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kthflow.py
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kthflow.py
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import networkx as nx
import matplotlib.pyplot as plt
INF = 9999999
class kthFlow:
def __init__(self, nodes_num):
self.nodes_num = nodes_num
self.edges = [[0 for x in range(nodes_num + 1)] for y in range(nodes_num + 1)]
self.parent = {}
self.if_pos = -1
self.G = nx.DiGraph()
self.original_edges = [[0 for x in range(nodes_num + 1)] for y in range(nodes_num + 1)]
def add_edge(self, from_node, to_node, cap):
self.edges[from_node][to_node] += cap
self.original_edges[from_node][to_node] += cap
# Bfs is used to find augmenting paths. Update the hashmap "parent"
# while bfs to find the path.
def bfs(self, source, target):
visited = [False for x in range(0, self.nodes_num + 1)]
visited[source] = True
queue = []
queue.append(source)
while len(queue) > 0:
i = queue[0]
queue.pop(0)
for j in range(1, self.nodes_num + 1):
if self.edges[i][j] > 0 and visited[j] == False:
visited[j] = True
self.parent[j] = i
queue.append(j)
return visited[target],
def init(self):
self.edges = self.original_edges
def next(self, source, target):
maximum_flow = 0
self.bfs(source, target)
new_flow = INF
curr = target
while curr != source:
prev = self.parent[curr]
new_flow = min(new_flow, self.edges[prev][curr])
curr = prev
maximum_flow += new_flow
# If no augmenting paths are found. the function return maximum flow
if new_flow == 0:
return maximum_flow
# We adjust the residual network
curr = target
while curr != source:
prev = self.parent[curr]
self.edges[prev][curr] -= new_flow
self.edges[curr][prev] += new_flow
curr = prev
def minimumcut(self, source, target):
visited = [False for x in range(0, self.nodes_num + 1)]
visited[source] = True
queue = []
queue.append(source)
while len(queue) > 0:
i = queue[0]
queue.pop(0)
for j in range(1, self.nodes_num + 1):
if self.edges[i][j] > 0 and visited[j] == False:
visited[j] = True
self.parent[j] = i
queue.append(j)
return visited
def get_pos(self):
return nx.spring_layout(self.G)
def print_next_result(self, source, target):
##flow
self.bfs(source, target)
new_flow = INF
curr = target
while curr != source:
prev = self.parent[curr]
new_flow = min(new_flow, self.edges[prev][curr])
curr = prev
edge_label = {}
for i in range(1, self.nodes_num + 1):
for j in range(1, self.nodes_num + 1):
if self.original_edges[i][j] > 0:
cap = self.original_edges[i][j]
flow = self.original_edges[i][j] - self.edges[i][j]
edge_label[(i, j)] = str(flow) + "/" + str(cap)
# We adjust the residual network
## flow
if new_flow == 0:
return
G = self.G
for i in range(1, self.nodes_num + 1):
G.add_node(i)
for i in range(1, self.nodes_num + 1):
for j in range(1, self.nodes_num + 1):
if self.original_edges[i][j] > 0:
G.add_edge(i, j)
plt.figure()
curr = target
colors = ['black' for u,v in G.edges()]
augmenting_path = []
while curr != source:
prev = self.parent[curr]
flow = self.original_edges[prev][curr] - self.edges[prev][curr]
cap = self.original_edges[prev][curr]
if self.original_edges[prev][curr] > 0:
edge_label[(prev, curr)] = "(" + str(flow) + "+" + str(new_flow) + ")/" + str(cap)
else:
edge_label[(prev, curr)] = "(" + str(-flow) + "-" + str(new_flow) + ")/" + str(cap)
self.edges[prev][curr] -= new_flow
self.edges[curr][prev] += new_flow
augmenting_path.append((prev, curr))
augmenting_path.append((curr, prev))
curr = prev
edge_index = 0
for edge in G.edges():
if edge in augmenting_path:
colors[edge_index] = 'red'
edge_index += 1
color = []
st = self.minimumcut(source, target)
for i in range(1, self.nodes_num + 1):
if st[i]:
color.append('green')
else:
color.append('red')
labels={node: node for node in G.nodes()}
labels[source] = 's=' + str(source)
labels[target] = 't=' + str(target)
if self.if_pos == -1:
self.pos = nx.spring_layout(G)
pos = self.pos
self.if_pos = 1
else:
pos = self.pos
nx.draw(
G, pos, edge_color = colors, width=1, linewidths=1,
node_size=500, node_color=color, alpha=0.9,
labels=labels
)
nx.draw_networkx_edge_labels(
G, pos,
edge_label,
font_color='red',
)