/
hungarian.go
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/
hungarian.go
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// Copyright 2012 The Gt Authors. All rights reserved. See the LICENSE file.
package gt
// Hungarian algorithm to solve the assigment problem.
import (
"math"
)
type env struct {
m, n int64
g *Matrix
T, S []bool
slack []int64
slackx []int64
prev []int64
xy, yx []int64
lx, ly []int64
}
func newEnv(n int64) *env {
e := new(env)
e.m = 0
e.n = n
e.T = make([]bool, n)
e.S = make([]bool, n)
e.slack = make([]int64, n)
e.slackx = make([]int64, n)
e.prev = make([]int64, n)
e.xy = make([]int64, n)
e.yx = make([]int64, n)
e.lx = make([]int64, n)
e.ly = make([]int64, n)
var i int64
for i = 0; i < n; i++ {
e.xy[i] = -1
e.yx[i] = -1
}
return e
}
func (e *env) update() {
var i int64
var d int64 = math.MaxInt64
for i = 0; i < e.n; i++ {
if !e.T[i] {
d = min(d, e.slack[i])
}
}
for i = 0; i < e.n; i++ {
if e.S[i] {
e.lx[i] -= d
}
}
for i = 0; i < e.n; i++ {
if e.T[i] {
e.ly[i] += d
}
}
for i = 0; i < e.n; i++ {
if !e.T[i] {
e.slack[i] -= d
}
}
}
func (e *env) add(i, p int64) {
var j int64
e.S[i] = true
e.prev[i] = p
for j = 0; j < e.n; j++ {
if e.lx[i]+e.ly[i]-e.g.Get(i, j) < e.slack[i] {
e.slack[i] = e.lx[i] + e.ly[i] - e.g.Get(i, j)
e.slackx[i] = j
}
}
}
func (e *env) augment() {
var i, j, wr, rd, r int64
wr = 0
rd = 0
q := make([]int64, e.n)
if e.m == e.n {
return
}
for i = 0; i < e.n; i++ {
if e.xy[i] == -1 {
wr++
q[wr] = i
r = i
e.prev[i] = -2
e.S[i] = true
break
}
}
for i = 0; i < e.n; i++ {
e.slack[i] = e.lx[r] + e.ly[i] - e.g.Get(r, i)
e.slackx[i] = r
}
for {
for rd < wr {
rd++
i = q[rd]
for j = 0; j < e.n; j++ {
if e.g.Get(i, j) == e.lx[i]+e.ly[j] && !e.T[j] {
if e.yx[j] == -1 {
break
}
e.T[j] = true
wr++
q[wr] = e.yx[j]
e.add(e.yx[j], i)
}
}
if j < e.n {
break
}
}
if j < e.n {
break
}
e.update()
wr = 0
rd = 0
for j = 0; j < e.n; j++ {
if !e.T[j] && e.slack[j] == 0 {
if e.yx[i] == -1 {
i = e.slackx[j]
break
} else {
e.T[j] = true
if !e.S[e.yx[j]] {
wr++
q[wr] = e.yx[j]
e.add(e.yx[j], e.slackx[j])
}
}
}
}
if j < e.n {
return
}
}
if j < e.n {
e.m++
for i != -2 {
k := e.xy[i]
e.yx[j] = i
e.xy[i] = j
i = e.prev[i]
j = k
}
e.augment()
}
}
func initH(g *Matrix) (e *env) {
var i, j int64
e = newEnv(g.N)
e.g = g
e.n = g.N
for i = 0; i < e.n; i++ {
for j = 0; j < e.n; j++ {
e.lx[i] = max(e.lx[i], e.g.Get(i, j))
}
}
return e
}
// Hungarian uses the Hungarian algorithm to solve the assigment problem.
func Hungarian(g *Matrix) (xy, yx []int64) {
e := initH(g)
e.augment()
return e.xy, e.yx
}