顶点，value：该顶点的所有邻接顶点 + adjList map[Vertex][]Vertex } /* 构造方法 */ -func newGraphAdjList(edges [][]vertex) *graphAdjList { +func newGraphAdjList(edges [][]Vertex) *graphAdjList { g := &graphAdjList{ - adjList: make(map[vertex]map[vertex]struct{}), + adjList: make(map[Vertex][]Vertex), } // 添加所有顶点和边 for _, edge := range edges { @@ -49,41 +38,41 @@ func (g *graphAdjList) size() int { } /* 添加边 */ -func (g *graphAdjList) addEdge(vet1 vertex, vet2 vertex) { +func (g *graphAdjList) addEdge(vet1 Vertex, vet2 Vertex) { _, ok1 := g.adjList[vet1] _, ok2 := g.adjList[vet2] if !ok1 || !ok2 || vet1 == vet2 { panic("error") } // 添加边 vet1 - vet2, 添加匿名 struct{}, - g.adjList[vet1][vet2] = struct{}{} - g.adjList[vet2][vet1] = struct{}{} + g.adjList[vet1] = append(g.adjList[vet1], vet2) + g.adjList[vet2] = append(g.adjList[vet2], vet1) } /* 删除边 */ -func (g *graphAdjList) removeEdge(vet1 vertex, vet2 vertex) { +func (g *graphAdjList) removeEdge(vet1 Vertex, vet2 Vertex) { _, ok1 := g.adjList[vet1] _, ok2 := g.adjList[vet2] if !ok1 || !ok2 || vet1 == vet2 { panic("error") } - // 删除边 vet1 - vet2, 借助 delete 来删除 map 中的键 - delete(g.adjList[vet1], vet2) - delete(g.adjList[vet2], vet1) + // 删除边 vet1 - vet2 + DeleteSliceElms(g.adjList[vet1], vet2) + DeleteSliceElms(g.adjList[vet2], vet1) } /* 添加顶点 */ -func (g *graphAdjList) addVertex(vet vertex) { +func (g *graphAdjList) addVertex(vet Vertex) { _, ok := g.adjList[vet] if ok { return } // 在邻接表中添加一个新链表 - g.adjList[vet] = make(map[vertex]struct{}) + g.adjList[vet] = make([]Vertex, 0) } /* 删除顶点 */ -func (g *graphAdjList) removeVertex(vet vertex) { +func (g *graphAdjList) removeVertex(vet Vertex) { _, ok := g.adjList[vet] if !ok { panic("error") @@ -91,9 +80,8 @@ func (g *graphAdjList) removeVertex(vet vertex) { // 在邻接表中删除顶点 vet 对应的链表 delete(g.adjList, vet) // 遍历其它顶点的链表，删除所有包含 vet 的边 - for _, set := range g.adjList { - // 操作 - delete(set, vet) + for _, list := range g.adjList { + DeleteSliceElms(list, vet) } } @@ -101,10 +89,11 @@ func (g *graphAdjList) removeVertex(vet vertex) { func (g *graphAdjList) print() { var builder strings.Builder fmt.Printf("邻接表 = \n") + // 使邻接表有序输出 for k, v := range g.adjList { - builder.WriteString("\t\t" + strconv.Itoa(k.val) + ": ") - for vet := range v { - builder.WriteString(strconv.Itoa(vet.val) + " ") + builder.WriteString("\t\t" + strconv.Itoa(k.Val) + ": ") + for _, vet := range v { + builder.WriteString(strconv.Itoa(vet.Val) + " ") } fmt.Println(builder.String()) builder.Reset() diff --git a/codes/go/chapter_graph/graph_adjacency_list_test.go b/codes/go/chapter_graph/graph_adjacency_list_test.go index 630bc494f..24e1b79e1 100644 --- a/codes/go/chapter_graph/graph_adjacency_list_test.go +++ b/codes/go/chapter_graph/graph_adjacency_list_test.go @@ -7,41 +7,39 @@ package chapter_graph import ( "fmt" "testing" + + . "github.com/krahets/hello-algo/pkg" ) func TestGraphAdjList(t *testing.T) { /* 初始化无向图 */ - v0 := newVertex(1) - v1 := newVertex(3) - v2 := newVertex(2) - v3 := newVertex(5) - v4 := newVertex(4) - edges := [][]vertex{{v0, v1}, {v1, v2}, {v2, v3}, {v0, v3}, {v2, v4}, {v3, v4}} + v := ValsToVets([]int{1, 3, 2, 5, 4}) + edges := [][]Vertex{{v[0], v[1]}, {v[0], v[3]}, {v[1], v[2]}, {v[2], v[3]}, {v[2], v[4]}, {v[3], v[4]}} graph := newGraphAdjList(edges) fmt.Println("初始化后，图为:") graph.print() /* 添加边 */ - // 顶点 1, 2 即 v0, v2 - graph.addEdge(v0, v2) + // 顶点 1, 2 即 v[0], v[2] + graph.addEdge(v[0], v[2]) fmt.Println("\n添加边 1-2 后，图为") graph.print() /* 删除边 */ - // 顶点 1, 3 即 v0, v1 - graph.removeEdge(v0, v1) + // 顶点 1, 3 即 v[0], v[1] + graph.removeEdge(v[0], v[1]) fmt.Println("\n删除边 1-3 后，图为") graph.print() /* 添加顶点 */ - v5 := newVertex(6) + v5 := NewVertex(6) graph.addVertex(v5) fmt.Println("\n添加顶点 6 后，图为") graph.print() /* 删除顶点 */ - // 顶点 3 即 v1 - graph.removeVertex(v1) + // 顶点 3 即 v[1] + graph.removeVertex(v[1]) fmt.Println("\n删除顶点 3 后，图为") graph.print() } diff --git a/codes/go/chapter_graph/graph_bfs.go b/codes/go/chapter_graph/graph_bfs.go new file mode 100644 index 000000000..1b1ecd580 --- /dev/null +++ b/codes/go/chapter_graph/graph_bfs.go @@ -0,0 +1,41 @@ +// File: graph_bfs.go +// Created Time: 2023-02-18 +// Author: Reanon (793584285@qq.com) + +package chapter_graph + +import ( + . "github.com/krahets/hello-algo/pkg" +) + +/* 广度优先遍历 BFS */ +// 使用邻接表来表示图，以便获取指定顶点的所有邻接顶点 +func graphBFS(g *graphAdjList, startVet Vertex) []Vertex { + // 顶点遍历序列 + res := make([]Vertex, 0) + // 哈希表，用于记录已被访问过的顶点 + visited := make(map[Vertex]struct{}) + visited[startVet] = struct{}{} + // 队列用于实现 BFS, 使用切片模拟队列 + queue := make([]Vertex, 0) + queue = append(queue, startVet) + // 以顶点 vet 为起点，循环直至访问完所有顶点 + for len(queue) > 0 { + // 队首顶点出队 + vet := queue[0] + queue = queue[1:] + // 记录访问顶点 + res = append(res, vet) + // 遍历该顶点的所有邻接顶点 + for _, adjVet := range g.adjList[vet] { + _, isExist := visited[adjVet] + // 只入队未访问的顶点 + if !isExist { + queue = append(queue, adjVet) + visited[adjVet] = struct{}{} + } + } + } + // 返回顶点遍历序列 + return res +} diff --git a/codes/go/chapter_graph/graph_bfs_test.go b/codes/go/chapter_graph/graph_bfs_test.go new file mode 100644 index 000000000..318a52f24 --- /dev/null +++ b/codes/go/chapter_graph/graph_bfs_test.go @@ -0,0 +1,29 @@ +// File: graph_bfs_test.go +// Created Time: 2023-02-18 +// Author: Reanon (793584285@qq.com) + +package chapter_graph + +import ( + "fmt" + "testing" + + . "github.com/krahets/hello-algo/pkg" +) + +func TestGraphBFS(t *testing.T) { + /* 初始化无向图 */ + vets := ValsToVets([]int{0, 1, 2, 3, 4, 5, 6, 7, 8, 9}) + edges := [][]Vertex{ + {vets[0], vets[1]}, {vets[0], vets[3]}, {vets[1], vets[2]}, {vets[1], vets[4]}, + {vets[2], vets[5]}, {vets[3], vets[4]}, {vets[3], vets[6]}, {vets[4], vets[5]}, + {vets[4], vets[7]}, {vets[5], vets[8]}, {vets[6], vets[7]}, {vets[7], vets[8]}} + graph := newGraphAdjList(edges) + fmt.Println("初始化后，图为:") + graph.print() + + /* 广度优先遍历 BFS */ + res := graphBFS(graph, vets[0]) + fmt.Println("广度优先遍历（BFS）顶点序列为:") + PrintSlice(VetsToVals(res)) +} diff --git a/codes/go/chapter_graph/graph_dfs.go b/codes/go/chapter_graph/graph_dfs.go new file mode 100644 index 000000000..b1d26f7b8 --- /dev/null +++ b/codes/go/chapter_graph/graph_dfs.go @@ -0,0 +1,36 @@ +// File: graph_dfs.go +// Created Time: 2023-02-18 +// Author: Reanon (793584285@qq.com) + +package chapter_graph + +import ( + . "github.com/krahets/hello-algo/pkg" +) + +/* 深度优先遍历 DFS 辅助函数 */ +func dfs(g *graphAdjList, visited map[Vertex]struct{}, res *[]Vertex, vet Vertex) { + // append 操作会返回新的的引用，必须让原引用重新赋值为新slice的引用 + *res = append(*res, vet) + visited[vet] = struct{}{} + // 遍历该顶点的所有邻接顶点 + for _, adjVet := range g.adjList[vet] { + _, isExist := visited[adjVet] + // 递归访问邻接顶点 + if !isExist { + dfs(g, visited, res, adjVet) + } + } +} + +/* 深度优先遍历 DFS */ +// 使用邻接表来表示图，以便获取指定顶点的所有邻接顶点 +func graphDFS(g *graphAdjList, startVet Vertex) []Vertex { + // 顶点遍历序列 + res := make([]Vertex, 0) + // 哈希表，用于记录已被访问过的顶点 + visited := make(map[Vertex]struct{}) + dfs(g, visited, &res, startVet) + // 返回顶点遍历序列 + return res +} diff --git a/codes/go/chapter_graph/graph_dfs_test.go b/codes/go/chapter_graph/graph_dfs_test.go new file mode 100644 index 000000000..903509fc7 --- /dev/null +++ b/codes/go/chapter_graph/graph_dfs_test.go @@ -0,0 +1,28 @@ +// File: graph_dfs_test.go +// Created Time: 2023-02-18 +// Author: Reanon (793584285@qq.com) + +package chapter_graph + +import ( + "fmt" + "testing" + + . "github.com/krahets/hello-algo/pkg" +) + +func TestGraphDFS(t *testing.T) { + /* 初始化无向图 */ + vets := ValsToVets([]int{0, 1, 2, 3, 4, 5, 6}) + edges := [][]Vertex{ + {vets[0], vets[1]}, {vets[0], vets[3]}, {vets[1], vets[2]}, + {vets[2], vets[5]}, {vets[4], vets[5]}, {vets[5], vets[6]}} + graph := newGraphAdjList(edges) + fmt.Println("初始化后，图为:") + graph.print() + + /* 深度优先遍历 DFS */ + res := graphDFS(graph, vets[0]) + fmt.Println("深度优先遍历（DFS）顶点序列为:") + PrintSlice(VetsToVals(res)) +} diff --git a/codes/go/pkg/vertex.go b/codes/go/pkg/vertex.go new file mode 100644 index 000000000..83390ffb2 --- /dev/null +++ b/codes/go/pkg/vertex.go @@ -0,0 +1,55 @@ +// File: vertex.go +// Created Time: 2023-02-18 +// Author: Reanon (793584285@qq.com) + +package pkg + +// Vertex 顶点类 +type Vertex struct { + Val int +} + +// NewVertex 构造方法 +func NewVertex(val int) Vertex { + return Vertex{ + Val: val, + } +} + +// ValsToVets Generate a vertex list tree given an array +func ValsToVets(vals []int) []Vertex { + vets := make([]Vertex, len(vals)) + for i := 0; i < len(vals); i++ { + vets[i] = NewVertex(vals[i]) + } + return vets +} + +// VetsToVals Serialize given vertex list to a value list +func VetsToVals(vets []Vertex) []int { + vals := make([]int, len(vets)) + for i := range vets { + vals[i] = vets[i].Val + } + return vals +} + +// DeleteSliceElms 删除切片指定元素 +func DeleteSliceElms[T any](a []T, elms ...T) []T { + if len(a) == 0 || len(elms) == 0 { + return a + } + // 先将元素转为 set + m := make(map[any]struct{}) + for _, v := range elms { + m[v] = struct{}{} + } + // 过滤掉指定元素 + res := make([]T, 0, len(a)) + for _, v := range a { + if _, ok := m[v]; !ok { + res = append(res, v) + } + } + return res +}