Sit-In Lab 1 Ob-CHESS-ion

N-Queens Puzzle Checker Famous N-Queens puzzle You want to check if the input solution is correct No 2 queens can be on the same row, column or diagonal Write a piece of code to verify the solution Input: N – Number of rows ( Number of queens on chessboard ) Followed by N rows of N numbers 0 – Empty space 1 – Queen Output whether the puzzle is a valid solution

Example – Valid? Output :

Example – Incorrect solution Output : INVALID

Example – Valid Solution Output : VALID

No other queen in same row, column and diagonal

Algorithm Loop through each square of the array: Start from the top left, iterate row by row For each queen found Starting from the square on its right, check if there exists another queen in the same row Starting from the square right below it, check if there exists another queen in the same column Starting from the square on its bottom right, check if there exists another queen in the same right diagonal Starting from the square on its bottom left, check if there exists another queen in the same left diagonal Return false if there exists another queen

Visualisation – Start from top left

Visualisation – Queen is found, check rows and diagonals

Visualisation – Queen is found, check rows and diagonals Valid

Visualisation – Iterate row by row - No queen in this space

Visualisation – Another Queen is found

Visualisation – Queen is found, check rows and diagonals Valid

Visualisation – Iterate row by row

Visualisation – Another Queen is found

Visualisation – Queen is found, check rows and diagonals Invalid

Visualisation – Break from loop and return false Invalid

Main method: Helper methods: Read in the inputs Call helper methods and print the output Helper methods: Check rows, columns and diagonals ( 4 directions ), returning false if another queen is found Check if given coordinates are out of array bounds ( >= N )

How to check diagonals?

0 1 2 3 4 5 6 7 1 2 [1][3] 3 4 5 6 7

0 1 2 3 4 5 6 7 1 2 [2][4] 3 4 5 6 7

0 1 2 3 4 5 6 7 1 2 3 4 5 6 7 [3][5]

0 1 2 3 4 5 6 7 1 2 3 4 5 6 7 [3][5] Row++ Col++

0 1 2 3 4 5 6 7 1 2 [1][3] 3 4 5 6 7

0 1 2 3 4 5 6 7 1 2 [2][2] 3 4 5 6 7

0 1 2 3 4 5 6 7 1 2 3 4 5 6 7 [3][1]

0 1 2 3 4 5 6 7 1 2 3 4 5 6 7 [3][1] Row++ Col--

Questions?