From 3a992b1de1ba552163d356655f1f07069825fc5e Mon Sep 17 00:00:00 2001
From: PrasiddhShah <prasiddhshah.18@gmail.com>
Date: Thu, 6 Nov 2025 12:54:23 -0800
Subject: [PATCH] Backtracking - 2 Completed

---
 problem1.java | 40 ++++++++++++++++++++++++++++++++
 program2.java | 64 +++++++++++++++++++++++++++++++++++++++++++++++++++
 2 files changed, 104 insertions(+)
 create mode 100644 problem1.java
 create mode 100644 program2.java

diff --git a/problem1.java b/problem1.java
new file mode 100644
index 00000000..faf53444
--- /dev/null
+++ b/problem1.java
@@ -0,0 +1,40 @@
+// Time Complexity : O(2^n)
+// Space Complexity :O(n)
+// Did this code successfully run on Leetcode : yes
+// Any problem you faced while coding this :yes
+
+/*
+ * Approach
+ * here are we using recursion to solve the problem,
+ * basically at each step we have to choose between pick or not pick a number
+ * for this we are using recurion
+ * 
+ * we are going to use the for loop based recursion and we are using backtrack clean up path
+ * and we will make a deepcopy of the path when pointer it to the result
+ * so that we avoid return null result. 
+ */
+class Solution {
+    public List<List<Integer>> subsets(int[] nums) {
+        List<List<Integer>> result = new ArrayList<>();
+        helper(nums, 0, new ArrayList<>(), result);
+        return result;
+    }
+
+    private void helper(int[] nums, int pivot, List<Integer> path, List<List<Integer>> result) {
+        // base
+        if (pivot > nums.length) {
+            return;
+        }
+
+        // logic
+        result.add(new ArrayList<>(path));
+        for (int i = pivot; i < nums.length; i++) {
+            path.add(nums[i]);
+            helper(nums, i + 1, path, result);
+
+            path.remove(path.size() - 1);
+
+        }
+
+    }
+}
\ No newline at end of file
diff --git a/program2.java b/program2.java
new file mode 100644
index 00000000..f7d17384
--- /dev/null
+++ b/program2.java
@@ -0,0 +1,64 @@
+// Time Complexity : O(2^n)
+// Space Complexity :O(n)
+// Did this code successfully run on Leetcode : yes
+// Any problem you faced while coding this :yes
+
+/*
+ * Approach
+ * here are we using recursion to solve the problem,
+ * basically at each step we have to choose between pick or not pick a number
+ * for this we are using recurion
+ * 
+ * we are going to use the for loop based recursion 
+ * in each recursive call we start a new for loop from pivot till s len
+ * create a new sub string from pivot to i+1
+ * do the palindrome check on the string if true
+ * add to path make the recursive call again with i+1
+ * finally backtrack to keep the path update for the cur level
+ * 
+ * 
+ * for the palindrome check
+ * we simply 
+ * loop from both ends of the string to see if the are equal of not
+ * 
+ */
+class Solution {
+    public List<List<String>> partition(String s) {
+        List<List<String>> result = new ArrayList<>();
+        helper(s, 0, new ArrayList<>(), result);
+        return result;
+    }
+
+    private void helper(String s, int pivot, List<String> path, List<List<String>> result) {
+        // base
+        if (pivot == s.length()) {
+            result.add(new ArrayList<>(path));
+            return;
+        }
+        // logic
+        for (int i = pivot; i < s.length(); i++) {
+
+            String cur = s.substring(pivot, i + 1);
+            if (isPalindrome(cur)) {
+                // add
+                path.add(cur);
+
+                // recurse
+                helper(s, i + 1, path, result);
+
+                // backtrack
+                path.remove(path.size() - 1);
+            }
+        }
+    }
+
+    private boolean isPalindrome(String s) {
+        int i = 0;
+        int j = s.length() - 1;
+        while (i <= j) {
+            if (s.charAt(i++) != s.charAt(j--))
+                return false;
+        }
+        return true;
+    }
+}
\ No newline at end of file