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.."] ] 思路: 简单题。全排列。(注意各行各列不同可以直接确定住)
void getSolution(veor<int> &r, vector<vector<string> > &vec) { int n = r.size(); vector<string> vec2; for(int i = 0; i < n; ++i) { vec2.push_back(string(n, '.')); vec2[i][r[i]] = 'Q'; } vec.push_back(vec2); } bool judge(vector<int> &r) { for(size_t i = 0; i < r.size(); ++i) for(size_t j = i+1; j < r.size(); ++j) if(j-i == r[j]-r[i] || j-i == r[i]-r[j]) return false; return true; } void getPosition(int cur, vector<int> &r, vector<vector<string> > &vec) { if(cur == r.size()) { if(judge(r)) getSolution(r, vec); return; } for(int e = cur; e < r.size(); ++e) { int t = r[cur]; r[cur] = r[e]; r[e] = t; getPosition(cur+1, r, vec); r[e] = r[cur]; r[cur] = t; } } class Solution { public: vector<vector<string> > solveNQueens(int n) { vector<vector<string> > vec; if(n <= 0) return vec; vector<int> r(n); for(int i = 0; i < n; ++i) r[i] = i; getPosition(0, r, vec); return vec; } };
N-Queens II
Follow up for N-Queens problem.
Now, instead outputting board configurations, return the total number of distinct solutions.
思路: 比上题好像更简单一些。
bool judge(vector<int> &r) { for(size_t i = 0; i < r.size(); ++i) for(size_t j = i+1; j < r.size(); ++j) if(j-i == r[j]-r[i] || j-i == r[i]-r[j]) return false; return true; } void getPosition(int cur, vector<int> &r, int &cnt) { if(cur == r.size()) { if(judge(r)) ++cnt; return; } for(int e = cur; e < r.size(); ++e) { int t = r[cur]; r[cur] = r[e]; r[e] = t; getPosition(cur+1, r, cnt); r[e] = r[cur]; r[cur] = t; } } class Solution { public: int totalNQueens(int n) { if(n <= 0) return 0; int cnt = 0; vector<int> r(n); for(int i = 0; i < n; ++i) r[i] = i; getPosition(0, r, cnt); return cnt; } };
可参考剑指 offer:题28