From c9298d3b7866d95d6dadb0ec05ff97692f26c7bf Mon Sep 17 00:00:00 2001
From: Manisha Rana <manisha1195@gmail.com>
Date: Sun, 1 Feb 2026 23:40:44 -0500
Subject: [PATCH] Backtracking-2 Done

---
 PalindromePartition.java | 47 +++++++++++++++++++++++++++++++++++++++
 Subsets.java             | 48 ++++++++++++++++++++++++++++++++++++++++
 2 files changed, 95 insertions(+)
 create mode 100644 PalindromePartition.java
 create mode 100644 Subsets.java

diff --git a/PalindromePartition.java b/PalindromePartition.java
new file mode 100644
index 00000000..8865c284
--- /dev/null
+++ b/PalindromePartition.java
@@ -0,0 +1,47 @@
+/*
+Time Complexity : O(L.2^L). L is the length of the input string
+Space Complexity : O(L), L characters in the recursion stack
+Did this code successfully run on Leetcode : yes
+Any problem you faced while coding this : No
+Approach :
+
+We need to partition the string, we can do that by creating substring between 2 indices(pivot and index).
+We need to check if all the substrings is valid palindrome, if yes, add the substrings to a result array.
+
+*/
+import java.util.ArrayList;
+import java.util.List;
+
+public class PalindromePartition {
+
+    public List<List<String>> partition(String s) {
+        List<List<String>> result = new ArrayList<>();
+        partitionRecursion(s, result, new ArrayList<>(), 0);
+        return result;
+    }
+
+    private void partitionRecursion(String s, List<List<String>> result, List<String> path, int pivot) {
+        if(pivot == s.length()){
+            result.add(new ArrayList<>(path));
+            return;
+        }
+
+        for (int i = pivot; i < s.length(); i++) {
+            String subString = s.substring(pivot, i+1);
+            if(isPalindrome(subString)){
+                path.add(subString);
+                partitionRecursion(s, result, path, i+1);
+                // backtrack
+                path.remove(path.size()-1);
+            }
+        }
+    }
+
+    boolean isPalindrome(String s){
+        int len = s.length();
+        for (int i = 0; i < len / 2; i++) {
+            if(s.charAt(i) != s.charAt(len-1-i)) return false;
+        }
+        return true;
+    }
+}
diff --git a/Subsets.java b/Subsets.java
new file mode 100644
index 00000000..98448a7b
--- /dev/null
+++ b/Subsets.java
@@ -0,0 +1,48 @@
+/*
+Time Complexity : O(2^N), nums array size
+Space Complexity : O(N), in the recursion stack
+Did this code successfully run on Leetcode : Yes
+Any problem you faced while coding this : No
+Approach :
+We need to find all combinations of the numbers in the input array. To find combination, we can either do choose and not choose
+recursion, 0/1 recursion or for loop based recursion. In either of the recursion, we need to maintain a path, that would store the current
+combination, once we are done visiting a number we can remove it. As in, we need to back track the last value added to the path.
+This is because we are using same path object to create all paths, if we want to avoid backtracking, we need to create a new array
+for each path. As this is not space efficient, we rather choose to back track.
+*/
+import java.util.ArrayList;
+import java.util.List;
+
+public class Subsets {
+    public List<List<Integer>> subsets(int[] nums) {
+        List<List<Integer>> result = new ArrayList<>();
+        getSubsets(nums, 0,new ArrayList<>(), result);
+       // getSubsets01Recursion(nums, 0, new ArrayList<>(), result);
+        return result;
+    }
+
+    private void getSubsets01Recursion(int[] nums, int index, List<Integer> path, List<List<Integer>> result) {
+        if(index == nums.length){
+            result.add(new ArrayList<>(path));
+            return;
+        }
+
+        path.add(nums[index]);
+        getSubsets01Recursion(nums, index+1, path, result);
+        path.remove(path.size()-1);
+
+        getSubsets01Recursion(nums, index+1, path, result);
+    }
+
+    // Time Complexity : O(N * 2^N),  Extra O(N) as we are creating deep copy of path and in worst case, path can have N values
+    // Space Complexity : O(N)
+    private void getSubsets(int[] nums, int pivot, List<Integer> path, List<List<Integer>> result) {
+        result.add(new ArrayList<>(path));
+
+        for (int i = pivot; i < nums.length; i++){
+            path.add(nums[i]);
+            getSubsets(nums, i+1, path, result);
+            path.remove(path.size()-1);
+        }
+    }
+}