From f0127097b94b83b239d98bcd594e2c06f4f65c76 Mon Sep 17 00:00:00 2001
From: kalyan <kalyan.ng22@gmail.com>
Date: Sat, 8 Nov 2025 15:56:08 -0600
Subject: [PATCH] Backtracking-3 solutions

---
 Nqueens.java    | 74 +++++++++++++++++++++++++++++++++++++++++++++++++
 wordSearch.java | 52 ++++++++++++++++++++++++++++++++++
 2 files changed, 126 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..e847722d
--- /dev/null
+++ b/Nqueens.java
@@ -0,0 +1,74 @@
+// Time Complexity : O(n!)
+// Space Complexity : O(n*n) for board + 0(n) recursive stack
+// Did this code successfully run on Leetcode : Yes
+// Approach : We start from 1st row 1st col by inserting queen and explore the next row's all columns if we can insert a queen by checking
+// the column, upper left diagonal and upper right diagonal for an existing queen. We repeat until we complete the board, construct
+// the result and return.
+
+class Solution {
+    List<List<String>> result;
+
+    public List<List<String>> solveNQueens(int n) {
+        this.result = new ArrayList<>();
+        boolean[][] arr = new boolean[n][n];//create a chess board 2d array
+        helper(arr, 0, n);
+        return result;
+    }
+
+    public void helper(boolean[][] arr, int row, int n) {
+        //base case
+        if (row == arr.length) { //when all row are parsed
+            List<String> li = new ArrayList<>();
+            for (int i = 0; i < n; i++) {
+                StringBuilder sb = new StringBuilder();
+                for (int j = 0; j < n; j++) {
+                    if (arr[i][j] == true) {
+                        sb.append("Q");
+                    } else {
+                        sb.append(".");
+                    }
+
+                }
+                li.add(sb.toString());
+            }
+            result.add(li);
+
+        }
+
+        for (int c = 0; c < n; c++) {
+            if (isSafe(arr, row, c)) { //checking if safe to add
+                arr[row][c] = true;
+                helper(arr, row + 1, n);
+                arr[row][c] = false; //backtrack
+            }
+        }
+
+    }
+
+    private boolean isSafe(boolean[][] arr, int row, int col) {
+        for (int i = row - 1; i >= 0; i--) { //column check
+            if (arr[i][col]) {
+                return false;
+            }
+        }
+        int i = row;
+        int j = col;
+        while (i >= 0 && j >= 0) { //upper left diagonal check
+            if (arr[i][j]) {
+                return false;
+            }
+            i--;
+            j--;
+        }
+        int a = row;
+        int b = col;
+        while (a >= 0 && b < arr.length) { //upper right diagonal check
+            if (arr[a][b]) {
+                return false;
+            }
+            a--;
+            b++;
+        }
+        return true;
+    }
+}
\ No newline at end of file
diff --git a/wordSearch.java b/wordSearch.java
new file mode 100644
index 00000000..c88b541e
--- /dev/null
+++ b/wordSearch.java
@@ -0,0 +1,52 @@
+// Time Complexity : O(m*n*3^(L)) where L is the length of word
+// Space Complexity : O(L)
+// Did this code successfully run on Leetcode : Yes
+// Approach : Performed DFW with backtracking to get to the solution. We start performing DFS when we encounter first char in word while
+// parsing the matrix. We mark the visited chars as # and continue exploring neighbors. When the next char si not found we backtrack and
+// unmark the visited node so that it can be visited again. Continuw until we reach the end of the word length.
+
+class Solution {
+    int[][] directions;
+    int m;
+    int n;
+
+    public boolean exist(char[][] board, String word) {
+        this.directions = new int[][] { { -1, 0 }, { 1, 0 }, { 0, -1 }, { 0, 1 } };// directions array
+        this.m = board.length;
+        this.n = board[0].length;
+        for (int i = 0; i < m; i++) {
+            for (int j = 0; j < n; j++) {
+                if (board[i][j] == word.charAt(0)) {//when first char is word is found
+                    if (helper(board, word, i, j, 0)) {
+                        return true;
+                    }
+
+                }
+            }
+        }
+        return false;
+    }
+
+    private boolean helper(char[][] board, String word, int i, int j, int index) {
+        if (index == word.length()) { //base case
+            return true;
+        }
+        if (i < 0 || j < 0 || i == m || j == n || board[i][j] == '#') { //bounds and visited condition check
+            return false;
+        }
+
+        if (board[i][j] == word.charAt(index)) { //match found
+            board[i][j] = '#';// marks as visited
+            for (int[] dir : directions) {
+                int nr = i + dir[0]; // neighbour row
+                int nc = j + dir[1]; // neighbour column
+                if (helper(board, word, nr, nc, index + 1)) {
+                    return true;
+                }
+            }
+            board[i][j] = word.charAt(index); //backtrack
+        }
+        return false;
+
+    }
+}
\ No newline at end of file