[Leetcode]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.."]
]

class Solution {
public:
/*algorithm: DFS
*/
void addSolution(vector<vector<string>>&result,vector<int>&solution){
int n = solution.size();
vector<string>board;
for(int i = 0;i < n;i++){
string line(n,'.');
line[solution[i]] = 'Q';
board.push_back(line);
}
result.push_back(board);
}

vector<int>getNextCandiates(vector<int>&solution,int n)
{
vector<int>result;
for(int i = 0; i < n;i++){
bool selected = true;
for(int k = 0;k < solution.size();k++){
if(i == solution[k] || //same column or same k (k=(y2-y1)/(x2-x1))
abs(i-solution[k])==abs((int)solution.size()-k)){
selected = false;
break;
}
}
if(selected)result.push_back(i);
}
return result;
}

void dfs(int n,int start,vector<vector<string>>&result,vector<int>&solution){
if(start == n){ //find one solution,reach last line
addSolution(result,solution);
return;
}
{
vector<int>candiates = getNextCandiates(solution,n);
for(int k = 0;k < candiates.size();k++){
solution.push_back(candiates[k]);
dfs(n,start+1,result,solution);
solution.pop_back();
}
}
}
vector<vector<string>> solveNQueens(int n) {
vector<int>solution;
vector<vector<string> >result;
dfs(n,0,result,solution);
return result;
}
};