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66 lines
2.3 KiB
66 lines
2.3 KiB
/**
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* File: n_queens.cpp
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* Created Time: 2023-05-04
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* Author: krahets (krahets@163.com)
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*/
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#include "../utils/common.hpp"
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/* Backtracking algorithm: n queens */
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void backtrack(int row, int n, vector<vector<string>> &state, vector<vector<vector<string>>> &res, vector<bool> &cols,
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vector<bool> &diags1, vector<bool> &diags2) {
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// When all rows are placed, record the solution
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if (row == n) {
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res.push_back(state);
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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] = diags1[diag1] = 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] = diags1[diag1] = 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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vector<vector<vector<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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vector<vector<string>> state(n, vector<string>(n, "#"));
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vector<bool> cols(n, false); // Record columns with queens
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vector<bool> diags1(2 * n - 1, false); // Record main diagonals with queens
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vector<bool> diags2(2 * n - 1, false); // Record minor diagonals with queens
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vector<vector<vector<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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int main() {
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int n = 4;
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vector<vector<vector<string>>> res = nQueens(n);
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cout << "Input the dimensions of the chessboard as " << n << endl;
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cout << "Total number of queen placement solutions = " << res.size() << endl;
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for (const vector<vector<string>> &state : res) {
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cout << "--------------------" << endl;
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for (const vector<string> &row : state) {
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printVector(row);
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}
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}
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return 0;
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}
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