122 lines
3.3 KiB
C++
122 lines
3.3 KiB
C++
// Source : https://oj.leetcode.com/problems/n-queens/
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// Author : Hao Chen
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// Date : 2014-08-22
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/**********************************************************************************
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*
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* The n-queens puzzle is the problem of placing n queens on an n×n chessboard
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* such that no two queens attack each other.
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*
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* Given an integer n, return all distinct solutions to the n-queens puzzle.
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*
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* Each solution contains a distinct board configuration of the n-queens' placement,
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* where 'Q' and '.' both indicate a queen and an empty space respectively.
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*
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* For example,
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* There exist two distinct solutions to the 4-queens puzzle:
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*
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* [
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* [".Q..", // Solution 1
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* "...Q",
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* "Q...",
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* "..Q."],
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*
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* ["..Q.", // Solution 2
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* "Q...",
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* "...Q",
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* ".Q.."]
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* ]
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*
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*
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**********************************************************************************/
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#include <stdlib.h>
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#include <iostream>
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#include <vector>
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#include <string>
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using namespace std;
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vector< vector<string> > solveNQueens(int n);
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void solveNQueensRecursive(int n, int currentRow, vector<int>& solution, vector< vector<string> >& result);
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bool isValid(int attemptedColumn, int attemptedRow, vector<int> &queenInColumn);
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vector< vector<string> > solveNQueens(int n) {
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vector< vector<string> > result;
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vector<int> solution(n);
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solveNQueensRecursive(n, 0, solution, result);
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return result;
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}
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//The following recursion is easy to understand. Nothing's tricky.
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// 1) recursively find all of possible columns row by row.
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// 2) solution[] array only stores the columns index. `solution[row] = col;`
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void solveNQueensRecursive(int n, int currentRow, vector<int>& solution, vector< vector<string> >& result) {
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//if no more row need to do, shape the result
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if (currentRow == n){
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vector<string> s;
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vector<string> s(n, string(n, '.'));
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for (int row = 0; row < n; row++) {
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s[row][solution[row]] = 'Q';
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}
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result.push_back(s);
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return;
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}
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//for each column
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for (int col = 0; col < n; col++) {
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//if the current column is valid
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if (isValid(col, currentRow, solution) ) {
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//place the Queue
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solution[currentRow] = col;
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//recursively put the Queen in next row
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solveNQueensRecursive(n, currentRow+1, solution, result);
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}
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}
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}
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//Attempting to put the Queen into [row, col], check it is valid or not
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//Notes:
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// 1) we just checking the Column not Row, because the row cannot be conflicted
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// 2) to check the diagonal, we just check |x'-x| == |y'-y|, (x',y') is a Queen will be placed
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bool isValid(int attemptedColumn, int attemptedRow, vector<int> &queenInColumn) {
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for(int i=0; i<attemptedRow; i++) {
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if (attemptedColumn == queenInColumn[i] ||
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abs(attemptedColumn - queenInColumn[i]) == abs(attemptedRow - i)) {
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return false;
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}
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}
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return true;
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}
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void printMatrix(vector< vector<string> >& matrix ){
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for (int i = 0; i < matrix.size(); i++) {
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cout << "-----------" << endl;
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for (int j = 0; j < matrix[i].size(); j++) {
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cout << matrix[i][j] << endl;
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}
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}
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}
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int main(int argc, char** argv)
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{
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int n = 8;
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if (argc>1){
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n = atoi(argv[1]);
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}
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vector< vector<string> > result = solveNQueens(n);
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printMatrix(result);
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return 0;
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}
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