标签：style blog http color io ar for strong sp
N-Queens
The n-queens puzzle is the problem of placing n queens on an n×n chessboard such that no two queens attack each other.
Given an integer n, return all distinct solutions to the n-queens puzzle.
Each solution contains a distinct board configuration of the n-queens‘ placement, where ‘Q‘ and ‘.‘ both indicate a queen and an empty space respectively.
For example,
There exist two distinct solutions to the 4-queens puzzle:
[ [".Q..", // Solution 1 "...Q", "Q...", "..Q."], ["..Q.", // Solution 2 "Q...", "...Q", ".Q.."] ]
这题和Sudoku Solver是一个套路，回溯法尝试所有可能性，将可行解的保存起来。可以对比着看。
我们先用vector<int>来存放可行解，下标代表行号，元素代表列号。
因此上图中Solution 1用vector<int>表示就是[1,3,0,2]
解题流程就是在下一行中尝试列数(0~n-1)，如果可行则递归下去，如果不可行则弹出继续尝试下一列。
代码中加入了大量注释，还是很好理解的。
class Solution { public: vector<vector<string> > solveNQueens(int n) { vector<vector<int> > result; //全局变量 vector<int> cur; //递归栈中的变量 solve(result, cur, n); //符合条件的cur加入result return transfer(result, n); //vector<int>转为vector<string> } void solve(vector<vector<int> > &result, vector<int> cur, int n) { if(cur.size() == n) {//找到解 result.push_back(cur); } else { for(int i = 0; i < n; i ++) {//尝试所有可能 cur.push_back(i); if(isValid(cur)) {//可行则递归下去 solve(result, cur, n); } cur.pop_back(); } } } vector<vector<string> > transfer(vector<vector<int> > &result, int n) { vector<vector<string> > ret; for(vector<vector<int> >::size_type st1 = 0; st1 < result.size(); st1 ++) {//第st1个解 vector<string> cur(n, string(n,‘.‘)); for(vector<int>::size_type st2 = 0; st2 < n; st2 ++) {//第st2行 cur[st2][result[st1][st2]] = ‘Q‘; } ret.push_back(cur); } return ret; } bool isValid(vector<int> &cur) {//针对新加点进行验证 int sz = cur.size(); int row = sz-1; //新加点的行数sz-1 int col = cur[sz-1]; //列数cur[sz-1] for(vector<int>::size_type st = 0; st < sz-1; st ++) { //验证同列错误(由于数组下标不同，同行错误不存在) if(col == cur[st]) return false; //验证同对角线错误 if(fabs((double)row-st)==fabs((double)col-cur[st])) return false; } return true; } };
标签：style blog http color io ar for strong sp
原文地址：http://www.cnblogs.com/ganganloveu/p/4020488.html
