From 45d8592f6a773691059df8f061a19e159f546bd8 Mon Sep 17 00:00:00 2001
From: Manassa2000 <manassavs2000@gmail.com>
Date: Sat, 15 Nov 2025 12:08:50 -0500
Subject: [PATCH] Backtracking-3

---
 NQueens.java    | 67 +++++++++++++++++++++++++++++++++++++++++++++++++
 WordSearch.java | 35 ++++++++++++++++++++++++++
 2 files changed, 102 insertions(+)
 create mode 100644 NQueens.java
 create mode 100644 WordSearch.java

diff --git a/NQueens.java b/NQueens.java
new file mode 100644
index 00000000..ef4c3ffb
--- /dev/null
+++ b/NQueens.java
@@ -0,0 +1,67 @@
+// Time Complexity :O(n*n!) n: checking isValid, n!: to place n queens in n rows
+// Space Complexity :O(n^2)+O(n)
+// Did this code successfully run on Leetcode :yes
+import java.util.ArrayList;
+import java.util.List;
+
+class Solution {
+    public List<List<String>> solveNQueens(int n) {
+        List<List<String>> answer = new ArrayList<>();
+        boolean[][] board = new boolean[n][n];
+        helper(board,0,n,answer);
+        return answer;
+    }
+    private void helper(boolean[][] board, int row, int n,List<List<String>> answer) {
+        if (row == n) {//there is a queen in each row
+            List<String> list = new ArrayList<>();
+            for (int i = 0; i < n; i++) {
+                StringBuilder sb = new StringBuilder();//build a string for each row
+                for (int j = 0; j < n; j++) {
+                    if (board[i][j]) {
+                        sb.append("Q");
+                    } else {
+                        sb.append(".");
+                    }
+                }
+                list.add(sb.toString());//add row to list
+            }
+            answer.add(list);//add list to answer
+            return;
+        }
+        for (int j = 0; j < n; j++) {
+            if (isValid(board, row, j, n)) {
+                //action
+                board[row][j] = true;
+                //recurse
+                helper(board, row + 1, n,answer);
+                //backtrack
+                board[row][j] = false;
+            }
+        }
+    }
+    private boolean isValid(boolean[][] board, int i, int j, int n) {
+        int r = i, c = j;
+        while (r >= 0) {//up
+            if (board[r][c])
+                return false;
+            r--;
+        }
+        r = i;
+        c = j;
+        while (r >= 0 && c >= 0) {//upper left diagonal
+            if (board[r][c])
+                return false;
+            r--;
+            c--;
+        }
+        r = i;
+        c = j;
+        while (r >= 0 && c < n) {//upper right diagonal
+            if (board[r][c])
+                return false;
+            r--;
+            c++;
+        }
+        return true;
+    }
+}
diff --git a/WordSearch.java b/WordSearch.java
new file mode 100644
index 00000000..62b0b261
--- /dev/null
+++ b/WordSearch.java
@@ -0,0 +1,35 @@
+// Time Complexity :O(m*n*4^L) L: Length of word
+// Space Complexity :O(L)
+// Did this code successfully run on Leetcode :yes
+class Solution {
+    int m,n;
+    int direction[][];
+    public boolean exist(char[][] board, String word) {
+        m = board.length;
+        n = board[0].length;
+        direction = new int[][]{{-1,0},{1,0},{0,1},{0,-1}};
+        for(int i=0;i<m;i++){//loop through all cells(i,j)
+            for(int j=0;j<n;j++){
+                if(board[i][j] == word.charAt(0)){//if (i,j) has 1st character of the word
+                if(helper(board,word,i,j,0)) return true;
+                //if we find a successful dfs, return true
+                }
+            }
+        }
+        return false;
+    }
+    private boolean helper(char[][] board,String word,int i,int j,int index){
+        if(index == word.length()) return true;//reached end
+        if(i < 0 || j < 0 || i == m || j == n || board[i][j] == '#') return false;//if out of grid or cell is already visited
+        if(board[i][j] != word.charAt(index)) return false;//wrong path
+        //mark as visited and move to find next index
+        board[i][j] = '#';
+        for(int[] dir: direction){
+            int r = dir[0] + i;
+            int c = dir[1] + j;
+            if(helper(board,word,r,c,index+1)) return true;
+        }
+        board[i][j] = word.charAt(index);//unmark
+        return false;
+    }
+}
\ No newline at end of file