Create N-Queens.cpp

Author: akashmodak97

Leet Code/N-Queens.cpp

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+/* Leet Code */
+/* Title - N-Queens */
+/* Created By - Akash Modak */
+/* Date - 08/06/2023 */
+
+// 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.
+
+ 
+
+// 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"]]
+
+class Solution {
+public:
+    bool canPlace(vector<string> &r, int n, int i, int j){
+        for(int x=0;x<i;x++){
+            if(r[x][j]=='Q') return false;
+        }
+        int x=i,y=j;
+        while(x>=0 and y>=0){
+            if(r[x][y]=='Q') return false;
+            x--,y--;
+        }
+        x=i,y=j;
+        while(x>=0 and y<n){
+            if(r[x][y]=='Q') return false;
+            x--,y++;
+        }
+        return true;
+    }
+    bool nQueen(vector<vector<string>> &res, vector<string> &r, int n, int i){
+        if(i==n){
+            res.push_back(r);
+            // intentionally making it false to generate all the cases
+            return false;
+        }
+        for(int j=0;j<n;j++){
+            bool place=canPlace(r,n,i,j);
+            if(place){
+                r[i][j]='Q';
+                bool success=nQueen(res,r,n,i+1);
+                if(success) return true;
+                r[i][j]='.';
+            }
+        }
+        return false;
+    }
+    vector<vector<string>> solveNQueens(int n) {
+        vector<vector<string>> res;
+        vector<string> r;
+        string str;
+        for(int i=1;i<=n;i++)str+='.';
+        for(int i=1;i<=n;i++)r.push_back(str);
+        nQueen(res,r,n,0);
+        return res;
+    }
+};