66 lines
2.0 KiB
C++
66 lines
2.0 KiB
C++
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/**
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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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/* <20><><EFBFBD><EFBFBD><EFBFBD>㷨<EFBFBD><E3B7A8>n <20>ʺ<EFBFBD> */
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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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// <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ʱ<EFBFBD><CAB1><EFBFBD><EFBFBD>¼<EFBFBD><C2BC>
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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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// <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
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for (int col = 0; col < n; col++) {
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// <20><><EFBFBD><EFBFBD><EFBFBD>ø<EFBFBD><C3B8>Ӷ<EFBFBD>Ӧ<EFBFBD><D3A6><EFBFBD><EFBFBD><EFBFBD>Խ<EFBFBD><D4BD>ߺʹζԽ<CEB6><D4BD><EFBFBD>
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int diag1 = row - col + n - 1;
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int diag2 = row + col;
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// <20><>֦<EFBFBD><D6A6><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ø<EFBFBD><C3B8><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>С<EFBFBD><D0A1><EFBFBD><EFBFBD>Խ<EFBFBD><D4BD>ߡ<EFBFBD><DFA1>ζԽ<CEB6><D4BD><EFBFBD><EFBFBD>ϴ<EFBFBD><CFB4>ڻʺ<DABB>
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if (!cols[col] && !diags1[diag1] && !diags2[diag2]) {
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// <20><><EFBFBD>ԣ<EFBFBD><D4A3><EFBFBD><EFBFBD>ʺ<EFBFBD><CABA><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ڸø<DAB8><C3B8><EFBFBD>
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state[row][col] = "Q";
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cols[col] = diags1[diag1] = diags2[diag2] = true;
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// <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD>һ<EFBFBD><D2BB>
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backtrack(row + 1, n, state, res, cols, diags1, diags2);
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// <20><><EFBFBD>ˣ<EFBFBD><CBA3><EFBFBD><EFBFBD>ø<EFBFBD><C3B8>ӻָ<D3BB>Ϊ<EFBFBD><CEAA>λ
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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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/* <20><><EFBFBD><EFBFBD> n <20>ʺ<EFBFBD> */
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vector<vector<vector<string>>> nQueens(int n) {
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// <20><>ʼ<EFBFBD><CABC> n*n <20><>С<EFBFBD><D0A1><EFBFBD><EFBFBD><EFBFBD>̣<EFBFBD><CCA3><EFBFBD><EFBFBD><EFBFBD> 'Q' <20><><EFBFBD><EFBFBD><EFBFBD>ʺ<EFBFBD><CABA><EFBFBD>'#' <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD>λ
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vector<vector<string>> state(n, vector<string>(n, "#"));
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vector<bool> cols(n, false); // <20><>¼<EFBFBD><C2BC><EFBFBD>Ƿ<EFBFBD><C7B7>лʺ<D0BB>
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vector<bool> diags1(2 * n - 1, false); // <20><>¼<EFBFBD><C2BC><EFBFBD>Խ<EFBFBD><D4BD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>Ƿ<EFBFBD><C7B7>лʺ<D0BB>
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vector<bool> diags2(2 * n - 1, false); // <20><>¼<EFBFBD>ζԽ<CEB6><D4BD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>Ƿ<EFBFBD><C7B7>лʺ<D0BB>
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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 << "<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>̳<EFBFBD><EFBFBD><EFBFBD>Ϊ " << n << endl;
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cout << "<EFBFBD>ʺ<EFBFBD><EFBFBD><EFBFBD><EFBFBD>÷<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> " << res.size() << " <20><>" << 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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