Door placement

lib/algorithms/kruskal.dart

@@ -0,0 +1,33 @@
+import 'package:dartterm/algorithms/union_find.dart';
+
+class Edge<T> {
+  final int src, dst;
+  final T value;
+  final double score; // higher score is better
+
+  const Edge(this.src, this.dst, this.value, this.score);
+}
+
+List<Edge<T>> kruskal<T>(int nRegions, List<Edge<T>> srcEdges) {
+  var edges = List.from(srcEdges); // copy so we can mutate it
+  edges.sort((e0, e1) => -e0.score.compareTo(e1.score));
+
+  List<Edge<T>> spanningEdges = [];
+  var connected = UnionFind(nRegions);
+
+  for (var i = 0; i < edges.length; i++) {
+    var edge = edges[i];
+    if (connected.find(edge.src) == connected.find(edge.dst)) {
+      continue;
+    }
+    spanningEdges.add(edge);
+    connected.union(edge.src, edge.dst);
+
+    // break early if we run out of regions
+    nRegions -= 1;
+    if (nRegions == 1) {
+      break;
+    }
+  }
+  return spanningEdges;
+}

lib/algorithms/regionalize.dart

@@ -26,7 +26,8 @@ class Region {
   }
 }
 
-List<Region> regionalize(geo.Rect rect, bool Function(int, int) isAccessible) {
+(List<Region>, Map<(int, int), int>) regionalize(
+    geo.Rect rect, bool Function(int, int) isAccessible) {
   int nextRegion = 0;
   Map<(int, int), int> regions = {};
 
@@ -62,7 +63,7 @@ List<Region> regionalize(geo.Rect rect, bool Function(int, int) isAccessible) {
       }
     }
   }
-  return _toExplicit(regions, nextRegion);
+  return (_toExplicit(regions, nextRegion), regions);
 }
 
 List<Region> _toExplicit(Map<(int, int), int> pointRegions, int nRegions) {

lib/algorithms/union_find.dart

@@ -0,0 +1,78 @@
+// Copyright (c) 2012, scribeGriff (Richard Griffith)
+// https://github.com/scribeGriff/graphlab
+// All rights reserved.  Please see the LICENSE.md file.
+//
+// Converted to modern Dart by Pyrex Panjakar.
+
+/// A disjoint sets ADT implemented with a Union-Find data structure.
+///
+/// Performs union-by-rank and path compression.  Elements are represented
+/// by ints, numbered from zero.
+///
+/// Each disjoint set has one element designated as its root.
+/// Negative values indicate the element is the root of a set.  The absolute
+/// value of a negative value is the number of elements in the set.
+/// Positive values are an index to where the root was last known to be.
+/// If the set has been unioned with another, the last known root will point
+/// to a more recent root.
+///
+///     var a = new UnionFind(myGraph.length);
+///
+///     var u = a.find(myGraph[i][0]);
+///     var v = a.find(myGraph[i][1]);
+///     a.union(u, v);
+///
+/// Reference: Direct port of Mark Allen Weiss' UnionFind.java
+class UnionFind {
+  late final List<int> array;
+
+  /// Construct a disjoint sets object.
+  ///
+  /// numElements is the initial number of elements--also the initial
+  /// number of disjoint sets, since every element is initially in its
+  /// own set.
+  UnionFind(int numElements) {
+    // The array is zero based but the vertices are 1 based,
+    // so we extend the array by 1 element to account for this.
+    array = [for (var i = 0; i < numElements; i++) -1];
+  }
+
+  /// union() unites two disjoint sets into a single set.  A union-by-rank
+  /// heuristic is used to choose the new root.
+  ///
+  /// a is an element in the first set.
+  /// b is an element in the first set.
+  void union(int a, int b) {
+    int rootA = find(a);
+    int rootB = find(b);
+
+    if (rootA == rootB) return;
+
+    if (array[rootB] < array[rootA]) {
+      // root_b has more elements, so leave it as the root.
+      // first, indicate that the set represented by root_b has grown.
+      array[rootB] += array[rootA];
+      // Then, point the root of set a at set b.
+      array[rootA] = rootB;
+    } else {
+      array[rootA] += array[rootB];
+      array[rootB] = rootA;
+    }
+  }
+
+  /// find() finds the (int) name of the set containing a given element.
+  /// Performs path compression along the way.
+  ///
+  /// x is the element sought.
+  /// returns the set containing x.
+  int find(int x) {
+    if (array[x] < 0) {
+      return x; // x is the root of the tree; return it
+    } else {
+      // Find out who the root is; compress path by making the root
+      // x's parent.
+      array[x] = find(array[x]);
+      return array[x]; // Return the root
+    }
+  }
+}