improved MagicSquareSolver

src/magic_squares/MagicSquareSolver.scala

@@ -1,10 +1,14 @@
 package magic_squares
 
+import scala.collection.mutable.ArrayBuffer
+
 abstract class MagicSquareSolver(initialGrid: Grid) extends Displayable {
   protected var _initial: Grid = initialGrid
+  protected var grid: Grid = copy(_initial)
   protected val _size: Int = _initial.length
   protected val SUM: Int = _size * (_size * _size + 1) / 2
   protected val DEBUG: Boolean = false
+  protected val NUMBERS: Array[Int] = Array.range(1, _size * _size + 1)
 
   protected def print(grid: Grid): Unit = {
     for (y: Int <- 0 until _size) {
@@ -17,53 +21,67 @@ abstract class MagicSquareSolver(initialGrid: Grid) extends Displayable {
   }
 
   def solve(): Unit = {
-    val sol: Option[Grid] = solveFrom(_initial, 0, 0)
-    if (sol.isEmpty) {
-      println("No solution")
-    } else {
-      print(sol.get)
-    }
-  }
-
-  private def solveFrom(grid: Grid, x: Int, y: Int): Option[Grid] = {
-    if (DEBUG) println(s"Solving from $x, $y")
-    if (DEBUG) print(grid)
-    display(grid)
-    if (!isValid(grid)) {
-      if (DEBUG) println("  Grid is invalid")
-      return None
-    }
-    if (y >= _size) {
-      if (DEBUG) println("  Found solution")
-      return Some(grid)
-    }
-    var values: Array[Int] = Array(_initial(y)(x))
-    if (values(0) == 0) values = (1 to _size * _size).toArray
-    if (DEBUG) println(s"  Values to test: " + values.mkString("[", ", ", "]"))
-
-    val newGrid: Grid = copy(grid)
-    var x2: Int = x + 1
-    var y2: Int = y
-    if (x2 >= _size) {
-      x2 -= _size
-      y2 += 1
-    }
-
-    for (i: Int <- values) {
-      if (DEBUG) println(s"    Testing $i")
-      newGrid(y)(x) = i
-      val sol: Option[Grid] = solveFrom(newGrid, x2, y2)
-      if (sol.isDefined) {
-        if (DEBUG) println("    Found solution, collapsing call stack")
-        return sol
+    val inGrid: ArrayBuffer[Int] = ArrayBuffer.empty
+    for (y: Int <- 0 until _size) {
+      for (x: Int <- 0 until _size) {
+        if (grid(y)(x) != 0) {
+          inGrid.addOne(grid(y)(x))
+        }
       }
     }
 
-    if (DEBUG) println(s"  No solution for this configuration")
-    return None
+    val solved: Boolean = _solve(inGrid.toArray)
+    if (solved) {
+      display(grid)
+    } else {
+      println("No solution")
+    }
   }
 
-  private def isValid(grid: Grid): Boolean = {
+  private def _solve(inGrid: Array[Int]): Boolean = {
+    display(grid)
+
+    if (DEBUG) print(grid)
+    if (!isValid()) {
+      if (DEBUG) println("  Grid is invalid")
+      return false
+    }
+
+    val (x: Int, y: Int) = getNextEmpty()
+    if (x == -1) {
+      if (DEBUG) println("  Found solution")
+      return true
+    }
+    val numbers: Array[Int] = NUMBERS.diff(inGrid)
+
+    if (DEBUG) println(s"  Values to test: " + numbers.mkString("[", ", ", "]"))
+
+    for (n: Int <- numbers) {
+      if (DEBUG) println(s"    Testing $n")
+      grid(y)(x) = n
+      if (_solve(inGrid.appended(n))) {
+        if (DEBUG) println("    Found solution, collapsing call stack")
+        return true
+      }
+    }
+    grid(y)(x) = 0
+
+    if (DEBUG) println(s"  No solution for this configuration")
+    return false
+  }
+
+  private def getNextEmpty(): (Int, Int) = {
+    for (y: Int <- 0 until _size) {
+      for (x: Int <- 0 until _size) {
+        if (grid(y)(x) == 0) {
+          return (x, y)
+        }
+      }
+    }
+    return (-1, -1)
+  }
+
+  private def isValid(): Boolean = {
     val values: Array[Int] = grid.reduce((a, b) => a.concat(b)).filter(_ != 0)
     if (values.distinct.length != values.length) return false
 
@@ -113,7 +131,7 @@ object MagicSquareSolver {
       Array(0, 0, 7),
       Array(0, 9, 0)
     )) with TextDisplay
-    solver1.solve()
+    //solver1.solve()
     println()
     /*
     8,1,6
@@ -126,7 +144,7 @@ object MagicSquareSolver {
       Array(0, 0, 7),
       Array(0, 8, 0)
     )) with TextDisplay
-    solver2.solve()
+    //solver2.solve()
     println()
     /*
     no solution