def make_graph_2():
# https://www.youtube.com/watch?v=-mOEd_3gTK0&ab_channel=TusharRoy-CodingMadeSimple
graph = AdjacencyList(5)
zero = graph.add_vertex(index=0, rep='(0)')
one = graph.add_vertex(index=1, rep='(1)')
two = graph.add_vertex(index=2, rep='(2)')
three = graph.add_vertex(index=3, rep='(3)')
four = graph.add_vertex(index=4, rep='(4)')
graph.add_edge(origin_vertex=zero, destination_vertex=one, weight=4)
graph.add_edge(origin_vertex=zero, destination_vertex=two, weight=5)
graph.add_edge(origin_vertex=one, destination_vertex=two, weight=-3)
graph.add_edge(origin_vertex=zero, destination_vertex=three, weight=8)
graph.add_edge(origin_vertex=three, destination_vertex=four, weight=2)
graph.add_edge(origin_vertex=four, destination_vertex=three, weight=1)
graph.add_edge(origin_vertex=two, destination_vertex=four, weight=4)
expected = [0, 4, 1, 6, 5]
return graph, zero, three, expected
def make_graph_with_neg_cycle():
# https://www.youtube.com/watch?v=-mOEd_3gTK0&t=969s&ab_channel=TusharRoy-CodingMadeSimple
graph = AdjacencyList(4)
zero = graph.add_vertex(index=0, rep='(0)')
one = graph.add_vertex(index=1, rep='(1)')
two = graph.add_vertex(index=2, rep='(2)')
three = graph.add_vertex(index=3, rep='(3)')
graph.add_edge(origin_vertex=zero, destination_vertex=one, weight=1)
graph.add_edge(origin_vertex=one, destination_vertex=two, weight=3)
graph.add_edge(origin_vertex=two, destination_vertex=three, weight=2)
graph.add_edge(origin_vertex=three, destination_vertex=one, weight=-6)
expected = False
return graph, zero, one, expected
def make_graph_1():
# https://www.youtube.com/watch?v=4OQeCuLYj-4&ab_channel=MichaelSambol
graph = AdjacencyList(4)
one = graph.add_vertex(index=0, rep='(1)')
two = graph.add_vertex(index=1, rep='(2)')
three = graph.add_vertex(index=2, rep='(3)')
four = graph.add_vertex(index=3, rep='(4)')
graph.add_edge(origin_vertex=one, destination_vertex=three, weight=-2)
graph.add_edge(origin_vertex=three, destination_vertex=four, weight=2)
graph.add_edge(origin_vertex=four, destination_vertex=two, weight=-1)
graph.add_edge(origin_vertex=two, destination_vertex=three, weight=3)
graph.add_edge(origin_vertex=two, destination_vertex=one, weight=4)
return graph, four, three
def make_graph_1():
# http://www.programming-algorithms.net/article/47389/Bellman-Ford-algorithm
graph = AdjacencyList(6)
S = graph.add_vertex(index=0, rep='S')
A = graph.add_vertex(index=1, rep='A')
B = graph.add_vertex(index=2, rep='B')
C = graph.add_vertex(index=3, rep='C')
D = graph.add_vertex(index=4, rep='D')
E = graph.add_vertex(index=5, rep='E')
graph.add_edge(origin_vertex=S, destination_vertex=A, weight=10)
graph.add_edge(origin_vertex=S, destination_vertex=E, weight=8)
graph.add_edge(origin_vertex=E, destination_vertex=D, weight=1)
graph.add_edge(origin_vertex=D, destination_vertex=A, weight=-4)
graph.add_edge(origin_vertex=D, destination_vertex=C, weight=-1)
graph.add_edge(origin_vertex=A, destination_vertex=C, weight=2)
graph.add_edge(origin_vertex=C, destination_vertex=B, weight=-2)
graph.add_edge(origin_vertex=B, destination_vertex=A, weight=1)
# S A B C D E
# 0 5 5 7 9 8
expected = [0, 5, 5, 7, 9, 8]
return graph, S, C, expected
def make_networks_codeforces():
flow_network = AdjacencyList(4)
one = flow_network.add_vertex(index=0, rep='(1)')
two = flow_network.add_vertex(index=1, rep='(2)')
three = flow_network.add_vertex(index=2, rep='(3)')
four = flow_network.add_vertex(index=3, rep='(4)')
flow_network.add_edge(origin_vertex=one,
destination_vertex=two,
capacity=10,
flow=0)
flow_network.add_edge(origin_vertex=one,
destination_vertex=three,
capacity=10,
flow=0)
flow_network.add_edge(origin_vertex=two,
destination_vertex=three,
capacity=1,
flow=0)
flow_network.add_edge(origin_vertex=two,
destination_vertex=four,
capacity=10,
flow=0)
flow_network.add_edge(origin_vertex=three,
destination_vertex=four,
capacity=10,
flow=0)
residual_network = AdjacencyList(4)
one_r = residual_network.add_vertex(index=0, rep='(1)')
two_r = residual_network.add_vertex(index=1, rep='(2)')
three_r = residual_network.add_vertex(index=2, rep='(3)')
four_r = residual_network.add_vertex(index=3, rep='(4)')
residual_network.add_edge(origin_vertex=one_r,
destination_vertex=two_r,
residual_capacity=10,
flow=0)
residual_network.add_edge(origin_vertex=one_r,
destination_vertex=three_r,
residual_capacity=10,
flow=0)
residual_network.add_edge(origin_vertex=two_r,
destination_vertex=three_r,
residual_capacity=1,
flow=0)
residual_network.add_edge(origin_vertex=two_r,
destination_vertex=four_r,
residual_capacity=10,
flow=0)
residual_network.add_edge(origin_vertex=three_r,
destination_vertex=four_r,
residual_capacity=10,
flow=0)
return flow_network, residual_network, one, four, one_r, four_r
def make_networks_mathspace():
# https://mathspace.co/learn/world-of-maths/networks/network-flow-18724/network-flow-1289/
flow_network = AdjacencyList(4)
A = flow_network.add_vertex(index=0, rep='A')
B = flow_network.add_vertex(index=1, rep='B')
D = flow_network.add_vertex(index=2, rep='D')
C = flow_network.add_vertex(index=3, rep='C')
flow_network.add_edge(origin_vertex=A,
destination_vertex=B,
capacity=12,
flow=0)
flow_network.add_edge(origin_vertex=A,
destination_vertex=D,
capacity=9,
flow=0)
flow_network.add_edge(origin_vertex=D,
destination_vertex=B,
capacity=8,
flow=0)
flow_network.add_edge(origin_vertex=B,
destination_vertex=C,
capacity=15,
flow=0)
flow_network.add_edge(origin_vertex=D,
destination_vertex=C,
capacity=11,
flow=0)
residual_network = AdjacencyList(4)
Ar = residual_network.add_vertex(index=0, rep='A')
Br = residual_network.add_vertex(index=1, rep='B')
Dr = residual_network.add_vertex(index=2, rep='D')
Cr = residual_network.add_vertex(index=3, rep='C')
residual_network.add_edge(origin_vertex=Ar,
destination_vertex=Br,
residual_capacity=12,
flow=0)
residual_network.add_edge(origin_vertex=Ar,
destination_vertex=Dr,
residual_capacity=9,
flow=0)
residual_network.add_edge(origin_vertex=Dr,
destination_vertex=Br,
residual_capacity=8,
flow=0)
residual_network.add_edge(origin_vertex=Br,
destination_vertex=Cr,
residual_capacity=15,
flow=0)
residual_network.add_edge(origin_vertex=Dr,
destination_vertex=Cr,
residual_capacity=11,
flow=0)
return flow_network, residual_network, A, C, Ar, Cr
def make_networks():
# Modeling 2nd graph from with max flow of 17: https://www.hackerearth.com/practice/algorithms/graphs/maximum-flow/tutorial/
flow_network = AdjacencyList(6)
S = flow_network.add_vertex(index=0, rep='S')
A = flow_network.add_vertex(index=1, rep='A')
B = flow_network.add_vertex(index=2, rep='B')
C = flow_network.add_vertex(index=3, rep='C')
D = flow_network.add_vertex(index=4, rep='D')
T = flow_network.add_vertex(index=5, rep='T')
# Set all flows to 0.
SA = flow_network.add_edge(origin_vertex=S,
destination_vertex=A,
capacity=10,
flow=0)
AC = flow_network.add_edge(origin_vertex=A,
destination_vertex=C,
capacity=8,
flow=0)
CT = flow_network.add_edge(origin_vertex=C,
destination_vertex=T,
capacity=10,
flow=0)
AB = flow_network.add_edge(origin_vertex=A,
destination_vertex=B,
capacity=2,
flow=0)
SB = flow_network.add_edge(origin_vertex=S,
destination_vertex=B,
capacity=8,
flow=0)
BC = flow_network.add_edge(origin_vertex=B,
destination_vertex=C,
capacity=6,
flow=0)
BD = flow_network.add_edge(origin_vertex=B,
destination_vertex=D,
capacity=7,
flow=0)
DT = flow_network.add_edge(origin_vertex=D,
destination_vertex=T,
capacity=10,
flow=0)
# Make residual graph.
residual_network = AdjacencyList(6)
Sr = residual_network.add_vertex(index=0, rep='S')
Ar = residual_network.add_vertex(index=1, rep='A')
Br = residual_network.add_vertex(index=2, rep='B')
Cr = residual_network.add_vertex(index=3, rep='C')
Dr = residual_network.add_vertex(index=4, rep='D')
Tr = residual_network.add_vertex(index=5, rep='T')
# All edges have residual capacity = capacity of edge - flow, all flow is 0 to start.
SAr = residual_network.add_edge(origin_vertex=Sr,
destination_vertex=Ar,
residual_capacity=10,
flow=0)
ACr = residual_network.add_edge(origin_vertex=Ar,
destination_vertex=Cr,
residual_capacity=8,
flow=0)
CTr = residual_network.add_edge(origin_vertex=Cr,
destination_vertex=Tr,
residual_capacity=10,
flow=0)
ABr = residual_network.add_edge(origin_vertex=Ar,
destination_vertex=Br,
residual_capacity=2,
flow=0)
SBr = residual_network.add_edge(origin_vertex=Sr,
destination_vertex=Br,
residual_capacity=8,
flow=0)
BCr = residual_network.add_edge(origin_vertex=Br,
destination_vertex=Cr,
residual_capacity=6,
flow=0)
BDr = residual_network.add_edge(origin_vertex=Br,
destination_vertex=Dr,
residual_capacity=7,
flow=0)
DTr = residual_network.add_edge(origin_vertex=Dr,
destination_vertex=Tr,
residual_capacity=10,
flow=0)
return flow_network, residual_network, S, T, Sr, Tr
def make_networks_example():
# Network based on: https://www.youtube.com/watch?v=rLIR89YyNjg&ab_channel=A%26A
flow_network = AdjacencyList(6)
A = flow_network.add_vertex(index=0, rep='A')
B = flow_network.add_vertex(index=1, rep='B')
C = flow_network.add_vertex(index=2, rep='C')
D = flow_network.add_vertex(index=3, rep='D')
E = flow_network.add_vertex(index=4, rep='E')
F = flow_network.add_vertex(index=5, rep='F')
flow_network.add_edge(origin_vertex=A,
destination_vertex=B,
capacity=16,
flow=0)
flow_network.add_edge(origin_vertex=B,
destination_vertex=C,
capacity=12,
flow=0)
flow_network.add_edge(origin_vertex=B,
destination_vertex=D,
capacity=4,
flow=0)
flow_network.add_edge(origin_vertex=A,
destination_vertex=D,
capacity=5,
flow=0)
flow_network.add_edge(origin_vertex=C,
destination_vertex=D,
capacity=9,
flow=0)
flow_network.add_edge(origin_vertex=C,
destination_vertex=F,
capacity=5,
flow=0)
flow_network.add_edge(origin_vertex=D,
destination_vertex=E,
capacity=20,
flow=0)
flow_network.add_edge(origin_vertex=C,
destination_vertex=E,
capacity=7,
flow=0)
flow_network.add_edge(origin_vertex=E,
destination_vertex=F,
capacity=20,
flow=0)
# Residual network:
residual_network = AdjacencyList(6)
Ar = residual_network.add_vertex(index=0, rep='A')
Br = residual_network.add_vertex(index=1, rep='B')
Cr = residual_network.add_vertex(index=2, rep='C')
Dr = residual_network.add_vertex(index=3, rep='D')
Er = residual_network.add_vertex(index=4, rep='E')
Fr = residual_network.add_vertex(index=5, rep='F')
residual_network.add_edge(origin_vertex=Ar,
destination_vertex=Br,
residual_capacity=16,
flow=0)
residual_network.add_edge(origin_vertex=Br,
destination_vertex=Cr,
residual_capacity=12,
flow=0)
residual_network.add_edge(origin_vertex=Br,
destination_vertex=Dr,
residual_capacity=4,
flow=0)
residual_network.add_edge(origin_vertex=Ar,
destination_vertex=Dr,
residual_capacity=5,
flow=0)
residual_network.add_edge(origin_vertex=Cr,
destination_vertex=Dr,
residual_capacity=9,
flow=0)
residual_network.add_edge(origin_vertex=Cr,
destination_vertex=Fr,
residual_capacity=5,
flow=0)
residual_network.add_edge(origin_vertex=Dr,
destination_vertex=Er,
residual_capacity=20,
flow=0)
residual_network.add_edge(origin_vertex=Cr,
destination_vertex=Er,
residual_capacity=7,
flow=0)
residual_network.add_edge(origin_vertex=Er,
destination_vertex=Fr,
residual_capacity=20,
flow=0)
return flow_network, residual_network, A, F, Ar, Fr
def make_networks_basic_test():
# A simple linear chain network showing that edges S->A and B->T will be restricted by the min flow in an edge in the augmenting path.
flow_network = AdjacencyList(4)
S = flow_network.add_vertex(index=0, rep='S')
A = flow_network.add_vertex(index=1, rep='A')
B = flow_network.add_vertex(index=2, rep='B')
T = flow_network.add_vertex(index=3, rep='T')
flow_network.add_edge(origin_vertex=S,
destination_vertex=A,
capacity=50,
flow=0)
flow_network.add_edge(origin_vertex=A,
destination_vertex=B,
capacity=2,
flow=0)
flow_network.add_edge(origin_vertex=B,
destination_vertex=T,
capacity=50,
flow=0)
residual_network = AdjacencyList(4)
Sr = residual_network.add_vertex(index=0, rep='S')
Ar = residual_network.add_vertex(index=1, rep='A')
Br = residual_network.add_vertex(index=2, rep='B')
Tr = flow_network.add_vertex(index=3, rep='T')
residual_network.add_edge(origin_vertex=Sr,
destination_vertex=Ar,
residual_capacity=50)
residual_network.add_edge(origin_vertex=Ar,
destination_vertex=Br,
residual_capacity=2)
residual_network.add_edge(origin_vertex=Br,
destination_vertex=Tr,
residual_capacity=50)
return flow_network, residual_network, S, T, Sr, Tr
dfs1_rec = depth_first_search_rec_driver(graph_map, source)
print(
"DFS on adjacent map, sometimes different order (all correct, check against 4 solns in test()"
)
print("DFS on adj_map graph (iterative): " + str(dfs1_itr))
print("DFS on adj_map graph (recursive): " + str(dfs1_rec))
""" Note
due to randomness with {} sometimes we get a different order using a adj map
however they are all correct orderings by picking arbitrary adjacent nodes
see the tests below
"""
print("Testing DSF on map graph.")
test_dictionary_adj_map_output()
print("\nTesting DFS on adjacent list")
graph_list = AdjacencyList(7)
# set up adj map graph, slightly different set up due to diff underlying structure
a = graph_list.add_vertex(0, 'A')
b = graph_list.add_vertex(1, 'B')
c = graph_list.add_vertex(2, 'C')
d = graph_list.add_vertex(3, 'D')
e = graph_list.add_vertex(4, 'E')
f = graph_list.add_vertex(5, 'F')
g = graph_list.add_vertex(6, 'G')
# Add edges both ways.
graph_list.add_edge(a, b)
graph_list.add_edge(a, c)
graph_list.add_edge(a, e)
graph_list.add_edge(b, f)
graph_list.add_edge(b, d)
graph_list.add_edge(c, g)
visited = [-1] * len(nodes)
component_number = 0 # Label each component starting at 0.
for node in nodes:
if visited[node.index] == -1: # Have not visited this node yet.
visited[node.index] = component_number
find_connected_component(graph, visited, node, component_number)
# We have found all components reachable from node so increment component number to
# find components reachable from another node, it is guaranteed a node can't be in 2 components
# as otherwise find_connected_component() would have found it.
component_number += 1
return component_number, visited
if __name__ == "__main__":
from algorithms_datastructures.graphs.implementations.adjacency_list import AdjacencyList
graph = AdjacencyList(4)
A = graph.add_vertex(0, "A")
B = graph.add_vertex(1, "B")
C = graph.add_vertex(2, "C")
D = graph.add_vertex(3, "D")
# Graph is just 4 nodes = 4 components.
num_components, node_components = connected_components(graph)
print("number of components %s is correct: %s" % (num_components, num_components == 4))
print("node components: " + str(node_components))
# Add edge b/w A and B.
graph.add_edge(origin_vertex=A, destination_vertex=B)
num_components, node_components = connected_components(graph)
print("number of components %s is correct: %s" % (num_components, num_components == 3))
print("node components: " + str(node_components))
graph_map.add_edge(A, B)
graph_map.add_edge(A, C)
graph_map.add_edge(A, E)
graph_map.add_edge(B, C)
graph_map.add_edge(B, F)
graph_map.add_edge(C, D)
graph_map.add_edge(E, D)
graph_map.add_edge(F, D)
source = A
bfs_adj_map = breadth_first_search(graph_map, source)
print("BFS on adj_map graph: " + str(bfs_adj_map))
# Sometimes the order of the adjacency_map changes (it is still correct, just not alphabetical)
# this is because there is some randomness with dictionaries.
print("\nTesting bfs on adjacency list.")
graph_list = AdjacencyList(6)
# This Graph List data structure assumes a directed graph
# set up adj map graph, slightly different set up due to diff underlying structure
a = graph_list.add_vertex(0, 'A')
b = graph_list.add_vertex(1, 'B')
c = graph_list.add_vertex(2, 'C')
d = graph_list.add_vertex(3, 'D')
e = graph_list.add_vertex(4, 'E')
f = graph_list.add_vertex(5, 'F')
# Undirected.
graph_list.add_edge(a, b)
graph_list.add_edge(a, c)
graph_list.add_edge(a, e)
graph_list.add_edge(b, c)
graph_list.add_edge(b, f)
graph_list.add_edge(c, d)
stack = deque()
for node in nodes: # O(n)
if visited[node.index] == 0:
topological_sort_rec(dag, node, visited, stack)
topological_ordering = []
while stack: # O(n)
topological_ordering.append(stack.pop().rep)
return topological_ordering
if __name__ == "__main__":
from algorithms_datastructures.graphs.implementations.adjacency_list import AdjacencyList
# Graph from https://www.youtube.com/watch?v=ddTC4Zovtbc
dag = AdjacencyList(8)
A = dag.add_vertex(0, 'A')
B = dag.add_vertex(1, 'B')
C = dag.add_vertex(2, 'C')
D = dag.add_vertex(3, 'D')
E = dag.add_vertex(4, 'E')
F = dag.add_vertex(5, 'F')
G = dag.add_vertex(6, 'G')
H = dag.add_vertex(7, 'H')
dag.add_edge(origin_vertex=A, destination_vertex=C)
dag.add_edge(origin_vertex=B, destination_vertex=C)
dag.add_edge(origin_vertex=B, destination_vertex=D)
dag.add_edge(origin_vertex=C, destination_vertex=E)
dag.add_edge(origin_vertex=D, destination_vertex=F)
dag.add_edge(origin_vertex=E, destination_vertex=H)
dag.add_edge(origin_vertex=E, destination_vertex=F)