Class: MinCostFlow

Inherits:
Object
  • Object
show all
Defined in:
lib/min_cost_flow.rb

Overview

Min Cost Flow Grapsh

Instance Method Summary collapse

Constructor Details

#initialize(n) ⇒ MinCostFlow

Returns a new instance of MinCostFlow.



5
6
7
8
9
10
11
12
13
14
15
 
# File 'lib/min_cost_flow.rb', line 5

def initialize(n)
  @n      = n
  @pos    = []
  @g_to   = Array.new(n) { [] }
  @g_rev  = Array.new(n) { [] }
  @g_cap  = Array.new(n) { [] }
  @g_cost = Array.new(n) { [] }
  @pv     = Array.new(n)
  @pe     = Array.new(n)
  @dual   = Array.new(n, 0)
end

Instance Method Details

#add(x, to = nil, cap = nil, cost = nil) ⇒ Object 



44
45
46
 
# File 'lib/min_cost_flow.rb', line 44

def add(x, to = nil, cap = nil, cost = nil)
  cost ? add_edge(x, to, cap, cost) : add_edges(x)
end

#add_edge(from, to, cap, cost) ⇒ Object 



17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
 
# File 'lib/min_cost_flow.rb', line 17

def add_edge(from, to, cap, cost)
  edge_number = @pos.size

  @pos << [from, @g_to[from].size]

  from_id = @g_to[from].size
  to_id   = @g_to[to].size
  to_id += 1 if from == to

  @g_to[from]   << to
  @g_rev[from]  << to_id
  @g_cap[from]  << cap
  @g_cost[from] << cost

  @g_to[to]     << from
  @g_rev[to]    << from_id
  @g_cap[to]    << 0
  @g_cost[to]   << -cost

  edge_number
end

#add_edges(edges) ⇒ Object 



39
40
41
42
 
# File 'lib/min_cost_flow.rb', line 39

def add_edges(edges)
  edges.each{ |from, to, cap, cost| add_edge(from, to, cap, cost) }
  self
end

#dual_ref(s, t) ⇒ Object 



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
 
# File 'lib/min_cost_flow.rb', line 70

def dual_ref(s, t)
  dist = Array.new(@n, Float::MAX)
  @pv.fill(-1)
  @pe.fill(-1)
  vis = Array.new(@n, false)

  que = PriorityQueue.new { |par, chi| par[0] < chi[0] }
  dist[s] = 0
  que.push([0, s])

  while (v = que.pop)
    v = v[1]

    next if vis[v]

    vis[v] = true
    break if v == t

    @g_to[v].size.times do |i|
      to = @g_to[v][i]
      next if vis[to] || @g_cap[v][i] == 0

      cost = @g_cost[v][i] - @dual[to] + @dual[v]
      next unless dist[to] - dist[v] > cost

      dist[to] = dist[v] + cost
      @pv[to] = v
      @pe[to] = i
      que.push([dist[to], to])
    end
  end

  return false unless vis[t]

  @n.times do |i|
    next unless vis[i]

    @dual[i] -= dist[t] - dist[i]
  end

  true
end

#edges ⇒ Object 



57
58
59
60
61
62
63
 
# File 'lib/min_cost_flow.rb', line 57

def edges
  @pos.map do |(from, id)|
    to = @g_to[from][id]
    rid = @g_rev[from][id]
    [from, to, @g_cap[from][id] + @g_cap[to][rid], @g_cap[to][rid], @g_cost[from][id]]
  end
end

#flow(s, t, flow_limit = Float::MAX) ⇒ Object Also known as: min_cost_max_flow 



65
66
67
 
# File 'lib/min_cost_flow.rb', line 65

def flow(s, t, flow_limit = Float::MAX)
  slope(s, t, flow_limit).last
end

#get_edge(i) ⇒ Object Also known as: edge, [] 



48
49
50
51
52
53
 
# File 'lib/min_cost_flow.rb', line 48

def get_edge(i)
  from, id = @pos[i]
  to = @g_to[from][id]
  rid = @g_rev[from][id]
  [from, to, @g_cap[from][id] + @g_cap[to][rid], @g_cap[to][rid], @g_cost[from][id]]
end

#slope(s, t, flow_limit = Float::MAX) ⇒ Object Also known as: min_cost_slop 



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
 
# File 'lib/min_cost_flow.rb', line 113

def slope(s, t, flow_limit = Float::MAX)
  flow = 0
  cost = 0
  prev_cost_per_flow = -1
  result = [[flow, cost]]

  while flow < flow_limit
    break unless dual_ref(s, t)

    c = flow_limit - flow
    v = t
    while v != s
      c = @g_cap[@pv[v]][@pe[v]] if c > @g_cap[@pv[v]][@pe[v]]
      v = @pv[v]
    end

    v = t
    while v != s
      nv = @pv[v]
      id = @pe[v]
      @g_cap[nv][id] -= c
      @g_cap[v][@g_rev[nv][id]] += c
      v = nv
    end

    d = -@dual[s]
    flow += c
    cost += c * d
    result.pop if prev_cost_per_flow == d
    result << [flow, cost]
    prev_cost_per_flow = d
  end

  result
end