77 lines
2.8 KiB
C#
77 lines
2.8 KiB
C#
/**
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* File: n_queens.cs
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* Created Time: 2023-05-04
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* Author: hpstory (hpstory1024@163.com)
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*/
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namespace hello_algo.chapter_backtracking;
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public class n_queens {
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/* Backtracking algorithm: n queens */
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void Backtrack(int row, int n, List<List<string>> state, List<List<List<string>>> res,
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bool[] cols, bool[] diags1, 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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List<List<string>> copyState = [];
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foreach (List<string> sRow in state) {
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copyState.Add(new List<string>(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] = 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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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 = [];
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for (int i = 0; i < n; i++) {
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List<string> row = [];
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for (int j = 0; j < n; j++) {
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row.Add("#");
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}
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state.Add(row);
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}
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bool[] cols = new bool[n]; // Record columns with queens
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bool[] diags1 = new bool[2 * n - 1]; // Record main diagonals with queens
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bool[] diags2 = new bool[2 * n - 1]; // 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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[Test]
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public void Test() {
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int n = 4;
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List<List<List<string>>> res = NQueens(n);
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Console.WriteLine("Input the dimensions of the chessboard as" + n);
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Console.WriteLine("There are " + res.Count + " solutions to place the queens");
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foreach (List<List<string>> state in res) {
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Console.WriteLine("--------------------");
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foreach (List<string> row in state) {
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PrintUtil.PrintList(row);
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}
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}
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}
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}
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