图论基础类的实现和深度优先搜索的实现

Author: AlexJakin

.gitignore

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+.idea
+composer.lock
+*.log
+.ipynb_checkpoints

Graph/AdjacencyList.py

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+"""
+@author: Alex
+@contact: [email protected] or [email protected]
+@file: AdjacencyList.py
+@time: 2019/10/20 19:12
+"""
+class AdjList:
+
+    def __init__(self, filename):
+        self.V = 0  # 顶点数
+        self.E = 0  # 边数
+        self.adj = None
+        with open(filename) as f:
+            line_num = 0  # 第一行是顶点数和边数
+            for line in f:
+                if line_num == 0:
+                    v, e = line.strip().split()
+                    self.V = int(v)
+                    self.E = int(e)
+                    self.adj = [[] for i in range(self.V)] # 创建二维数组即邻接表
+                else:
+                    # 读取边 写入邻接表
+                    v1, v2 = line.strip().split()
+                    # 转化为整数
+                    v1 = int(v1)
+                    v2 = int(v2)
+                    self.adj[v1].append(v2)
+                    self.adj[v2].append(v1)
+                line_num += 1
+
+    def get_graph_information(self):
+        """
+        打印图的邻接表
+        :return:
+        """
+        print("V={}, E={}".format(self.V, self.E))
+        for i, v in enumerate(self.adj):
+            print("{} : {}".format(i, v))
+
+    def validateVertex(self, v):
+        """
+        验证顶点取值
+        :param v:
+        :return:
+        """
+        if v<0 or v>=self.V:
+            raise ValueError("v值超出范围")
+
+    def hasEdge(self, v, w):
+        """
+        判断两个顶点是否存在
+        :param v: 第一个顶点
+        :param w: 第二个顶点
+        :return: true or false
+        """
+        self.validateVertex(v)
+        self.validateVertex(w)
+        return w in self.adj[v]
+
+    def degree(self, v):
+        """
+        求某个顶点的度
+        :param v:
+        :return:
+        """
+        self.validateVertex(v)
+        return len(self.adj[v])
+
+
+    def graphDFS(self):
+        visited = [False for i in range(self.V)]
+        pre_order = [] # 前序遍历结果
+        post_order = [] # 后序遍历结果
+
+        def dfs(v):
+            # 标记v顶点已经遍历过了
+            visited[v] = True
+            # 添加
+            pre_order.append(v)
+            for w in self.adj[v]:
+                if visited[w] == False:
+                    dfs(w)
+            post_order.append(v)
+        dfs(0)
+        return pre_order,post_order
+
+if __name__ == '__main__':
+    adjm = AdjList("../g.txt")
+    adjm.get_graph_information()
+    print(adjm.hasEdge(0,4))
+    print(adjm.degree(1))
+    print(adjm.graphDFS())

Graph/AdjacencyMatrix.py

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+"""
+@author: Alex
+@contact: [email protected] or [email protected]
+@file: AdjacencyMatrix.py
+@time: 2019/10/20 18:31
+"""
+# 邻接矩阵
+class AdjMatrix:
+
+    def __init__(self, filename):
+        self.V = 0 # 顶点数
+        self.E = 0 # 边数
+        self.adj = None
+        with open(filename) as f:
+            line_num = 0 # 第一行是顶点数和边数
+            for line in f:
+                if line_num == 0:
+                    v, e = line.strip().split()
+                    self.V = int(v)
+                    self.E = int(e)
+                    # self.adj = [[0] * self.V] * self.V # 该创建方式不正确 修改任何一个元素都会改变整个列表
+                    self.adj = [([0] * self.V) for i in range(self.V)] # 创建二维数组即邻接矩阵
+                else:
+                    # 读取边 写入邻接矩阵
+                    v1, v2 = line.strip().split()
+                    # 转化为整数
+                    v1 = int(v1)
+                    v2 = int(v2)
+                    self.adj[v1][v2] = 1
+                    self.adj[v2][v1] = 1
+                line_num += 1
+
+    def get_graph_information(self):
+        """
+        打印图的邻接矩阵
+        :return:
+        """
+        print("V={}, E={}".format(self.V, self.E))
+        print(adjm.adj)
+
+    def validateVertex(self, v):
+        """
+        验证顶点取值
+        :param v:
+        :return:
+        """
+        if v<0 or v>=self.V:
+            raise ValueError("v值超出范围")
+
+    def hasEdge(self, v, w):
+        """
+        判断两个顶点是否存在
+        :param v: 第一个顶点
+        :param w: 第二个顶点
+        :return: true or false
+        """
+        self.validateVertex(v)
+        self.validateVertex(w)
+        return self.adj[v][w]==1
+
+    def degree(self, v):
+        """
+        求某个顶点的度
+        :param v:
+        :return:
+        """
+        self.validateVertex(v)
+        return sum(self.adj[v])
+
+    def AdjMatrixDFS(self):
+        visited = [False for i in range(self.V)]
+        pre_order = [] # 前序遍历结果
+        post_order = [] # 后序遍历结果
+
+        def dfs(v):
+            # 标记v顶点已经遍历过了
+            visited[v] = True
+            # 添加
+            pre_order.append(v)
+            for w in self.adj[v]:
+                if visited[w] == False:
+                    dfs(w)
+            post_order.append(v)
+        for i in range(self.V):
+            if visited[i] == False:
+                dfs(i)
+        return pre_order,post_order
+
+if __name__ == '__main__':
+    adjm = AdjMatrix("../g.txt")
+    adjm.get_graph_information()
+    print(adjm.hasEdge(6, 6))
+    print(adjm.degree(1))
+    print(adjm.AdjMatrixDFS())

Graph/__init__.py

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+"""
+@author: Alex
+@contact: [email protected] or [email protected]
+@file: __init__.py.py
+@time: 2019/10/20 18:30
+"""
+

Graph/test.py

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+"""
+@author: Alex
+@contact: [email protected] or [email protected]
+@file: test.py
+@time: 2019/10/20 19:03
+"""
+
+adj = [[0, 1, 0, 1, 0, 0, 0], [1, 0, 1, 0, 0, 0, 1], [0, 1, 0, 1, 0, 1, 0], [1, 0, 1, 0, 1, 0, 0], [0, 0, 0, 1, 0, 1, 0], [0, 0, 1, 0, 1, 0, 1], [0, 1, 0, 0, 0, 1, 0]]
+
+print(sum(adj[0]))

g.txt

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+7 9
+0 1
+0 3
+1 2
+1 6
+2 3
+2 5
+3 4
+4 5
+5 6

graph_basic.ipynb

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+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.7.3"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}

readme.md

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+## 1.介绍
+
+图论算法python实现，封装图的邻接矩阵和邻接表的基础类，实现深度优先搜索（前序和后序）和广度优先搜索，图的各种应用方面的实现，哈密顿图，有向图算法，最短路径算法，欧拉回路和欧拉路径，网络流，匹配问题等等