[LeetCode] 060: N-Queens

[Problem]

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.."]]

[Solution]

class Solution {
public:
/**
 * check if the position is valid
 */
bool check(int pos[], int level){
// 
map<int, bool> first;
for(int i = 0; i <= level; ++i){
if(first.find(i+pos[i]) != first.end()){
return false;
}
else{
first[i+pos[i]] = true;
}
}

// 
int tmp;
map<int, bool> second;
for(int i = 0; i <= level; ++i){
tmp = i-pos[i];
if(second.find(tmp) != second.end()){
return false;
}
else{
second[tmp] = true;
}
}
return true;
}
/**
 * generate result with 'Q' in position k
 */
string generate(int n, int k){
string res = "";
for(int i = 0; i < n; ++i){
if(i == k){
res += "Q";
}
else{
res += ".";
}
}
return res;
}
/**
 * result of N Queens in level 'level'
 */
vector<vector<string> > solveNQueens(int n, int pos[], bool used[], int level){
vector<vector<string> > res;

// the last level
if(level == n-1){
// put in each position
for(int i = 0; i < n; ++i){
pos[level] = i;
// valid
if(!used[i] && check(pos, level)){
vector<string> row;
row.push_back(generate(n, i));
res.push_back(row);
}
}
}
else{
for(int i = 0; i < n; ++i){
pos[level] = i;
if(!used[i] && check(pos, level)){
used[i] = true;
// generate result in the next level
vector<vector<string> > nextRes = solveNQueens(n, pos, used, level+1);

// merge result
string line = generate(n, i);
for(int j = 0; j < nextRes.size(); ++j){
vector<string> row;
row.push_back(line);
for(int k = 0; k < nextRes[j].size(); ++k){
row.push_back(nextRes[j][k]);
}
res.push_back(row);
}
used[i] = false;
}
}
}
return res;
}
/**
 * result of N Queens
 */
vector<vector<string> > solveNQueens(int n) {
// Note: The Solution object is instantiated only once and is reused by each test case.
vector<vector<string> > res;
if(n <= 0)return res;
int pos[n];
bool used[n];
for(int i = 0; i < n; ++i)used[i] = false;
return solveNQueens(n, pos, used, 0);
}
};

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