source: https://leetcode.com/problems/n-queens/
C/C++ Solution to LeetCode problem 51. N-Queens.
Problem
The n-queens puzzle is the problem of placing n
queens on an n x n
chessboard such that no two queens attack each other.
Given an integer n
, return all distinct solutions to the n-queens puzzle. You may return the answer in any order.
Each solution contains a distinct board configuration of the n-queens’ placement, where 'Q'
and '.'
both indicate a queen and an empty space, respectively.
Examples
Example 1:
Input: n = 4
Output: [[“.Q..”,”…Q”,”Q…”,”..Q.”],[”..Q.”,”Q…”,”…Q”,”.Q..”]]
Explanation: There exist two distinct solutions to the 4-queens puzzle as shown above.
Example 2:
Input: n = 1
Output: [[“Q”]]
Constraints
1 <= n <= 9
Solution
I will use the backtracking technique, I propose two solutions, same algorithm, but different implementation.
- First solution, uses a
set
to keep tracking only of theQueens
positions. The problem with this solution is that, once a solution is found, then we need to generate the strings to represent the board. - Second solution uses directly strings to represent the whole board at all times.
Solution 1:
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class Solution {
private:
vector<vector<string>> result;
bool isValid(int n, int r, int c, set<pair<int, int>>& tmpSol) {
for (const auto& pair: tmpSol) {
if (pair.first == r || pair.second == c)
return false;
if (abs(pair.first - r) == abs(pair.second - c))
return false;
}
return true;
}
void addSolution(int n, set<pair<int, int>>& tmpSol) {
vector<string> tmp;
for (int r=0; r<n; r++) {
string sol = ""s;
for (int c=0; c<n; c++) {
if (tmpSol.find({r,c}) == tmpSol.end())
sol = sol + ".";
else
sol = sol + "Q";
}
tmp.push_back(sol);
}
result.push_back(tmp);
}
void solve(int n, set<pair<int, int>>& tmpSol, int r) {
if (r == n) {
addSolution(n, tmpSol);
return;
}
for (int c=0; c<n; c++) {
if (!isValid(n, r, c, tmpSol))
continue;
tmpSol.insert({r, c});
solve(n, tmpSol, r+1);
tmpSol.erase({r, c});
}
}
public:
vector<vector<string>> solveNQueens(int n) {
set<pair<int,int>> tmpSol;
solve(n, tmpSol, 0);
return result;
}
};
Solution 2:
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class Solution {
private:
vector<vector<string>> result;
bool isValid(int n, vector<string>& tmpSol, int row, int col){
for (int i=0; i<n; i++){
if (tmpSol[i][col] == 'Q')
return false;
}
for(int i=row-1, j=col-1; i>=0 && j>=0; i--, j--){
if(tmpSol[i][j] == 'Q')
return false;
}
for (int i=row-1, j=col+1; i>=0 && j<n; i--, j++) {
if(tmpSol[i][j] == 'Q')
return false;
}
return true;
}
void solve(int n, vector<string>& tmpSol, int r){
if (r == n) {
result.push_back(tmpSol);
return;
}
for (int c=0; c<n; c++) {
if (isValid(n, tmpSol, r, c)) {
tmpSol[r][c] = 'Q';
solve(n, tmpSol, r+1);
tmpSol[r][c] = '.';
}
}
}
public:
vector<vector<string>> solveNQueens(int n) {
vector<string> tmpSol(n , string(n, '.'));
solve(n, tmpSol, 0);
return result;
}
};