From 0baa366f2729df35ec4347f6cf2d4d198e479df2 Mon Sep 17 00:00:00 2001
From: Vidya Sreekumar <vdy.sreekumar@gmail.com>
Date: Fri, 26 Sep 2025 12:55:47 -0500
Subject: [PATCH] Completed Backtracking-3

---
 Problem-1 | 77 +++++++++++++++++++++++++++++++++++++++++++++++++++++++
 Problem-2 | 45 ++++++++++++++++++++++++++++++++
 2 files changed, 122 insertions(+)
 create mode 100644 Problem-1
 create mode 100644 Problem-2

diff --git a/Problem-1 b/Problem-1
new file mode 100644
index 00000000..dd4c77bc
--- /dev/null
+++ b/Problem-1
@@ -0,0 +1,77 @@
+// Time Complexity: O(n * n!)
+// Space Complexity: O(n^2)
+
+// Place queens row by row recursively by checking if its safe to place
+// To check the safety of a position check the column up, left diagonal up and right diagonal up to see if a queen has been placed in those lines using a boolean matrix
+// Create the result list from the boolean matrix after placing all the queens
+
+class Solution {
+    List<List<String>> result;
+    public List<List<String>> solveNQueens(int n) {
+        this.result = new ArrayList<>();
+        boolean[][] grid = new boolean[n][n];
+        helper(grid, 0, n);
+        return result;
+    }
+
+    private void helper(boolean[][] grid, int row, int n) {
+        if(row == n) {
+            // Create result list from the boolean grid which contains the positions of the queens
+            List<String> list = new ArrayList<>();
+            for(int i = 0; i < n; i++) {
+                StringBuilder sb = new StringBuilder();
+                for(int j = 0; j < n; j++) {
+                    if(grid[i][j]) {
+                        sb.append("Q");
+                    }
+                    else {
+                        sb.append(".");
+                    }
+                }
+                list.add(sb.toString());
+            }
+            result.add(list);
+            return;
+        }
+
+        for(int j = 0; j < n; j++) {
+            // Check if a queen can placed at this position
+            if(isSafe(grid, row, j, n)) {
+                grid[row][j] = true;
+                helper(grid, row+1, n);
+                grid[row][j] = false;
+            }
+        }
+    }
+
+    private boolean isSafe(boolean[][] grid, int r, int c, int n) {
+        // check column up
+        int i = r;
+        int j = c;
+        while(i >= 0) {
+            if(grid[i][j])
+                return false;
+            i--;
+        }
+
+        // check left diagonal up
+        i = r;
+        while(i >= 0 && j >= 0) {
+            if(grid[i][j])
+                return false;
+            i--;
+            j--;
+        }
+
+        // check right diagonal up
+        i = r;
+        j = c;
+        while(i >= 0 && j < n) {
+            if(grid[i][j])
+                return false;
+            i--;
+            j++;
+        }
+        return true;
+    }
+}
\ No newline at end of file
diff --git a/Problem-2 b/Problem-2
new file mode 100644
index 00000000..4f36c558
--- /dev/null
+++ b/Problem-2
@@ -0,0 +1,45 @@
+// Time Complexity: O(m*n*4^l) , l->length of word
+// Space Complexity: O(l)
+
+// Traverse through the board, and do dfs from all the starting characters of the word on the board
+// mark a position on the board as visited if it matches with the current character in the word
+// if it matches all characters in the word return true, otherwise backtrack
+
+class Solution {
+    int[][] dir;
+    public boolean exist(char[][] board, String word) {
+        dir = new int[][]{{0,1}, {1,0}, {-1,0}, {0,-1}};
+        int m = board.length;
+        int n = board[0].length;
+
+        for(int i = 0 ; i < m; i++) {
+            for(int j = 0; j < n; j++) {
+                // If the first character matches do dfs on the remaining characters
+                if(board[i][j] == word.charAt(0)) {
+                    if(backtrack(board, word, i, j, 0))
+                        return true;
+                }
+            }
+        }
+        return false;
+    }
+
+    private boolean backtrack(char[][] board, String word, int i, int j, int idx) {
+        if(idx == word.length())
+            return true;
+        if(i < 0 || i >= board.length || j < 0 || j >= board[0].length || board[i][j] == '#' || board[i][j] != word.charAt(idx)) 
+            return false;
+
+        board[i][j] = '#'; // marking as visited
+        // check neighbours
+        for(int[] d : dir) {
+            int r = d[0] + i;
+            int c = d[1] + j;
+            if(backtrack(board, word, r, c, idx+1))
+                return true;
+        }
+        board[i][j] = word.charAt(idx); //backtrack
+        
+        return false;
+    }
+}
\ No newline at end of file