From bfd1d5c3df87567eec0acd8dd42dd621545d4efe Mon Sep 17 00:00:00 2001
From: spencerkrebs <krebsspencer@gmail.com>
Date: Sat, 16 May 2026 16:01:03 -0400
Subject: [PATCH] a

---
 partition.py | 62 ++++++++++++++++++++++++++++++++++++++++++++++++++++
 subsets.py   | 35 +++++++++++++++++++++++++++++
 2 files changed, 97 insertions(+)
 create mode 100644 partition.py
 create mode 100644 subsets.py

diff --git a/partition.py b/partition.py
new file mode 100644
index 00000000..df3d554b
--- /dev/null
+++ b/partition.py
@@ -0,0 +1,62 @@
+# Time: O(n*2^n) - at every index the algorithm makes a binary choice (choose or no choose) - 2^n leaf nodes
+# path + [nums[idx]] copies entire list into new list (n)
+
+# Space: O(n^2) because we create list copies at each recursive call, keep track of separate path lists
+
+class Solution:
+    def subsets(self, nums: List[int]) -> List[List[int]]:
+        self.result = []
+
+        def helper(idx,path):
+            if idx == len(nums):
+                self.result.append(path)
+                return
+
+            # no choose
+            helper(idx+1,path)
+
+            # choose
+            # + creates a brand new path, meaning left and right branches of tree look at diff spots in memory
+            helper(idx+1,path+[nums[idx]])
+
+        helper(0,[])
+        return self.result 
+
+
+# Time: O(n*2^n) - at every index the algorithm makes a binary choice (choose or no choose) - 2^n leaf nodes
+# path + [nums[idx]] copies entire list into new list (n)
+# Space: O(n) with backtrack
+class Solution:
+    def subsets(self, nums: List[int]) -> List[List[int]]:
+        self.result = []
+        path =[]
+        def helper(idx):
+            if idx == len(nums):
+                self.result.append(path.copy())
+                return
+
+            # no choose
+            helper(idx+1)
+            # choose
+            path.append(nums[idx])
+            helper(idx+1)
+            # backtrack
+            path.pop()
+
+        helper(0)
+        return self.result 
+
+# basic loop solution
+# Time: O(n*2^n)
+# space: O(n)
+class Solution:
+    def subsets(self, nums: List[int]) -> List[List[int]]:
+        result=[[]]
+        for num in nums:
+            size = len(result)
+            for j in range(size):
+                temp = result[j][:]
+                temp.append(num)
+                result.append(temp)
+
+        return result 
\ No newline at end of file
diff --git a/subsets.py b/subsets.py
new file mode 100644
index 00000000..e98290d6
--- /dev/null
+++ b/subsets.py
@@ -0,0 +1,35 @@
+
+# for loop based recursion
+class Solution:
+    def partition(self, s: str) -> List[List[str]]:
+        self.result = []
+
+        def helper(s,pivot,path):
+            if pivot == len(s):
+                self.result.append(list(path))
+                return
+
+            for i in range(pivot,len(s)):
+                # we keep track of substring between pivot and i
+                # whereas 0,1 recursion (without pivot) - for this problem we need 2 indices - so use for loop based recursion
+                subStr = s[pivot:i+1]
+                if isPalindrome(subStr):
+                    # action 
+                    path.append(subStr)
+                    # recurse
+                    helper(s,i+1,path)
+                    # backtrack
+                    path.pop()
+
+        def isPalindrome(s):
+            i = 0
+            j = len(s)-1
+            while i <= j:
+                if s[i] != s[j]:
+                    return False 
+                i+=1
+                j-=1
+            return True
+        
+        helper(s,0,[])
+        return self.result
\ No newline at end of file