# 252d1614e2d9

`Comments`
author Steve Losh Thu, 10 Aug 2017 20:22:09 -0400 4f58a841ae48 540f1cb1093a (none) src/hungarian.lisp src/problems.lisp

## Changes

```diff -r 4f58a841ae48 -r 252d1614e2d9 src/hungarian.lisp
--- a/src/hungarian.lisp	Thu Aug 10 20:09:14 2017 -0400
+++ b/src/hungarian.lisp	Thu Aug 10 20:22:09 2017 -0400
@@ -1,6 +1,16 @@
(in-package :euler.hungarian)

-;;;; Data
+;;;; Hungarian/Munkres Algorithm ----------------------------------------------
+;;; This is an implementation of the Hungarian algorithm for finding a minimal
+;;; assignment for a cost matrix in polynomial (O(n³)) time.
+;;;
+;;; Useful references:
+;;;
+;;; * http://www.netlib.org/utk/lsi/pcwLSI/text/node222.html
+;;; * http://csclab.murraystate.edu/~bob.pilgrim/445/munkres.html
+
+
+;;;; Data ---------------------------------------------------------------------
(defstruct (assignment-problem (:conc-name ap-)
(:constructor make-assignment-problem%))
original-matrix
@@ -41,7 +51,7 @@
:primed-cols (make-array cols :initial-element nil))))

-;;;; Debug
+;;;; Debug --------------------------------------------------------------------
(defun dump (data)
(with-assignment-problem (data)
(format t "   ~{   ~A ~^ ~}~%"
@@ -63,19 +73,34 @@
(pr))

-;;;; Marking
+;;;; Marking ------------------------------------------------------------------
(defun mark (row col row-vector col-vector)
(setf (aref row-vector row) col
(aref col-vector col) row))

(defun unmark (row col row-vector col-vector)
+  ;; This is a bit fucky.
+  ;;
+  ;; Intuitively you would think that there should be at most one starred entry
+  ;; in each row/col, and at the end of each step this is true.  But when we're
+  ;; processing the alternating star/prime list, we start with the prime and
+  ;; star it before moving to the next entry in the list, which is what removes
+  ;; the existing star.
+  ;;
+  ;; If we just blindly nil out both vectors we might overwrite the coordinate
+  ;; that was just starred.  The solution is to make sure we're only niling out
+  ;; data for the actual thing we're unmarking.
+  ;;
+  ;; Another (possibly cleaner?) solution would be to reverse the alternating
+  ;; prime/star list.  That was we'd unstar the existing zeros before starring
+  ;; their primed twin, and everything would work nicely.
(when (eql (aref row-vector row) col)
(setf  (aref row-vector row) nil))
(when (eql (aref col-vector col) row)
(setf (aref col-vector col) nil)))

-;;;; Starring
+;;;; Starring -----------------------------------------------------------------
(defun star (data row col)
(with-assignment-problem (data)
(mark row col starred-rows starred-cols)))
@@ -106,7 +131,7 @@
(eql (starred-col-for-row data row) col))

-;;;; Priming
+;;;; Priming ------------------------------------------------------------------
(defun prime (data row col)
(with-assignment-problem (data)
(mark row col primed-rows primed-cols)))
@@ -129,7 +154,7 @@
(eql (primed-col-for-row data row) col))

-;;;; Covering
+;;;; Covering -----------------------------------------------------------------
(defun cover-row (data row)
(setf (aref (ap-covered-rows data) row) t))

@@ -187,7 +212,7 @@
(every #'identity (ap-covered-cols data)))

-;;;; Incrementing
+;;;; Incrementing -------------------------------------------------------------
(defun incf-row (data row i)
(with-assignment-problem (data)
(dotimes (col cols)```
```diff -r 4f58a841ae48 -r 252d1614e2d9 src/problems.lisp
--- a/src/problems.lisp	Thu Aug 10 20:09:14 2017 -0400
+++ b/src/problems.lisp	Thu Aug 10 20:22:09 2017 -0400
@@ -1744,6 +1744,8 @@
( 34 124   4 878 450 476 712 914 838 669 875 299 823 329 699)
(815 559 813 459 522 788 168 586 966 232 308 833 251 631 107)
(813 883 451 509 615  77 281 613 459 205 380 274 302  35 805)))))
+    ;; The hungarian algorithm finds a minimal assignment, but we want a maximal
+    ;; one, so we'll just negate all the values and flip the sign at the end.
(do-array (val matrix)
(negatef val))
(iterate```