From 4547e60b71f441a05c63d8eef6bf5564373b3847 Mon Sep 17 00:00:00 2001
From: Hardik Prajapati <hprajapa@usc.edu>
Date: Fri, 26 Sep 2025 16:02:54 -0700
Subject: [PATCH] Backtracking2:All done

---
 palindrome partitioning.py | 46 +++++++++++++++++++++++++++++++++++
 subsets.py                 | 50 ++++++++++++++++++++++++++++++++++++++
 2 files changed, 96 insertions(+)
 create mode 100644 palindrome partitioning.py
 create mode 100644 subsets.py

diff --git a/palindrome partitioning.py b/palindrome partitioning.py
new file mode 100644
index 00000000..ee2978df
--- /dev/null
+++ b/palindrome partitioning.py	
@@ -0,0 +1,46 @@
+'''
+Solution : FOR loop based DFS with backtracking
+    - At each character in the string, we either partition at that character or not
+    - If this partitioned string is valid palindrome than we recurse to the next step
+      which is partitioning the rest of the string. 
+    - If we end up reaching end of string in the recursive call, then we have a valid
+      palindrome partitioning.
+Time Complexity: O(N*2^N), where N = length of string. 
+                 - At each character, we have choose/Not choose to partition.
+                 - for partitioned, we do palindrome check. 
+Space Complexity: O(N), depth of recursive stack. 
+'''
+
+class Solution:
+    def partition(self, s: str) -> List[List[str]]:
+        validPalindromePartitions  = [] # to store the answers
+
+        self.helper(s,0,[],validPalindromePartitions) # string, pivot, path, answer_list
+
+        return validPalindromePartitions
+    
+    def helper(self,s,pivot_index,path,validPalindromePartitions):
+        # base
+        if pivot_index==len(s): # new valid partitioned path found  
+            validPalindromePartitions.append(deepcopy(path))
+            return 
+
+        # logic
+        for i in range(pivot_index,len(s)):
+            partitioned_string = s[pivot_index:i+1] # partition string
+            if self.isPalindrome(partitioned_string): # check if pallindrome
+                path.append(partitioned_string) # action
+                self.helper(s,i+1,path,validPalindromePartitions)
+                path.pop() # backtrack
+    
+    def isPalindrome(self,string):
+        left = 0
+        right = len(string)-1
+
+        while left<right:
+            if string[left]!=string[right]: # palindrome breach
+                return False
+            left+=1
+            right-=1
+        
+        return True
\ No newline at end of file
diff --git a/subsets.py b/subsets.py
new file mode 100644
index 00000000..13f28b69
--- /dev/null
+++ b/subsets.py
@@ -0,0 +1,50 @@
+'''
+Solution 1: Choose/No choose based recursion with backtracking
+Time Complexity: O(2^N), N =len(nums)
+Space Complexity: O(N), recursive stack, height of tree. 
+'''
+class Solution:
+    def subsets(self, nums: List[int]) -> List[List[int]]:
+        subsets_list = []
+        self.helper(nums,0,[],subsets_list) #nums, current_index, current path, answer list
+
+        return subsets_list
+
+    def helper(self, nums, current_index, current_path, subsets_list):
+        # base
+        if current_index==len(nums): # captured the new subset
+            subsets_list.append(deepcopy(current_path))
+            return
+        
+        # logic
+        # no choose
+        self.helper(nums, current_index+1, current_path, subsets_list)
+
+        # choose
+        current_path.append(nums[current_index]) # action
+        self.helper(nums, current_index+1, current_path, subsets_list)
+        current_path.pop() # backtrack
+
+'''
+Solution 2: For loop based recursion with backtracking
+Time Complexity: O(2^N), N =len(nums)
+Space Complexity: O(N), recursive stack, height of tree. 
+'''
+class Solution:
+    def subsets(self, nums: List[int]) -> List[List[int]]:
+        subsets_list = []
+        self.helper(nums,0,[],subsets_list) #nums, pivot index, current path, answer list
+
+        return subsets_list
+
+    def helper(self, nums, pivot_index, current_path, subsets_list):
+        # base - not needed
+        
+        
+        
+        # logic
+        subsets_list.append(deepcopy(current_path))
+        for i in range(pivot_index,len(nums)):
+            current_path.append(nums[i]) # action
+            self.helper(nums, i+1, current_path, subsets_list)
+            current_path.pop() # backtrack