【算法——Python实现】有负权图求单源最短路径BellmanFord算法

class Edge(object):
    """边"""
    def __init__(self, a, b, weight):
        self.a = a # 第一个顶点
        self.b = b # 第二个顶点
        self.weight = weight # 权值

    def v(self):
        return self.a

    def w(self):
        return self.b

    def wt(self):
        return self.weight

    def other(self, x):
        # 返回x顶点连接的另一个顶点
        if x == self.a or x == self.b:
            if x == self.a:
                return self.b
            else:
                return self.a

    def __lt__(self, other):
        # 小于号重载
        return self.weight < other.wt()

    def __le__(self, other):
        # 小于等于号重载
        return self.weight <= other.wt()

    def __gt__(self, other):
        # 大于号重载
        return self.weight > other.wt()

    def __ge__(self, other):
        # 大于等于号重载
        return self.weight >= other.wt()

    def __eq__(self, other):
        # ==号重载
        return self.weight == other.wt()


class DenseGraph(object):
    """有权稠密图 - 邻接矩阵"""
    def __init__(self, n, directed):
        self.n = n  # 图中的点数
        self.m = 0  # 图中的边数
        self.directed = directed  # bool值，表示是否为有向图
        self.g = [[None for _ in range(n)] for _ in range(n)]  # 矩阵初始化都为None的二维矩阵

    def V(self):
        # 返回图中点数
        return self.n

    def E(self):
        # 返回图中边数
        return self.m

    def addEdge(self, v, w, weight):
        # v和w中增加一条边，v和w都是[0,n-1]区间
        if v >= 0 and v < n and w >= 0 and w < n:
            if self.hasEdge(v, w):
                self.m -= 1
            self.g[v][w] = Edge(v, w, weight)
            if not self.directed:
                self.g[w][v] = Edge(w, v, weight)
            self.m += 1

    def hasEdge(self, v, w):
        # v和w之间是否有边，v和w都是[0,n-1]区间
        if v >= 0 and v < n and w >= 0 and w < n:
            return self.g[v][w] != None

    class adjIterator(object):
        """相邻节点迭代器"""
        def __init__(self, graph, v):
            self.G = graph  # 需要遍历的图
            self.v = v  # 遍历v节点相邻的边
            self.index = 0  # 遍历的索引

        def __iter__(self):
            return self

        def next(self):
            while self.index < self.G.V():
                # 当索引小于节点数量时遍历，否则为遍历完成，停止迭代
                if self.G.g[self.v][self.index]:
                    r = self.G.g[self.v][self.index]
                    self.index += 1
                    return r
                self.index += 1
            raise StopIteration()


class SparseGraph(object):
    """有权稀疏图- 邻接表"""
    def __init__(self, n, directed):
        self.n = n  # 图中的点数
        self.m = 0  # 图中的边数
        self.directed = directed  # bool值，表示是否为有向图
        self.g = [[] for _ in range(n)]  # 矩阵初始化都为空的二维矩阵

    def V(self):
        # 返回图中点数
        return self.n

    def E(self):
        # 返回图中边数
        return self.m

    def addEdge(self, v, w, weight):
        # v和w中增加一条边，v和w都是[0,n-1]区间
        if v >= 0 and v < n and w >= 0 and w < n:
            # 考虑到平行边会让时间复杂度变为最差为O(n)
            # if self.hasEdge(v, w):
            #   return None
            self.g[v].append(Edge(v, w, weight))
            if v != w and not self.directed:
                self.g[w].append(Edge(w, v, weight))
            self.m += 1

    def hasEdge(self, v, w):
        # v和w之间是否有边，v和w都是[0,n-1]区间
        # 时间复杂度最差为O(n)
        if v >= 0 and v < n and w >= 0 and w < n:
            for i in self.g[v]:
                if i.other(v) == w:
                    return True
            return False

    class adjIterator(object):
        """相邻节点迭代器"""
        def __init__(self, graph, v):
            self.G = graph  # 需要遍历的图
            self.v = v  # 遍历v节点相邻的边
            self.index = 0  # 遍历的索引

        def __iter__(self):
            return self

        def next(self):
            if len(self.G.g[self.v]):
                # v有相邻节点才遍历
                if self.index < len(self.G.g[self.v]):
                    r = self.G.g[self.v][self.index]
                    self.index += 1
                    return r
                else:
                    raise StopIteration()
            else:
                raise StopIteration()


class ReadGraph(object):
    """读取文件中的图"""
    def __init__(self, graph, filename):
        with open(filename, 'r') as f:
            line = f.readline()
            line = line.strip('\n')
            line = line.split()
            v = int(line[0])
            e = int(line[1])
            if v == graph.V():
                lines = f.readlines()
                for i in lines:
                    a, b, w = self.stringstream(i)
                    if a >= 0 and a < v and b >=0 and b < v:
                        graph.addEdge(a, b, w)

    def stringstream(self, text):
        result = text.strip('\n')
        result = result.split()
        a, b, w = result
        return int(a), int(b), int(w)


class BellmanFord(object):
    """BellmanFord求单源最短路径，可以有负权值。多次执行松弛操作，一点到一点最短路径最多有V-1条边V个顶点，松弛时超过这个数则证明有负权环，无最短路径
    只能处理有向图，无向图如果两个点之间权值都为负会直接形成负权环"""
    def __init__(self, graph, s):
        self.G = graph  # 图
        self.s = s  # 原点s
        self.distTo = [0 for _ in range(self.G.V())]  # 从原点到每个节点的权值，初始都为0
        self.fromed = [None for _ in range(self.G.V())] # 记录此节点来自哪个节点的连接，存储边。None表示未被访问过
        self.hasNegativeCircle = False  # 是否有负权环

        # BellmanFord
        # 共对所有顶点做V-1次松弛
        for p in range(self.G.V()-1):
            # 每一轮松弛要对所有节点都做松弛操作
            for i in range(self.G.V()):
                # 只对原点s或者其他已经到达的顶点做松弛操作
                if self.fromed[i] or self.s == i:
                    adj = self.G.adjIterator(self.G, i)
                    for e in adj:
                        # 如果w还未被访问过，或经过v的最短路径再到w节点的权值小于w之前被访问时记录的路径，则用经过v再到w的路径替代
                        if not self.fromed[e.w()] or self.distTo[i] + e.wt() <  self.distTo[e.w()]:
                            self.distTo[e.w()] = self.distTo[i] + e.wt()
                            self.fromed[e.w()] = e

        self.hasNegativeCircle = self.detectNegativeCircle()

    def detectNegativeCircle(self):
        # 再做一轮对所有顶点的松弛操作，如果还能松弛则表示有负权环
        for i in range(self.G.V()):
            # 只对原点s或者其他已经到达的顶点做松弛操作
            if self.fromed[i] or self.s == i:
                adj = self.G.adjIterator(self.G, i)
                for e in adj:
                    # 如果w还未被访问过，或经过v的最短路径再到w节点的权值小于w之前被访问时记录的路径，则表示一定有负权环
                    if not self.fromed[e.w()] or self.distTo[i] + e.wt() <  self.distTo[e.w()]:
                        return True
        return False

    def negativeCycle(self):
        # 查询是否有负权环
        return self.hasNegativeCircle

    def shortestPathTo(self, w):
        # 从原点到w节点的权值
        if not self.hasNegativeCycle and w >= 0 and w < self.G.V():
            return self.distTo[w]
        else:
            return None

    def hasPathTo(self, w):
        # 从原点到w是否有路径
        if w >= 0 and w < self.G.V():
            return self.fromed[w] != None

    def shortestPath(self, w):
        # 从原点到w的最短路径
        if not self.hasNegativeCycle and w >= 0 and w < self.G.V():
            s = []
            e = self.fromed[w]
            while e:
                s.append(e)
                e = self.fromed[e.v()]
            s.reverse()
            return s
        else:
            return None

    def showPath(self, w):
        # 输出路径
        if not self.hasNegativeCycle and w >= 0 and w < self.G.V():
            s = self.shortestPath(w)
            i = 0
            while i < len(s):
                print s[i].v()
                if i == len(s) - 1:
                    print s[i].w()
                i += 1