From 6124ac7a5a3553720f0b08e5726915548d650687 Mon Sep 17 00:00:00 2001
From: sainathek <erukullasainath@gmail.com>
Date: Thu, 26 Mar 2026 22:23:36 -0400
Subject: [PATCH] Done Backtracking-3

---
 problem1.java |  81 ++++++++++++++++++++++++++++++++++++++
 problem2.java | 107 ++++++++++++++++++++++++++++++++++++++++++++++++++
 2 files changed, 188 insertions(+)
 create mode 100644 problem1.java
 create mode 100644 problem2.java

diff --git a/problem1.java b/problem1.java
new file mode 100644
index 00000000..531e0edb
--- /dev/null
+++ b/problem1.java
@@ -0,0 +1,81 @@
+    /**
+    Time Complexity : O(M * N * 4^L)
+    Explanation:
+    - We start DFS from each cell → M * N
+    - For each step, we explore up to 4 directions
+    - Depth of recursion = length of word (L)
+    So worst case: O(M * N * 4^L)
+
+    Space Complexity : O(L)
+    Explanation:
+    Recursion depth can go up to length of the word.
+
+    Did this code successfully run on LeetCode : Yes
+
+    Any problem you faced while coding this :
+    Initially forgot to mark visited cells, which caused revisiting
+    the same cell and incorrect paths.
+    Fixed it by marking the cell as '#' during recursion and restoring
+    it after backtracking.
+    Also needed to carefully handle boundary conditions and base case
+    when the entire word is matched.
+    */
+
+    class Solution {
+
+
+        public boolean exist(char[][] board, String word) {
+    
+            int m = board.length;
+            int n = board[0].length;
+    
+            int[][] adj = {{1,0}, {-1,0}, {0,1}, {0,-1}};
+    
+            // Try starting from every cell
+            for (int i = 0; i < m; i++) {
+                for (int j = 0; j < n; j++) {
+    
+                    if (board[i][j] == word.charAt(0)) {
+                        if (helper(board, i, j, adj, word, 0, m, n)) {
+                            return true;
+                        }
+                    }
+                }
+            }
+    
+            return false;
+        }
+    
+        private boolean helper(char[][] board, int r, int c, int[][] adj,
+                               String word, int idx, int m, int n) {
+    
+            // Base case: matched entire word
+            if (idx == word.length()) {
+                return true;
+            }
+    
+            // Boundary + mismatch check
+            if (r < 0 || c < 0 || r >= m || c >= n || board[r][c] != word.charAt(idx)) {
+                return false;
+            }
+    
+            // Mark visited
+            char temp = board[r][c];
+            board[r][c] = '#';
+    
+            // Explore all 4 directions
+            for (int[] dir : adj) {
+                int nr = r + dir[0];
+                int nc = c + dir[1];
+    
+                if (helper(board, nr, nc, adj, word, idx + 1, m, n)) {
+                    return true;
+                }
+            }
+    
+            // Backtrack
+            board[r][c] = temp;
+    
+            return false;
+        }
+    }
\ No newline at end of file
diff --git a/problem2.java b/problem2.java
new file mode 100644
index 00000000..f294e26d
--- /dev/null
+++ b/problem2.java
@@ -0,0 +1,107 @@
+    /**
+    Time Complexity : O(N!)
+    Explanation:
+    We try placing a queen in each column for every row.
+    In worst case, number of configurations grows factorially.
+    For each placement, we check safety in O(N).
+
+    Space Complexity : O(N^2)
+    Explanation:
+    Board takes O(N^2) space and recursion stack goes up to N.
+
+    Did this code successfully run on LeetCode : Yes
+
+    Any problem you faced while coding this :
+    Initially struggled with validating safe positions for queens.
+    Fixed it by checking:
+        1) Same column (upward)
+        2) Left diagonal
+        3) Right diagonal
+    Also needed to carefully backtrack (place → recurse → remove)
+    to explore all valid configurations.
+    */
+    class Solution {
+
+
+
+        List<List<String>> result;
+    
+        public List<List<String>> solveNQueens(int n) {
+    
+            this.result = new ArrayList<>();
+            boolean[][] board = new boolean[n][n];
+    
+            helper(n, 0, board);
+            return result;
+        }
+    
+        private void helper(int n, int r, boolean[][] board) {
+    
+            // Base case: all queens placed
+            if (r == n) {
+    
+                List<String> li = new ArrayList<>();
+    
+                for (int i = 0; i < n; i++) {
+                    StringBuilder row = new StringBuilder();
+    
+                    for (int j = 0; j < n; j++) {
+                        if (board[i][j]) row.append('Q');
+                        else row.append('.');
+                    }
+    
+                    li.add(row.toString());
+                }
+    
+                result.add(li);
+                return;
+            }
+    
+            // Try placing queen in each column
+            for (int c = 0; c < n; c++) {
+    
+                if (isSafeToPlace(n, r, c, board)) {
+    
+                    board[r][c] = true;
+    
+                    helper(n, r + 1, board);
+    
+                    // Backtrack
+                    board[r][c] = false;
+                }
+            }
+        }
+    
+        private boolean isSafeToPlace(int n, int i, int j, boolean[][] board) {
+    
+            int r, c;
+    
+            // Check column (up)
+            r = i;
+            c = j;
+            while (r >= 0) {
+                if (board[r][c]) return false;
+                r--;
+            }
+    
+            // Check left diagonal
+            r = i;
+            c = j;
+            while (r >= 0 && c >= 0) {
+                if (board[r][c]) return false;
+                r--;
+                c--;
+            }
+    
+            // Check right diagonal
+            r = i;
+            c = j;
+            while (r >= 0 && c < n) {
+                if (board[r][c]) return false;
+                r--;
+                c++;
+            }
+    
+            return true;
+        }
+    }
\ No newline at end of file