From fa9b37e461d3281578bab767efcdd47b82505d52 Mon Sep 17 00:00:00 2001
From: kalyan <kalyan.ng22@gmail.com>
Date: Thu, 6 Nov 2025 18:46:51 -0600
Subject: [PATCH] Backtracking-2 solutions

---
 PalindromePartitioning.java | 43 +++++++++++++++++++++++++++++++++++++
 Subsets.java                | 30 ++++++++++++++++++++++++++
 2 files changed, 73 insertions(+)
 create mode 100644 PalindromePartitioning.java
 create mode 100644 Subsets.java

diff --git a/PalindromePartitioning.java b/PalindromePartitioning.java
new file mode 100644
index 00000000..ba1c34c7
--- /dev/null
+++ b/PalindromePartitioning.java
@@ -0,0 +1,43 @@
+// Time Complexity : O(2^(n) * n) where n is the length of String s.
+// Space Complexity : O(n^2)
+// Did this code successfully run on Leetcode : Yes
+// Approach : I followed for loop recursion with backtracking to get the result. For each substring from pivot to i we each if it is a palindrome and then
+// proceed ahead.Once the pivot reaches the end of the string we add it to the result, backtrack it and continue the checks with the rest of the substring.
+
+
+class Solution {
+    List<List<String>> result;
+    public List<List<String>> partition(String s) {
+        this.result = new ArrayList<>();
+        helper(s, 0, new ArrayList<>());
+        return result;
+    }
+
+    private void helper(String s, int pivot, List<String> path){
+        if(pivot == s.length()){
+            result.add(new ArrayList<>(path));
+            return;
+        }
+
+        for(int i=pivot; i<s.length(); i++){
+            String subStr = s.substring(pivot, i+1);
+            if(isPalindrome(subStr)){ //check if it is palindrome
+                path.add(subStr);
+                helper(s, i+1, path);//recurse
+                path.remove(path.size() - 1);//backtracking
+            }
+        }
+    }
+
+    private boolean isPalindrome(String s){
+        int start = 0, end = s.length()-1;
+        while(start < end){
+            if(s.charAt(start) != s.charAt(end)){
+                return false;
+            }
+            start++;
+            end--;
+        }
+        return true;
+    }
+}
diff --git a/Subsets.java b/Subsets.java
new file mode 100644
index 00000000..06296ef0
--- /dev/null
+++ b/Subsets.java
@@ -0,0 +1,30 @@
+// Time Complexity : O(2^(n)) where n is the length of nums array.
+// Space Complexity : O(n)
+// Did this code successfully run on Leetcode : Yes
+// Approach : I followed 0/1 recursion with backtracking and while the base condition is met, before storing the result we store a deep
+// copy of it so that the rest of recursion happens without any issues. In no choose and choose condition, index needs to be increased as we dont need
+// duplicates in subsets. Once we find the result or we reach the end of the recursive function, we remove the last element in the path so that it can continue recursion.
+
+
+class Solution {
+    List<List<Integer>> result;
+    public List<List<Integer>> subsets(int[] nums) {
+        this.result = new ArrayList<>();
+        helper(nums, 0, new ArrayList<>());
+        return result;
+    }
+
+    private void helper(int[] nums, int index, List<Integer> path){
+        if(index == nums.length){
+            result.add(new ArrayList<>(path));//add deep copy to result
+            return;
+        }
+        //don't choose
+        helper(nums, index+1, path);
+
+        //choose
+        path.add(nums[index]);
+        helper(nums, index+1, path);//recurse
+        path.remove(path.size()-1); //backtrack
+    }
+}
\ No newline at end of file