Add the Python codes for the chapter of Graph and Heap (#382)

codes/python/chapter_graph/graph_adjacency_list.py

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+"""
+File: graph_adjacency_list.py
+Created Time: 2023-02-23
+Author: Krahets (krahets@163.com)
+"""
+
+import sys, os.path as osp
+sys.path.append(osp.dirname(osp.dirname(osp.abspath(__file__))))
+from include import *
+
+
+""" 基于邻接表实现的无向图类  """                                                               
+class GraphAdjList:
+    # 邻接表，key: 顶点，value：该顶点的所有邻接结点
+    adj_list = {}
+
+    """ 构造方法 """
+    def __init__(self, edges: List[List[Vertex]]) -> None:
+        self.adj_list = {}
+        # 添加所有顶点和边
+        for edge in edges:
+            self.add_vertex(edge[0])
+            self.add_vertex(edge[1])
+            self.add_edge(edge[0], edge[1])
+
+    """ 获取顶点数量 """
+    def size(self) -> int:
+        return len(self.adj_list)
+
+    """ 添加边 """
+    def add_edge(self, vet1: Vertex, vet2: Vertex) -> None:
+        if vet1 not in self.adj_list or vet2 not in self.adj_list or vet1 == vet2:
+            raise ValueError
+        # 添加边 vet1 - vet2
+        self.adj_list[vet1].append(vet2)
+        self.adj_list[vet2].append(vet1)
+
+    """ 删除边 """
+    def remove_edge(self, vet1: Vertex, vet2: Vertex) -> None:
+        if vet1 not in self.adj_list or vet2 not in self.adj_list or vet1 == vet2:
+            raise ValueError
+        # 删除边 vet1 - vet2
+        self.adj_list[vet1].remove(vet2)
+        self.adj_list[vet2].remove(vet1)
+
+    """ 添加顶点 """
+    def add_vertex(self, vet: Vertex) -> None:
+        if vet in self.adj_list:
+            return
+        # 在邻接表中添加一个新链表
+        self.adj_list[vet] = []
+
+    """ 删除顶点 """
+    def remove_vertex(self, vet: Vertex) -> None:
+        if vet not in self.adj_list:
+            raise ValueError
+        # 在邻接表中删除顶点 vet 对应的链表
+        self.adj_list.pop(vet)
+        # 遍历其它顶点的链表，删除所有包含 vet 的边
+        for vertex in self.adj_list:
+            if vet in self.adj_list[vertex]:
+                self.adj_list[vertex].remove(vet)
+
+    """ 打印邻接表 """
+    def print(self) -> None:
+        print("邻接表 =")
+        for vertex in self.adj_list:
+            tmp = [v.val for v in self.adj_list[vertex]]
+            print(f"{vertex.val}: {tmp},")
+
+
+""" Driver Code """
+if __name__ == "__main__":
+    """ 初始化无向图 """
+    v = vals_to_vets([1, 3, 2, 5, 4])
+    edges = [[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 = GraphAdjList(edges)
+    print("\n初始化后，图为")
+    graph.print()
+
+    """ 添加边 """
+    # 顶点 1, 2 即 v[0], v[2]
+    graph.add_edge(v[0], v[2])
+    print("\n添加边 1-2 后，图为")
+    graph.print()
+
+    """ 删除边 """
+    # 顶点 1, 3 即 v[0], v[1]
+    graph.remove_edge(v[0], v[1])
+    print("\n删除边 1-3 后，图为")
+    graph.print()
+
+    """ 添加顶点 """
+    v5 = Vertex(6)
+    graph.add_vertex(v5)
+    print("\n添加顶点 6 后，图为")
+    graph.print()
+
+    """ 删除顶点 """
+    # 顶点 3 即 v[1]
+    graph.remove_vertex(v[1])
+    print("\n删除顶点 3 后，图为")
+    graph.print()

codes/python/chapter_graph/graph_adjacency_matrix.py

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+"""
+File: graph_adjacency_matrix.py
+Created Time: 2023-02-23
+Author: Krahets (krahets@163.com)
+"""
+
+import sys, os.path as osp
+sys.path.append(osp.dirname(osp.dirname(osp.abspath(__file__))))
+from include import *
+
+""" 基于邻接矩阵实现的无向图类 """
+class GraphAdjMat:
+    # 顶点列表，元素代表“顶点值”，索引代表“顶点索引”
+    vertices = []
+    # 邻接矩阵，行列索引对应“顶点索引”
+    adj_mat = []
+
+    """ 构造方法 """
+    def __init__(self, vertices, edges):
+        self.vertices = []
+        self.adj_mat = []
+        # 添加顶点
+        for val in vertices:
+            self.add_vertex(val)
+        # 添加边
+        # 请注意，edges 元素代表顶点索引，即对应 vertices 元素索引
+        for e in edges:
+            self.add_edge(e[0], e[1])
+
+    """ 获取顶点数量 """
+    def size(self):
+        return len(self.vertices)
+
+    """ 添加顶点 """
+    def add_vertex(self, val):
+        n = self.size()
+        # 向顶点列表中添加新顶点的值
+        self.vertices.append(val)
+        # 在邻接矩阵中添加一行
+        new_row = [0]*n
+        self.adj_mat.append(new_row)
+        # 在邻接矩阵中添加一列
+        for row in self.adj_mat:
+            row.append(0)
+
+
+    """ 删除顶点 """
+    def remove_vertex(self, index):
+        if index >= self.size():
+            raise IndexError()
+        # 在顶点列表中移除索引 index 的顶点
+        self.vertices.pop(index)
+        # 在邻接矩阵中删除索引 index 的行
+        self.adj_mat.pop(index)
+        # 在邻接矩阵中删除索引 index 的列
+        for row in self.adj_mat:
+            row.pop(index)
+
+    """ 添加边 """
+    # 参数 i, j 对应 vertices 元素索引
+    def add_edge(self, i, j):
+        # 索引越界与相等处理
+        if i < 0 or j < 0 or i >= self.size() or j >= self.size() or i == j:
+            raise IndexError()
+        # 在无向图中，邻接矩阵沿主对角线对称，即满足 (i, j) == (j, i)
+        self.adj_mat[i][j] = 1
+        self.adj_mat[j][i] = 1
+
+    """ 删除边 """
+    # 参数 i, j 对应 vertices 元素索引
+    def remove_edge(self, i, j):
+        # 索引越界与相等处理
+        if i < 0 or j < 0 or i >= self.size() or j >= self.size() or i == j:
+            raise IndexError()
+        self.adj_mat[i][j] = 0
+        self.adj_mat[j][i] = 0
+
+    # 打印邻接矩阵
+    def print(self):
+        print("顶点列表 =", self.vertices)
+        print("邻接矩阵 =")
+        print_matrix(self.adj_mat)
+
+
+""" Driver Code """
+if __name__ == "__main__":
+    """ 初始化无向图 """
+    # 请注意，edges 元素代表顶点索引，即对应 vertices 元素索引
+    vertices = [1, 3, 2, 5, 4]
+    edges = [[0, 1], [0, 3], [1, 2], [2, 3], [2, 4], [3, 4]]
+    graph = GraphAdjMat(vertices, edges)
+    print("\n初始化后，图为")
+    graph.print()
+
+    """ 添加边 """
+    # 顶点 1, 2 的索引分别为 0, 2
+    graph.add_edge(0, 2)
+    print("\n添加边 1-2 后，图为")
+    graph.print()
+
+    """ 删除边 """
+    # 顶点 1, 3 的索引分别为 0, 1
+    graph.remove_edge(0, 1)
+    print("\n删除边 1-3 后，图为")
+    graph.print()
+
+    """ 添加顶点 """
+    graph.add_vertex(6)
+    print("\n添加顶点 6 后，图为")
+    graph.print()
+
+    """ 删除顶点 """
+    # 顶点 3 的索引为 1
+    graph.remove_vertex(1)
+    print("\n删除顶点 3 后，图为")
+    graph.print()

codes/python/chapter_graph/graph_bfs.py

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+"""
+File: graph_bfs.py
+Created Time: 2023-02-23
+Author: Krahets (krahets@163.com)
+"""
+
+import sys, os.path as osp
+sys.path.append(osp.dirname(osp.dirname(osp.abspath(__file__))))
+from include import *
+from graph_adjacency_list import GraphAdjList
+
+""" 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
+def graph_bfs(graph: GraphAdjList, start_vet: Vertex) -> List[Vertex]:
+    # 顶点遍历序列
+    res = []
+    # 哈希表，用于记录已被访问过的顶点
+    visited = set([start_vet])
+    # 队列用于实现 BFS
+    que = collections.deque([start_vet])
+    # 以顶点 vet 为起点，循环直至访问完所有顶点
+    while len(que) > 0:
+        vet = que.popleft()  # 队首顶点出队
+        res.append(vet)      # 记录访问顶点
+        # 遍历该顶点的所有邻接顶点
+        for adj_vet in graph.adj_list[vet]:
+            if adj_vet in visited:
+                continue         # 跳过已被访问过的顶点
+            que.append(adj_vet)  # 只入队未访问的顶点
+            visited.add(adj_vet) # 标记该顶点已被访问
+    # 返回顶点遍历序列
+    return res
+
+
+if __name__ == "__main__":
+    """初始化无向图"""
+    v = vals_to_vets([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])
+    edges = [[v[0], v[1]], [v[0], v[3]], [v[1], v[2]], [v[1], v[4]],
+             [v[2], v[5]], [v[3], v[4]], [v[3], v[6]], [v[4], v[5]],
+             [v[4], v[7]], [v[5], v[8]], [v[6], v[7]], [v[7], v[8]]]
+    graph = GraphAdjList(edges)
+    print("\n初始化后，图为")
+    graph.print()
+
+    """广度优先遍历 BFS"""
+    res = graph_bfs(graph, v[0])
+    print("\n广度优先遍历（BFS）顶点序列为")
+    print(vets_to_vals(res))

codes/python/chapter_graph/graph_dfs.py

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+"""
+File: graph_dfs.py
+Created Time: 2023-02-23
+Author: Krahets (krahets@163.com)
+"""
+
+import sys, os.path as osp
+sys.path.append(osp.dirname(osp.dirname(osp.abspath(__file__))))
+from include import *
+from graph_adjacency_list import GraphAdjList
+
+
+""" 深度优先遍历 DFS 辅助函数 """
+def dfs(graph: GraphAdjList, visited: Set[Vertex], res: List[Vertex], vet: Vertex):
+    res.append(vet)     # 记录访问顶点
+    visited.add(vet) # 标记该顶点已被访问
+    # 遍历该顶点的所有邻接顶点
+    for adjVet in graph.adj_list[vet]:
+        if adjVet in visited:
+            continue # 跳过已被访问过的顶点
+        # 递归访问邻接顶点
+        dfs(graph, 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
+def graph_dfs(graph: GraphAdjList, start_vet: Vertex) -> List[Vertex]:
+    # 顶点遍历序列
+    res = []
+    # 哈希表，用于记录已被访问过的顶点
+    visited = set()
+    dfs(graph, visited, res, start_vet)
+    return res
+
+
+""" Driver Code """
+if __name__ == "__main__":
+    # 初始化无向图
+    v = vals_to_vets([0, 1, 2, 3, 4, 5, 6])
+    edges = [[v[0], v[1]], [v[0], v[3]], [v[1], v[2]], 
+             [v[2], v[5]], [v[4], v[5]], [v[5], v[6]]]
+    graph = GraphAdjList(edges)
+    print("\n初始化后，图为")
+    graph.print()
+    
+    # 深度优先遍历 BFS
+    res = graph_dfs(graph, v[0])
+    print("\n深度优先遍历（DFS）顶点序列为")
+    print(vets_to_vals(res))