refactor

graphs/Eulerian_path_and_circuit_for_undirected_graph.py

@@ -0,0 +1,93 @@
+# Eulerian Path is a path in graph that visits every edge exactly once.
+# Eulerian Circuit is an Eulerian Path which starts and ends on the same
+# vertex.
+# time complexity is O(V+E)
+# space complexity is O(VE)
+
+
+# using dfs for finding eulerian path traversal
+def dfs(u, graph, visited_edge, path=[]):
+    path = path + [u]
+    for v in graph[u]:
+        if visited_edge[u][v] == False:
+            visited_edge[u][v], visited_edge[v][u] = True, True
+            path = dfs(v, graph, visited_edge, path)
+    return path
+
+
+# for checking in graph has euler path or circuit
+def check_circuit_or_path(graph, max_node):
+    odd_degree_nodes = 0
+    odd_node = -1
+    for i in range(max_node):
+        if i not in graph.keys():
+            continue
+        if len(graph[i]) % 2 == 1:
+            odd_degree_nodes += 1
+            odd_node = i
+    if odd_degree_nodes == 0:
+        return 1, odd_node
+    if odd_degree_nodes == 2:
+        return 2, odd_node
+    return 3, odd_node
+
+
+def check_euler(graph, max_node):
+    visited_edge = [[False for _ in range(max_node + 1)] for _ in range(max_node + 1)]
+    check, odd_node = check_circuit_or_path(graph, max_node)
+    if check == 3:
+        print("graph is not Eulerian")
+        print("no path")
+        return
+    start_node = 1
+    if check == 2:
+        start_node = odd_node
+        print("graph has a Euler path")
+    if check == 1:
+        print("graph has a Euler cycle")
+    path = dfs(start_node, graph, visited_edge)
+    print(path)
+
+
+def main():
+    G1 = {
+        1: [2, 3, 4],
+        2: [1, 3],
+        3: [1, 2],
+        4: [1, 5],
+        5: [4]
+    }
+    G2 = {
+        1: [2, 3, 4, 5],
+        2: [1, 3],
+        3: [1, 2],
+        4: [1, 5],
+        5: [1, 4]
+    }
+    G3 = {
+        1: [2, 3, 4],
+        2: [1, 3, 4],
+        3: [1, 2],
+        4: [1, 2, 5],
+        5: [4]
+    }
+    G4 = {
+        1: [2, 3],
+        2: [1, 3],
+        3: [1, 2],
+    }
+    G5 = {
+        1: [],
+        2: []
+        # all degree is zero
+    }
+    max_node = 10
+    check_euler(G1, max_node)
+    check_euler(G2, max_node)
+    check_euler(G3, max_node)
+    check_euler(G4, max_node)
+    check_euler(G5, max_node)
+
+
+if __name__ == "__main__":
+    main()

graphs/edmonds_karp_multiple_source_and_sink.py

@@ -0,0 +1,182 @@
+class FlowNetwork:
+    def __init__(self, graph, sources, sinks):
+        self.sourceIndex = None
+        self.sinkIndex = None
+        self.graph = graph
+
+        self._normalizeGraph(sources, sinks)
+        self.verticesCount = len(graph)
+        self.maximumFlowAlgorithm = None
+
+    # make only one source and one sink
+    def _normalizeGraph(self, sources, sinks):
+        if sources is int:
+            sources = [sources]
+        if sinks is int:
+            sinks = [sinks]
+
+        if len(sources) == 0 or len(sinks) == 0:
+            return
+
+        self.sourceIndex = sources[0]
+        self.sinkIndex = sinks[0]
+
+        # make fake vertex if there are more
+        # than one source or sink
+        if len(sources) > 1 or len(sinks) > 1:
+            maxInputFlow = 0
+            for i in sources:
+                maxInputFlow += sum(self.graph[i])
+
+
+            size = len(self.graph) + 1
+            for room in self.graph:
+                room.insert(0, 0)
+            self.graph.insert(0, [0] * size)
+            for i in sources:
+                self.graph[0][i + 1] = maxInputFlow
+            self.sourceIndex  = 0
+
+            size = len(self.graph) + 1
+            for room in self.graph:
+                room.append(0)
+            self.graph.append([0] * size)
+            for i in sinks:
+                self.graph[i + 1][size - 1] = maxInputFlow
+            self.sinkIndex = size - 1
+
+
+    def findMaximumFlow(self):
+        if self.maximumFlowAlgorithm is None:
+            raise Exception("You need to set maximum flow algorithm before.")
+        if self.sourceIndex is None or self.sinkIndex is None:
+            return 0
+
+        self.maximumFlowAlgorithm.execute()
+        return self.maximumFlowAlgorithm.getMaximumFlow()
+
+    def setMaximumFlowAlgorithm(self, Algorithm):
+        self.maximumFlowAlgorithm = Algorithm(self)
+
+
+class FlowNetworkAlgorithmExecutor(object):
+    def __init__(self, flowNetwork):
+        self.flowNetwork = flowNetwork
+        self.verticesCount = flowNetwork.verticesCount
+        self.sourceIndex = flowNetwork.sourceIndex
+        self.sinkIndex = flowNetwork.sinkIndex
+        # it's just a reference, so you shouldn't change
+        # it in your algorithms, use deep copy before doing that
+        self.graph = flowNetwork.graph
+        self.executed = False
+
+    def execute(self):
+        if not self.executed:
+            self._algorithm()
+            self.executed = True
+
+    # You should override it
+    def _algorithm(self):
+        pass
+
+
+
+class MaximumFlowAlgorithmExecutor(FlowNetworkAlgorithmExecutor):
+    def __init__(self, flowNetwork):
+        super(MaximumFlowAlgorithmExecutor, self).__init__(flowNetwork)
+        # use this to save your result
+        self.maximumFlow = -1
+
+    def getMaximumFlow(self):
+        if not self.executed:
+            raise Exception("You should execute algorithm before using its result!")
+
+        return self.maximumFlow
+
+class PushRelabelExecutor(MaximumFlowAlgorithmExecutor):
+    def __init__(self, flowNetwork):
+        super(PushRelabelExecutor, self).__init__(flowNetwork)
+
+        self.preflow = [[0] * self.verticesCount for i in range(self.verticesCount)]
+
+        self.heights = [0] * self.verticesCount
+        self.excesses = [0] * self.verticesCount
+
+    def _algorithm(self):
+        self.heights[self.sourceIndex] = self.verticesCount
+
+        # push some substance to graph
+        for nextVertexIndex, bandwidth in enumerate(self.graph[self.sourceIndex]):
+            self.preflow[self.sourceIndex][nextVertexIndex] += bandwidth
+            self.preflow[nextVertexIndex][self.sourceIndex] -= bandwidth
+            self.excesses[nextVertexIndex] += bandwidth
+
+        # Relabel-to-front selection rule
+        verticesList = [i for i in range(self.verticesCount)
+                        if i != self.sourceIndex and i != self.sinkIndex]
+
+        # move through list
+        i = 0
+        while i < len(verticesList):
+            vertexIndex = verticesList[i]
+            previousHeight = self.heights[vertexIndex]
+            self.processVertex(vertexIndex)
+            if self.heights[vertexIndex] > previousHeight:
+                # if it was relabeled, swap elements
+                # and start from 0 index
+                verticesList.insert(0, verticesList.pop(i))
+                i = 0
+            else:
+                i += 1
+
+        self.maximumFlow = sum(self.preflow[self.sourceIndex])
+
+    def processVertex(self, vertexIndex):
+        while self.excesses[vertexIndex] > 0:
+            for neighbourIndex in range(self.verticesCount):
+                # if it's neighbour and current vertex is higher
+                if self.graph[vertexIndex][neighbourIndex] - self.preflow[vertexIndex][neighbourIndex] > 0\
+                        and self.heights[vertexIndex] > self.heights[neighbourIndex]:
+                    self.push(vertexIndex, neighbourIndex)
+
+            self.relabel(vertexIndex)
+
+    def push(self, fromIndex, toIndex):
+        preflowDelta = min(self.excesses[fromIndex],
+                           self.graph[fromIndex][toIndex] - self.preflow[fromIndex][toIndex])
+        self.preflow[fromIndex][toIndex] += preflowDelta
+        self.preflow[toIndex][fromIndex] -= preflowDelta
+        self.excesses[fromIndex] -= preflowDelta
+        self.excesses[toIndex] += preflowDelta
+
+    def relabel(self, vertexIndex):
+        minHeight = None
+        for toIndex in range(self.verticesCount):
+            if self.graph[vertexIndex][toIndex] - self.preflow[vertexIndex][toIndex] > 0:
+                if minHeight is None or self.heights[toIndex] < minHeight:
+                    minHeight = self.heights[toIndex]
+
+        if minHeight is not None:
+            self.heights[vertexIndex] = minHeight + 1
+
+if __name__ == '__main__':
+    entrances = [0]
+    exits = [3]
+    # graph = [
+    #     [0, 0, 4, 6, 0, 0],
+    #     [0, 0, 5, 2, 0, 0],
+    #     [0, 0, 0, 0, 4, 4],
+    #     [0, 0, 0, 0, 6, 6],
+    #     [0, 0, 0, 0, 0, 0],
+    #     [0, 0, 0, 0, 0, 0],
+    # ]
+    graph = [[0, 7, 0, 0], [0, 0, 6, 0], [0, 0, 0, 8], [9, 0, 0, 0]]
+
+    # prepare our network
+    flowNetwork = FlowNetwork(graph, entrances, exits)
+    # set algorithm
+    flowNetwork.setMaximumFlowAlgorithm(PushRelabelExecutor)
+    # and calculate
+    maximumFlow = flowNetwork.findMaximumFlow()
+
+    print("maximum flow is {}".format(maximumFlow))

graphs/page_rank.py

@@ -0,0 +1,72 @@
+'''
+Author: https://github.com/bhushan-borole
+'''
+'''
+The input graph for the algorithm is:
+
+  A B C
+A 0 1 1
+B 0 0 1
+C 1 0 0
+
+'''
+
+graph = [[0, 1, 1],
+    	[0, 0, 1],
+    	[1, 0, 0]]
+
+
+class Node:
+    def __init__(self, name):
+        self.name = name
+        self.inbound = []
+        self.outbound = []
+    
+    def add_inbound(self, node):
+        self.inbound.append(node)
+    
+    def add_outbound(self, node):
+        self.outbound.append(node)
+    
+    def __repr__(self):
+        return 'Node {}: Inbound: {} ; Outbound: {}'.format(self.name,
+                                                      	self.inbound,
+                                                      	self.outbound)
+
+
+def page_rank(nodes, limit=3, d=0.85):
+    ranks = {}
+    for node in nodes:
+        ranks[node.name] = 1
+
+    outbounds = {}
+    for node in nodes:
+        outbounds[node.name] = len(node.outbound)
+
+    for i in range(limit):
+        print("======= Iteration {} =======".format(i+1))
+        for j, node in enumerate(nodes):
+            ranks[node.name] = (1 - d) + d * sum([ ranks[ib]/outbounds[ib] for ib in node.inbound ])
+        print(ranks)
+
+
+def main():
+    names = list(input('Enter Names of the Nodes: ').split())
+
+    nodes = [Node(name) for name in names]
+    
+    for ri, row in enumerate(graph):
+        for ci, col in enumerate(row):
+            if col == 1:
+                nodes[ci].add_inbound(names[ri])
+                nodes[ri].add_outbound(names[ci])
+
+    print("======= Nodes =======")
+    for node in nodes:
+        print(node)
+
+    page_rank(nodes)
+
+
+if __name__ == '__main__':
+    main()