problem038

Author: TipsyPixie

README.md

@@ -53,3 +53,4 @@ Number | Difficulty | Asked By | Title
 [#35](problem035) | HARD | Google
 [#36](problem036) | MEDIUM | Dropbox | Finding the second largest node in BST
 [#37](problem037) | EASY | Google | Generating the power set of a set
+[#38](problem038) | HARD | Microsoft | Arranging queens without threatening one another

problem038/README.md

@@ -0,0 +1,8 @@
+## Daily Coding Problem: Problem #38 [HARD]
+
+Good morning! Here's your coding interview problem for today.
+
+This problem was asked by Microsoft.
+
+You have an N by N board. Write a function that, given N, returns the number of possible arrangements of the board where N queens can be placed on the board without threatening each other, i.e. no two queens share the same row, column, or diagonal.
+

problem038/problem038.go

@@ -0,0 +1,84 @@
+package problem038
+
+type chessBoard [][]bool
+
+func newChessBoard(size int) *chessBoard {
+	board := make(chessBoard, size, size)
+	for i := range board {
+		board[i] = make([]bool, size, size)
+	}
+	return &board
+}
+
+func (thisBoard *chessBoard) hasQueen(row int, column int) bool {
+	return (*thisBoard)[row][column]
+}
+
+func (thisBoard *chessBoard) putQueen(row int, column int) {
+	(*thisBoard)[row][column] = true
+}
+
+func (thisBoard *chessBoard) removeQueen(row int, column int) {
+	(*thisBoard)[row][column] = false
+}
+
+func (thisBoard *chessBoard) isSafe(row int, column int) bool {
+	onBoard := func(r int, c int) bool {
+		return r >= 0 && r < len(*thisBoard) && c >= 0 && c < len(*thisBoard)
+	}
+
+	// horizontal check is unnecessary
+
+	// vertical
+	for otherRow := 0; onBoard(otherRow, column); otherRow++ {
+		if thisBoard.hasQueen(otherRow, column) {
+			return false
+		}
+	}
+
+	// diagonal
+	for otherRow, otherColumn := row, column; onBoard(otherRow, otherColumn); otherRow, otherColumn = otherRow+1, otherColumn+1 {
+		if thisBoard.hasQueen(otherRow, otherColumn) {
+			return false
+		}
+	}
+	for otherRow, otherColumn := row, column; onBoard(otherRow, otherColumn); otherRow, otherColumn = otherRow-1, otherColumn-1 {
+		if thisBoard.hasQueen(otherRow, otherColumn) {
+			return false
+		}
+	}
+	for otherRow, otherColumn := row, column; onBoard(otherRow, otherColumn); otherRow, otherColumn = otherRow+1, otherColumn-1 {
+		if thisBoard.hasQueen(otherRow, otherColumn) {
+			return false
+		}
+	}
+	for otherRow, otherColumn := row, column; onBoard(otherRow, otherColumn); otherRow, otherColumn = otherRow-1, otherColumn+1 {
+		if thisBoard.hasQueen(otherRow, otherColumn) {
+			return false
+		}
+	}
+
+	return true
+}
+
+func arrange(boardState *chessBoard, alreadyDeployed int) int {
+	boardSize := len(*boardState)
+	if alreadyDeployed == boardSize {
+		return 1
+	}
+
+	arrangementCount := 0
+	for column := 0; column < boardSize; column++ {
+		if boardState.isSafe(alreadyDeployed, column) {
+			boardState.putQueen(alreadyDeployed, column)
+			arrangementCount += arrange(boardState, alreadyDeployed+1)
+			boardState.removeQueen(alreadyDeployed, column)
+		}
+	}
+	return arrangementCount
+}
+
+func GetArrangementsCount(boardSize int) int {
+	board := newChessBoard(boardSize)
+	return arrange(board, 0)
+}

problem038/problem038_test.go

@@ -0,0 +1,17 @@
+package problem038
+
+import (
+	"fmt"
+	"testing"
+)
+
+func TestGetArrangementsCount(t *testing.T) {
+	correctAnswers := []int{1, 1, 0, 0, 2, 10, 4, 40, 92, 352, 724, 2680, 14200, 73712}
+	for i := range correctAnswers {
+		answer := GetArrangementsCount(i)
+		if answer != correctAnswers[i] {
+			t.Log(fmt.Sprintf("%d: %d != %d", i, answer, correctAnswers[i]))
+			t.FailNow()
+		}
+	}
+}