56 lines
1.9 KiB
JavaScript
56 lines
1.9 KiB
JavaScript
/**
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* File: n_queens.js
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* Created Time: 2023-05-13
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* Author: Justin (xiefahit@gmail.com)
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*/
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/* Backtracking algorithm: n queens */
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function backtrack(row, n, state, res, cols, diags1, 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(state.map((row) => row.slice()));
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return;
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}
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// Traverse all columns
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for (let col = 0; col < n; col++) {
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// Calculate the main and minor diagonals corresponding to the cell
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const diag1 = row - col + n - 1;
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const 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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function nQueens(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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const state = Array.from({ length: n }, () => Array(n).fill('#'));
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const cols = Array(n).fill(false); // Record columns with queens
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const diags1 = Array(2 * n - 1).fill(false); // Record main diagonals with queens
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const diags2 = Array(2 * n - 1).fill(false); // Record minor diagonals with queens
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const 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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const n = 4;
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const res = nQueens(n);
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console.log(`输入棋盘长宽为 ${n}`);
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console.log(`皇后放置方案共有 ${res.length} 种`);
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res.forEach((state) => {
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console.log('--------------------');
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state.forEach((row) => console.log(row));
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});
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