File size: 5,078 Bytes
e9caa70 884c797 e9caa70 3dce864 e9caa70 3dce864 e9caa70 884c797 e9caa70 845403e e9caa70 845403e a7905a1 884c797 845403e a7905a1 884c797 a7905a1 884c797 a7905a1 845403e e9caa70 |
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 |
import streamlit as st
import graphviz
import random
import gurobipy as gp
from gurobipy import GRB
import colorsys
def hsv2rgb(h, s, v):
r, g, b = colorsys.hsv_to_rgb(h, s, v)
return int(255 * r), int(255 * g), int(255 * b)
def format_color(color):
return '#%02x%02x%02x' % color
def generate_colors(n):
colors = [hsv2rgb(i / n, 0.5, 1.0) for i in range(n)]
return [format_color(color) for color in colors]
def generate_random_graph(V, density):
E = [(u, v) for u in range(V - 1) for v in range(u + 1, V)]
random.shuffle(E)
E = E[:int(density * V * (V - 1) / 2)]
return V, E
def solve_matching(V, E):
m = gp.Model()
x = m.addVars(E, vtype=GRB.BINARY)
m.setObjective(x.sum(), GRB.MAXIMIZE)
m.addConstrs(x.sum(u, '*') + x.sum('*', u) <= 1 for u in range(V))
m.optimize()
return [e for e in E if x[e].x > 0.5]
def app_matching(V, E):
M = set(solve_matching(V, E))
if len(M) == V // 2:
st.success('Perfect matching found')
else:
st.metric('Matching size', len(M))
G = graphviz.Graph()
for u, v in E:
if (u, v) in M:
G.edge(str(u), str(v), color='red')
else:
G.edge(str(u), str(v), color='gray', style='dashed')
st.graphviz_chart(G)
def solve_hamilton(V, E):
m = gp.Model()
x = m.addVars(range(V), range(V), vtype=GRB.BINARY)
m.addConstrs(x.sum(u, '*') == 1 for u in range(V))
m.addConstrs(x.sum('*', i) == 1 for i in range(V))
for u in range(V):
for v in range(V):
if (u, v) not in E and (v, u) not in E:
for i in range(V - 1):
m.addConstr(x[u, i] + x[v, i + 1] <= 1)
m.addConstr(x[u, V - 1] + x[v, 0] <= 1)
m.optimize()
if m.status != GRB.OPTIMAL:
return None
cycle = []
for i in range(V):
for u in range(V):
if x[u, i].x > 0.5:
cycle.append(u)
break
return cycle
def app_hamilton(V, E):
cycle = solve_hamilton(V, E)
if cycle is None:
st.error('Hamilton cycle not found')
else:
st.success('Hamilton cycle found')
G = graphviz.Graph()
if cycle is not None:
for u in range(V):
G.node(str(cycle.index(u)))
for u, v in E:
if ((cycle.index(u) + 1) % len(cycle)) == cycle.index(v):
G.edge(str(cycle.index(u)), str(cycle.index(v)), dir='forward')
elif ((cycle.index(u) - 1) % len(cycle)) == cycle.index(v):
G.edge(str(cycle.index(u)), str(cycle.index(v)), dir='back')
else:
G.edge(str(cycle.index(u)), str(cycle.index(v)), style='dashed', color='gray')
else:
for u in range(V):
G.node(str(u))
for u, v in E:
G.edge(str(u), str(v))
st.graphviz_chart(G)
def solve_vertex_cover(V, E):
m = gp.Model()
x = m.addVars(range(V), vtype=GRB.BINARY)
m.setObjective(x.sum(), GRB.MINIMIZE)
m.addConstrs(x[u] + x[v] >= 1 for u, v in E)
m.optimize()
return [u for u in range(V) if x[u].x > 0.5]
def app_vertex_cover(V, E):
cover = solve_vertex_cover(V, E)
st.metric('Vertex cover size', len(cover))
G = graphviz.Graph()
for u in range(V):
if u in cover:
G.node(str(u), style='filled', fillcolor='lightblue')
else:
G.node(str(u), color='gray')
for u, v in E:
G.edge(str(u), str(v))
st.graphviz_chart(G)
def solve_coloring(V, E):
m = gp.Model()
vertex_color = m.addVars(range(V), vtype=GRB.INTEGER, lb=0)
or_helper = m.addVars(E, vtype=GRB.BINARY)
chi = m.addVar(vtype=GRB.INTEGER)
m.setObjective(chi, GRB.MINIMIZE)
m.addConstrs(vertex_color[u] <= chi for u in range(V))
m.addConstrs((or_helper[u, v] == 0) >> (vertex_color[u] - vertex_color[v] >= 1) for u, v in E)
m.addConstrs((or_helper[u, v] == 1) >> (vertex_color[v] - vertex_color[u] >= 1) for u, v in E)
m.optimize()
return [round(vertex_color[u].x) for u in range(V)]
def app_coloring(V, E):
coloring = solve_coloring(V, E)
st.metric('Chromatic number', max(coloring) + 1)
colors = generate_colors(max(coloring) + 1)
G = graphviz.Graph()
for u in range(V):
G.node(str(u), style='filled', fillcolor=colors[coloring[u]])
for u, v in E:
G.edge(str(u), str(v))
st.graphviz_chart(G)
def main():
V = st.number_input('Number of vertices', min_value=1, value=10)
density = st.slider('Density', min_value=0.0, max_value=1.0, value=0.5)
st.button('Generate')
V, E = generate_random_graph(V, density)
if len(E) > 40:
st.warning('Too many edges to display')
return
apps = [
app_matching,
app_hamilton,
app_vertex_cover,
app_coloring,
]
tabs = st.tabs([
'Matching',
'Hamilton',
'Vertex cover',
'Coloring',
])
for t, a in zip(tabs, apps):
with t:
a(V, E)
if __name__ == '__main__':
main()
|