Implement Zipper lines.

data/example_puzzles.js

@@ -303,6 +303,16 @@ const EXAMPLES = {
     input: '.~R1C1_1_2~R2C2_1_2_9~R2C4_1_3~R1C5_1_4_6~R2C5_8_9~R4C2_2_3~R5C2_7_9~R9C1_2_3~R7C3_8_9~R8C3_1_2_3_8_9~R6C3_6_7~R3C3_5_6_9~R4C4_3_4_5~R4C5_4_9~R5C5_6_7_8~R8C5_1_2~R7C4_4_6~R9C5_5_6~R1C6_6_9~R3C6_5_7~R4C6_6_9~R6C6_1_4_7~R8C6_1_8~R9C9_3_4_5~R8C8_2_8_9~R7C7_6_7_8~R6C8_4_8~R5C9_4_6~R4C7_5_6~R3C7_7_9~R2C8_1_2_3_5_8_9~R1C8_1_9~R1C9_1_3',
     solution: '278569413916384752435127968123496587894275136567831249759643821642718395381952674',
   },
+  'Zipper lines - easy': {
+    src: 'https://logic-masters.de/Raetselportal/Raetsel/zeigen.php?chlang=en&id=000FNA',
+    input: '.Zipper~R5C1~R5C2~R5C3.Zipper~R7C2~R7C1~R8C1~R9C1~R9C2~R9C3~R8C3.Zipper~R8C2~R7C3~R6C4~R7C5~R8C6.Zipper~R8C5~R9C5~R9C6~R9C7~R8C7~R7C7~R7C6.Zipper~R4C8~R4C7~R5C7~R6C7~R6C8~R6C9~R5C9.Zipper~R2C9~R3C9~R3C8~R3C7~R2C7~R1C7~R1C8.Zipper~R2C6~R1C6~R1C5~R1C4~R2C4~R3C4~R3C5.Zipper~R2C5~R3C6~R4C5.',
+    solution: '329764518547182396168359742695213487473598621281647935734825169856931274912476853',
+  },
+  'Zipper lines': {
+    src: 'https://www.youtube.com/watch?v=qP_oxUzGD5g',
+    input: '.Zipper~R1C2~R1C1~R2C1~R2C2~R3C2~R3C1~R4C1~R5C1~R4C2.Zipper~R2C3~R1C3~R1C4~R2C4~R3C4.Zipper~R2C6~R3C5~R3C6~R2C7~R1C6~R1C5.Zipper~R9C3~R8C2~R7C1~R6C1~R5C2~R4C3~R4C4~R5C4~R6C3.Zipper~R8C3~R7C3~R6C4~R6C5~R5C5~R4C5~R4C6~R5C6~R6C6~R6C7~R6C8~R6C9.Zipper~R5C7~R5C8~R4C7~R3C7~R2C8.Zipper~R7C5~R7C6~R8C6~R8C7~R7C7~R7C8~R7C9~R8C9~R9C9~R9C8~R9C7~R9C6~R9C5~R8C5.',
+    solution: '354897126672451839189632574231564987597328641846719352415973268968245713723186495'
+  },
 
   // Classic grids that used to be slow. 3 and 4 used to take 2+ seconds.
   'Classic sudoku, was slow (1)': {

js/debug.js

@@ -251,6 +251,7 @@ const runSolveTests = async (onFailure) => {
     'Quadruple - repeated values',
     'Odd-even thermo',
     'Nabner thermo - easy',
+    'Zipper lines - easy',
   ], onFailure);
   result.collection = '9x9';
   results.push(result);

js/render_page.js

@@ -157,6 +157,7 @@ class ExampleHandler {
     'Between lines',
     'Lockout lines',
     'Palindromes',
+    'Zipper lines',
     'Jigsaw',
     'X-Windoku',
     'Region sum lines',
@@ -731,6 +732,7 @@ class ConstraintManager {
       case 'Modular':
       case 'Entropic':
       case 'Palindrome':
+      case 'Zipper':
       case 'Between':
       case 'Lockout':
       case 'RegionSumLine':
@@ -1024,10 +1026,23 @@ class ConstraintManager {
       },
       Palindrome: {
         text: 'Palindrome',
-        displayConfig: { color: 'rgb(200, 200, 255)' },
+        displayConfig: {
+          color: 'rgb(200, 200, 255)'
+        },
         description:
           "The values along the line form a palindrome."
       },
+      Zipper: {
+        text: 'Zipper Line',
+        displayConfig: {
+          color: 'rgb(200, 200, 255)',
+        },
+        description:
+          `
+          Digits which are equal distance from the center of the zipper have the
+          same sum. For odd length lines, the center digit is the sum.
+          `
+      },
       WhiteDot: {
         validateFn: ConstraintManager._cellsAreAdjacent,
         text: '○ ±1',

js/sudoku_builder.js

@@ -639,6 +639,13 @@ class SudokuConstraint {
     );
   }
 
+  static Zipper = class Zipper extends SudokuConstraintBase {
+    constructor(...cells) {
+      super(arguments);
+      this.cells = cells;
+    }
+  }
+
   static NoBoxes = class NoBoxes extends SudokuConstraintBase._Meta { }
   static StrictKropki = class StrictKropki extends SudokuConstraintBase._Meta {
     static fnKey = memoize((numValues) =>
@@ -1386,6 +1393,37 @@ class SudokuBuilder {
               SudokuConstraint.Palindrome.fnKey(shape.numValues));
           }
           break;
+        case 'Zipper':
+          cells = constraint.cells.map(c => shape.parseCellId(c).cell);
+          {
+            const pairs = [];
+            const numCells = cells.length;
+            for (let i = 0; i < ((numCells / 2) | 0); i++) {
+              pairs.push([cells[i], cells[numCells - 1 - i]]);
+            }
+            if (numCells % 2 == 1) {
+              // If there are an odd numbers of cells, then treat this as a
+              // set of arrows from the center cell to each pair.
+              // We don't bother to also add constraints between each pair, as
+              // the constraint on the total sum should propagate through the
+              // center cell.
+              const centerCell = [cells[(numCells / 2) | 0]];
+              for (const pair of pairs) {
+                yield new SudokuConstraintHandler.SumWithNegative(
+                  pair, centerCell, 0);
+              }
+            } else {
+              // Otherwise create an equal sum constraint between each pair.
+              const numPairs = pairs.length;
+              for (let i = 1; i < numPairs; i++) {
+                for (let j = 0; j < i; j++) {
+                  yield new SudokuConstraintHandler.SumWithNegative(
+                    pairs[i], pairs[j], 0);
+                }
+              }
+            }
+          }
+          break;
 
         case 'WhiteDot':
           cells = constraint.cells.map(c => shape.parseCellId(c).cell);