Merge pull request neetcode-gh#775 from apurvtaneja/patch-1

Solution Taught in the Video

cpp/neetcode_150/10_backtracking/n-queens.cpp

@@ -8,48 +8,43 @@
 */
 
 class Solution {
-public:
- vector<vector<string>> solveNQueens(int n) {
- vector<string> board(n, string(n, '.'));
- vector<vector<string>> result;
- dfs(n, 0, board, result);
- return result;
- }
 private:
- void dfs(int n, int row, vector<string>& board, vector<vector<string>>& result) {
- if (row == n) {
- result.push_back(board);
- return;
- }
-
- for (int col = 0; col < n; col++) {
- if (isValid(n, row, col, board)) {
- board[row][col] = 'Q';
- dfs(n, row + 1, board, result);
- board[row][col] = '.';
- }
- }
- }
+ unordered_set<int> cols; //for Columns
+ unordered_set<int> negDiag; //for negative diagnals R-C
+ unordered_set<int> posDiag; //for positive diagnals R+C
 
- bool isValid(int n, int row, int col, vector<string>& board) {
- for (int i = 0; i < row; i++) {
- if (board[i][col] == 'Q') {
- return false;
- }
+ void backtrack(int n, int row, vector<vector<string>>& res, vector<string>& board){
+ if(row==n){
+ res.push_back(board);
+ return ; 
  }
 
- for (int i = row - 1, j = col - 1; i >= 0 && j >= 0; i--, j--) {
- if (board[i][j] == 'Q') {
- return false;
- }
+ for(int col = 0; col < n; col++){ //Shifting through each col
+ if( cols.find(col) != cols.end() or //if queen alread placed in this col
+ negDiag.find(row - col) != negDiag.end() or //if queen in negDiag
+ posDiag.find(row + col) != posDiag.end() //if queen in posDiag
+ )
+ continue;
+
+ cols.insert(col);
+ negDiag.insert(row - col);
+ posDiag.insert(row + col);
+ board[row][col] = 'Q';
+
+ backtrack(n, row +1, res, board);
+
+ cols.erase(col);
+ negDiag.erase(row - col);
+ posDiag.erase(row + col);
+ board[row][col] = '.';
  }
-  
-  for (int i = row - 1, j = col + 1; i >= 0 && j < n; i--, j++) {
- if (board[i][j] == 'Q') {
-  return false;
-  }
- }
-
- return true;
+ }
+
+public:
+ vector<vector<string>> solveNQueens(int n) {
+ vector<vector<string>> res;
+ vector<string> board(n, string(n,'.'));
+ backtrack(n, 0, res, board);
+ return res;
  }
 };