76 lines
2.2 KiB
Dart
76 lines
2.2 KiB
Dart
/**
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* File: n_queens.dart
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* Created Time: 2023-08-10
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* Author: liuyuxin (gvenusleo@gmail.com)
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*/
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/* Backtracking algorithm: n queens */
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void backtrack(
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int row,
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int n,
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List<List<String>> state,
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List<List<List<String>>> res,
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List<bool> cols,
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List<bool> diags1,
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List<bool> diags2,
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) {
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// When all rows are placed, record the solution
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if (row == n) {
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List<List<String>> copyState = [];
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for (List<String> sRow in state) {
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copyState.add(List.from(sRow));
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}
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res.add(copyState);
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return;
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}
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// Traverse all columns
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for (int col = 0; col < n; col++) {
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// Calculate the main and minor diagonals corresponding to the cell
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int diag1 = row - col + n - 1;
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int diag2 = row + col;
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// Pruning: do not allow queens on the column, main diagonal, or minor diagonal of the cell
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if (!cols[col] && !diags1[diag1] && !diags2[diag2]) {
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// Attempt: place the queen in the cell
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state[row][col] = "Q";
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cols[col] = true;
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diags1[diag1] = true;
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diags2[diag2] = true;
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// Place the next row
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backtrack(row + 1, n, state, res, cols, diags1, diags2);
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// Retract: restore the cell to an empty spot
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state[row][col] = "#";
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cols[col] = false;
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diags1[diag1] = false;
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diags2[diag2] = false;
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}
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}
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}
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/* Solve n queens */
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List<List<List<String>>> nQueens(int n) {
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// Initialize an n*n size chessboard, where 'Q' represents the queen and '#' represents an empty spot
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List<List<String>> state = List.generate(n, (index) => List.filled(n, "#"));
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List<bool> cols = List.filled(n, false); // Record columns with queens
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List<bool> diags1 = List.filled(2 * n - 1, false); // Record main diagonals with queens
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List<bool> diags2 = List.filled(2 * n - 1, false); // Record minor diagonals with queens
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List<List<List<String>>> res = [];
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backtrack(0, n, state, res, cols, diags1, diags2);
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return res;
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}
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/* Driver Code */
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void main() {
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int n = 4;
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List<List<List<String>>> res = nQueens(n);
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print("Input chessboard dimensions as $n");
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print("There are ${res.length} queen placement solutions");
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for (List<List<String>> state in res) {
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print("--------------------");
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for (List<String> row in state) {
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print(row);
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}
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}
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}
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