18b41e49f53b

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/data/082-matrix.txt	Sat Feb 24 19:10:54 2018 -0500
@@ -0,0 +1,80 @@
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+171,3771,7134,8927,4778,2913,3326,2004,3089,7853,1378,1729,4777,2706,9578,1360,5693,3036,1851,7248,2403,2273,8536,6501,9216,613,9671,7131,7719,6425,773,717,8803,160,1114,7554,7197,753,4513,4322,8499,4533,2609,4226,8710,6627,644,9666,6260,4870,5744,7385,6542,6203,7703,6130,8944,5589,2262,6803,6381,7414,6888,5123,7320,9392,9061,6780,322,8975,7050,5089,1061,2260,3199,1150,1865,5386,9699,6501
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--- a/src/problems.lisp	Sat Feb 24 18:42:36 2018 -0500
+++ b/src/problems.lisp	Sat Feb 24 19:10:54 2018 -0500
@@ -1761,7 +1761,7 @@
              (cost (prev point)
                (declare (ignore prev))
                (value-at point)))
-      (summation (astar :start top-left
+      (summation (astar :start (list top-left)
                         :neighbors #'neighbors
                         :goal-p (curry #'vec2= bottom-right)
                         :cost #'cost
@@ -1769,6 +1769,55 @@
                         :test #'equalp)
                  :key #'value-at))))
 
+(defun problem-82 ()
+  ;; NOTE: This problem is a more challenging version of Problem 81.
+  ;;
+  ;; The minimal path sum in the 5 by 5 matrix below, by starting in any cell in
+  ;; the left column and finishing in any cell in the right column, and only
+  ;; moving up, down, and right, is indicated in red and bold; the sum is equal
+  ;; to 994.
+  ;;
+  ;; Find the minimal path sum, in matrix.txt, a 31K text file containing a 80
+  ;; by 80 matrix, from the left column to the right column.
+  (let* ((data (convert-to-multidimensional-array
+                 (iterate
+                   (for line :in-csv-file "data/082-matrix.txt"
+                        :key #'parse-integer)
+                   (collect line))))
+         (rows (array-dimension data 0))
+         (cols (array-dimension data 1))
+         (up (vec2 0 -1))
+         (down (vec2 0 1))
+         (right (vec2 1 0))
+         (minimum-value (iterate (for value :in-array data)
+                                 (minimizing value))))
+    (labels ((value-at (point)
+               (aref data (vy point) (vx point)))
+             (neighbors (point)
+               (remove nil (list (when (< (vx point) (1- cols))
+                                   (vec2+ point right))
+                                 (when (< 0 (vy point))
+                                   (vec2+ point up))
+                                 (when (< (vy point) (1- rows))
+                                   (vec2+ point down)))))
+             (remaining-moves (point)
+               (+ (- cols (vx point))
+                  (- rows (vy point))))
+             (goalp (point)
+               (= (1- rows) (vx point)))
+             (heuristic (point)
+               (* minimum-value (remaining-moves point)))
+             (cost (prev point)
+               (declare (ignore prev))
+               (value-at point)))
+      (summation (astar :start (mapcar (curry #'vec2 0) (range 0 rows))
+                        :neighbors #'neighbors
+                        :goal-p #'goalp
+                        :cost #'cost
+                        :heuristic #'heuristic
+                        :test #'equalp)
+                 :key #'value-at))))
+
 (defun problem-92 ()
   ;; A number chain is created by continuously adding the square of the digits
   ;; in a number to form a new number until it has been seen before.
@@ -2381,6 +2430,7 @@
 (test p74 (is (= 402 (problem-74))))
 (test p79 (is (= 73162890 (problem-79))))
 (test p81 (is (= 427337 (problem-81))))
+(test p82 (is (= 260324 (problem-82))))
 (test p92 (is (= 8581146 (problem-92))))
 (test p97 (is (= 8739992577 (problem-97))))
 (test p99 (is (= 709 (problem-99))))

--- a/src/utils.lisp	Sat Feb 24 18:42:36 2018 -0500
+++ b/src/utils.lisp	Sat Feb 24 19:10:54 2018 -0500
@@ -921,7 +921,7 @@
 ;;;; A* Search ----------------------------------------------------------------
 (defstruct path
   state
-  estimate
+  (estimate 0)
   (cost 0)
   (previous nil))
 
@@ -937,7 +937,7 @@
 
   The following parameters are all required:
 
-  * `start`: the starting state.
+  * `start`: a sequence of starting states.
 
   * `neighbors`: a function that takes a state and returns all states reachable
     from it.
@@ -961,35 +961,37 @@
   the algorithm would end up blowing the heap, which is unpleasant.
 
   "
-  (iterate
-    (with seen = (make-hash-table :test test))
-    (with frontier = (pileup:make-heap #'< :key #'path-estimate))
-
-    (initially (pileup:heap-insert (make-path :state start :estimate 0) frontier)
-               (setf (gethash start seen) 0))
+  (let ((seen (make-hash-table :test test))
+        (frontier (pileup:make-heap #'< :key #'path-estimate)))
+    (labels ((mark-seen (path)
+               (setf (gethash (path-state path) seen) (path-cost path)))
+             (push-path (path)
+               (mark-seen path)
+               (pileup:heap-insert path frontier)))
+      (iterate
+        (initially (doseq (state start)
+                     (push-path (make-path :state state))))
 
-    (for (values current found) = (pileup:heap-pop frontier))
-    (unless found
-      (return (values nil nil)))
+        (for (values current found) = (pileup:heap-pop frontier))
+        (unless found
+          (return (values nil nil)))
 
-    (for current-state = (path-state current))
-
-    (when (funcall goal-p current-state)
-      (return (values (path-to-list current) t)))
+        (for current-state = (path-state current))
 
-    (for current-cost = (path-cost current))
+        (when (funcall goal-p current-state)
+          (return (values (path-to-list current) t)))
+
+        (for current-cost = (path-cost current))
 
-    (iterate
-      (for next-state :in (funcall neighbors current-state))
-      (for next-cost = (+ current-cost (funcall cost current-state next-state)))
-      (for (values seen-cost previously-seen) = (gethash next-state seen))
-      (when (or (not previously-seen)
-                (< next-cost seen-cost))
-        (for next-estimate = (+ next-cost (funcall heuristic next-state)))
-        (for next = (make-path :state next-state
-                               :cost next-cost
-                               :estimate next-estimate
-                               :previous current))
-        (setf (gethash next-state seen) next-cost)
-        (pileup:heap-insert next frontier)))))
+        (iterate
+          (for next-state :in (funcall neighbors current-state))
+          (for next-cost = (+ current-cost (funcall cost current-state next-state)))
+          (for (values seen-cost previously-seen) = (gethash next-state seen))
+          (when (or (not previously-seen)
+                    (< next-cost seen-cost))
+            (for next-estimate = (+ next-cost (funcall heuristic next-state)))
+            (push-path (make-path :state next-state
+                                  :cost next-cost
+                                  :estimate next-estimate
+                                  :previous current))))))))