From 4f75c81564f8919492b17c02abfa38b45bfb9345 Mon Sep 17 00:00:00 2001
From: michaeldonato <mmd1130@gmail.com>
Date: Mon, 27 Oct 2025 20:27:38 -0500
Subject: [PATCH] Backtracking-3 Completed

---
 exist.java        | 45 +++++++++++++++++++++++++++++++++
 solveNQueens.java | 63 +++++++++++++++++++++++++++++++++++++++++++++++
 2 files changed, 108 insertions(+)
 create mode 100644 exist.java
 create mode 100644 solveNQueens.java

diff --git a/exist.java b/exist.java
new file mode 100644
index 00000000..61d6ef23
--- /dev/null
+++ b/exist.java
@@ -0,0 +1,45 @@
+// Time Complexity : O(m * n * 4^L)
+// Space Complexity : O(L)
+// Did this code successfully run on Leetcode : Yes
+// Any problem you faced while coding this : None
+class Solution {
+    int[][] dirs;
+    int m,n;
+    public boolean exist(char[][] board, String word) {
+        this.dirs = new int[][]{{-1,0},{1,0},{0,1},{0,-1}};
+        this.m = board.length;
+        this.n = board[0].length;
+
+        for(int i=0; i<m; i++){
+            for(int j=0; j<n; j++){
+                if(dfs(board, i, j, word, 0)) return true;
+            }
+        }
+
+        return false;
+    }
+
+    private boolean dfs(char[][] board, int i, int j, String word, int idx){
+        if(idx == word.length()) return true;
+
+        if(i < 0 || j < 0 || i == m || j == n || board[i][j] == '#') return false;
+
+        if(board[i][j] != word.charAt(idx)) return false;
+
+        //action
+        board[i][j] = '#';
+
+        //recurse
+        for(int[] dir: dirs){
+            int r = dir[0] + i;
+            int c = dir[1] + j;
+
+            if(dfs(board, r, c, word, idx+1)) return true;
+        }
+
+        //backtrack
+        board[i][j] = word.charAt(idx);
+
+        return false;
+    }
+}
diff --git a/solveNQueens.java b/solveNQueens.java
new file mode 100644
index 00000000..4e71faa3
--- /dev/null
+++ b/solveNQueens.java
@@ -0,0 +1,63 @@
+// Time Complexity : O(n * n!)
+// Space Complexity : O(n^2)  + O(n)
+// Did this code successfully run on Leetcode : Yes
+// Any problem you faced while coding this : None
+class Solution {
+    List<List<String>> result;
+    public List<List<String>> solveNQueens(int n) {
+        this.result = new ArrayList<>();
+        boolean[][] board = new boolean[n][n];
+        helper(board, 0, n);
+        return result;
+    }
+
+    private void helper(boolean[][] board, int row, int n){
+        if(row == n){
+            List<String> list = new ArrayList<>();
+            for(int i=0; i<n; i++){
+                StringBuilder sb = new StringBuilder();
+                for(int j=0; j<n; j++){
+                    if(board[i][j]){
+                        sb.append("Q");
+                    }else{
+                        sb.append(".");
+                    }
+                }
+                list.add(sb.toString());
+            }
+
+            result.add(list);
+            return;
+        }
+
+        for(int j=0; j<n; j++){
+            if(isValid(board, row, j, n)){
+                board[row][j] = true;
+                helper(board, row+1, n);
+                board[row][j] = false;
+            }
+        }
+    }
+
+    private boolean isValid(boolean[][] board, int i, int j, int n){
+        int r = i, c = j;
+        while(r >=0){
+            if(board[r][c]) return false;
+            r--;
+        }
+
+        r = i; c = j;
+        while(r>=0 && c>=0){
+            if(board[r][c]) return false;
+            r--; c--;
+        }
+
+        r = i; c = j;
+        while(r>=0 && c < n){
+            if(board[r][c]) return false;
+            r--; c++;
+        }
+
+        return true;
+    }
+}