添加无向无权图的最短路径、环检测、二部图检测算法实现

Author: AlexJakin

Graph_BFS/BiPartitionDetection.py

@@ -0,0 +1,77 @@
+"""
+@author: Alex
+@contact: 1272296763@qq.com or jakinmili@gmail.com
+@file: BiPartitionDetection.py
+@time: 2019/10/26 16:11
+"""
+import queue
+class BiPartitionDetection:
+
+    def __init__(self, filename):
+        self.V = 0  # 顶点数
+        self.E = 0  # 边数
+        self.adj = None
+        self.__initGraph(filename)
+        self.__isBiPartitie = True
+
+        # 检测二部图
+        self.visited = [False for i in range(self.V)]
+        self.colors = [-1 for i in range(self.V)]
+        for v in range(self.V):
+            if self.visited[v] == False:
+                if self.bfs(v) == False:
+                    self.__isBiPartitie = False
+                    break
+
+
+    def __initGraph(self, filename):
+       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 bfs(self, s):
+        que = queue.Queue(self.V)
+        # 往队列中添加顶点s
+        que.put(s)
+        self.visited[s] = True
+        self.colors[s] = 0
+
+        while que.empty() == False:
+            v = que.get()
+
+            for w in self.adj[v]:
+                if self.visited[w] == False:
+                    que.put(w)
+                    self.visited[w] = True
+                    self.colors[w] = 1 - self.colors[v]
+                elif self.colors[w] == self.colors[v]:
+                    return False
+        return True
+
+    def isBiPartite(self):
+        return self.__isBiPartitie
+
+if __name__ == '__main__':
+    print("=====first graph======")
+    g = BiPartitionDetection("g.txt")
+    print(g.isBiPartite())
+    print("=====second graph======")
+    g = BiPartitionDetection("g2.txt")
+    print(g.isBiPartite())
+    print("=====third graph======")
+    g = BiPartitionDetection("g3.txt")
+    print(g.isBiPartite())

Graph_BFS/USSSPath.py

@@ -0,0 +1,101 @@
+"""
+@author: Alex
+@contact: 1272296763@qq.com or jakinmili@gmail.com
+@file: USSSPath.py
+@time: 2019/10/26 16:41
+"""
+import queue
+class USSSPath:
+
+    def __init__(self, filename, s):
+        self.V = 0  # 顶点数
+        self.E = 0  # 边数
+        self.adj = None
+        self.__initGraph(filename)
+
+        # 计算路径和最短路径
+        self.visited = [False for i in range(self.V)]
+        self.__dis = [-1 for i in range(self.V)] # 记录每个结点离根节点的最小距离
+        self.pre = [-1 for i in range(self.V)] # 每一个结点的上一个结点
+        self.s = s
+        self.bfs(s)
+
+    def __initGraph(self, filename):
+       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 bfs(self, s):
+        que = queue.Queue(self.V)
+        self.visited[s] = True
+        que.put(s)
+        self.pre[s] = s
+        self.__dis[s] = 0
+        while que.empty() == False:
+            v = que.get()
+
+            for w in self.adj[v]:
+                if self.visited[w] == False:
+                    que.put(w)
+                    self.visited[w] = True
+                    self.pre[w] = v
+                    self.__dis[w] = self.__dis[v] + 1
+
+    def isConnectedTo(self, t):
+        self.validateVertex(t)
+        return self.visited[t]
+
+    def dis(self, t):
+        self.validateVertex(t)
+        print("{} -> {}的距离为：{}".format(self.s, t, self.__dis[t]))
+
+    def path(self, t):
+        res = []
+        if self.isConnectedTo(t) == False:
+            return res
+        cur = t
+        while cur != self.s:
+            res.append(cur)
+            cur = self.pre[cur]
+        res.append(self.s)
+
+        res.reverse()
+        print("{} -> {}的路径为：{}".format(self.s, t, res))
+
+if __name__ == '__main__':
+    usssp = USSSPath("../g_ssp.txt", 0)
+    usssp.get_graph_information()
+    usssp.path(6)
+    usssp.dis(6)

Graph_BFS/g.txt

@@ -0,0 +1,7 @@
+7 6
+0 1
+0 2
+1 3
+1 4
+2 3
+2 6

Graph_BFS/g2.txt

@@ -0,0 +1,7 @@
+4 6
+0 1
+0 2
+0 3
+1 2
+1 3
+2 3

Graph_BFS/g3.txt

@@ -0,0 +1,5 @@
+4 4
+0 1
+0 3
+1 2
+2 3

readme.md

@@ -110,20 +110,22 @@ BFS类中,和树的广度优先遍历类似，区别在于图的广度优先遍
     bfs.get_BFSorder()
 
 > PS：此处可以注意到dfs和bfs的在非递归实现的相同之处,除了使用不同的数据结构存放遍历过程的数据外，其他基本相同
-> visited[0 .... v-1] = false
-> for v in range(self.V):
->   if visited[v] == False:   
->       search(v)
->
-> search(s):
->   x.push(s)
->   visited[s] = True
->   while !x.isEmplty():
->       v = x.pop()
->       for w in self.adj[w]:
->           if visited[w] == False:
->               x.push(w)
->               visited[w] = True
+ 
+     visited[0 .... v-1] = false
+     for v in range(self.V):
+       if visited[v] == False:   
+           search(v)
+    
+     search(s):
+       x.push(s)
+       visited[s] = True
+       while !x.isEmplty():
+           v = x.pop()
+           for w in self.adj[w]:
+               if visited[w] == False:
+                   x.push(w)
+                   visited[w] = True
+                   
 > 此处当x为栈时，为广度优先遍历，为队列的时候为深度优先遍历，除此之外还可以是随机队列等其他数据结构，发挥不同的作用
 
 #### 2.2 环检测
@@ -140,5 +142,22 @@ SingleSourcePath类中
     ssp.path(4)
 
 #### 2.4 二部图检测
-
-#### 2.5 最短路径（注意！此处是无向无权图）
+BiPartitionDetection类中
+
+    print("=====first graph======")
+    g = BiPartitionDetection("g.txt")
+    print(g.isBiPartite())
+    print("=====second graph======")
+    g = BiPartitionDetection("g2.txt")
+    print(g.isBiPartite())
+    print("=====third graph======")
+    g = BiPartitionDetection("g3.txt")
+    print(g.isBiPartite())
+
+#### 2.5 最短路径（注意！此处是无向无权图）
+USSSPath类中
+
+    usssp = USSSPath("../g_ssp.txt", 0)
+    usssp.get_graph_information()
+    usssp.path(6)
+    usssp.dis(6)