Given the initial Sudoku board state, what will be the board after the first successful number placement by the backtracking algorithm?
const board = [ [5,3,0,0,7,0,0,0,0], [6,0,0,1,9,5,0,0,0], [0,9,8,0,0,0,0,6,0], [8,0,0,0,6,0,0,0,3], [4,0,0,8,0,3,0,0,1], [7,0,0,0,2,0,0,0,6], [0,6,0,0,0,0,2,8,0], [0,0,0,4,1,9,0,0,5], [0,0,0,0,8,0,0,7,9] ]; // After one step of backtracking, the first 0 replaced with a valid number // What is the updated board?
Look for the first empty cell (0) and find the smallest valid number that fits according to Sudoku rules.
The first empty cell is at position (0,2). The smallest valid number that can be placed there without breaking Sudoku rules is 1.
Before placing a number in an empty cell during Sudoku backtracking, which of the following must be true?
Sudoku rules require unique numbers in row, column, and box.
Sudoku requires that each number appears only once per row, column, and 3x3 box. This condition ensures the placement is valid.
Consider this TypeScript snippet for checking if a number can be placed:
function isSafe(board: number[][], row: number, col: number, num: number): boolean {
for (let x = 0; x < 9; x++) {
if (board[row][x] === num || board[x][col] === num) {
return false;
}
}
const startRow = row - row % 3;
const startCol = col - col % 3;
for (let i = 0; i < 3; i++) {
for (let j = 0; j < 3; j++) {
if (board[startRow + i][startCol + j] === num) {
return false;
}
}
}
return true;
}
// What error does this code cause if any?Check the calculation of startRow and startCol and the loops for the 3x3 box.
The code correctly calculates the starting indices of the 3x3 box and checks all cells inside it. The for loops and conditions are valid, so no error occurs.
Given a Sudoku board with 40 empty cells, approximately how many recursive calls will the backtracking algorithm make in the worst case?
Consider the branching factor and depth of recursion in backtracking.
Each empty cell can try up to 9 numbers, so in the worst case, the number of recursive calls can be up to 9 to the power of the number of empty cells.
Given this incomplete Sudoku board, what is the fully solved board after the backtracking solver completes?
const board = [ [5,3,0,0,7,0,0,0,0], [6,0,0,1,9,5,0,0,0], [0,9,8,0,0,0,0,6,0], [8,0,0,0,6,0,0,0,3], [4,0,0,8,0,3,0,0,1], [7,0,0,0,2,0,0,0,6], [0,6,0,0,0,0,2,8,0], [0,0,0,4,1,9,0,0,5], [0,0,0,0,8,0,0,7,9] ]; // What is the solved board?
Check carefully the placement of numbers in the 8th and 9th columns of the first row.
Option A matches the correct solved Sudoku board with all rules satisfied.