Backtracking 2

Sample.py

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+# Backtracking-2
+
+## Problem1 
+# Subsets (https://leetcode.com/problems/subsets/)
+
+# Solved Subsets using the classic choose/not-choose backtracking pattern:
+# At each index, make two recursive calls:
+# Not choose current element → skip it (idx + 1, path unchanged)
+# Choose current element → add to path, then recurse (idx + 1)
+# Base case: When idx == len(nums), add current path to results
+# Backtrack: Remove last added element after "choose" branch to restore state
+
+# Time Complexity: O(2^N) — generate all subsets
+# Space Complexity: O(N) — recursion depth + path storage
+# 💡 Key insight: This binary decision tree (include/exclude each element) naturally generates all 2^N subsets without duplicates. 
+# The same pattern works for any "generate all combinations" problem!
+
+class Solution:
+    def subsets(self, nums: List[int]) -> List[List[int]]:
+        self.res = []
+        self.helper(nums, 0, [])
+        return self.res
+
+    def helper(self, nums, idx, path):
+        # base
+        if idx == len(nums):
+            self.res.append(list(path))
+            return
+
+        # recursion
+        #dont choose
+        self.helper(nums, idx + 1, path)
+
+        # choose
+        path.append(nums[idx])
+        self.helper(nums, idx + 1, path)
+
+        # backtrack
+        path.pop()
+
+
+
+## Problem2
+
+# Palindrome Partitioning(https://leetcode.com/problems/palindrome-partitioning/)
+
+
+# Recursive partitioning: At each position pivot, try all possible substrings s[pivot:i+1]
+# Prune invalid paths: Only recurse if substring is a palindrome (checked via two-pointer method)
+# Build solution: Add valid palindromes to path, recurse on remaining string (i+1), then backtrack
+# Base case: When pivot == len(s), add current path to results
+
+# Time Complexity: O(N * 2^N) — worst case checks all partitions, each palindrome check is O(N)
+# Space Complexity: O(N) — recursion depth + path storage
+
+class Solution:
+    def partition(self, s: str) -> List[List[str]]:
+        self.res = []
+        self.helper(0,s,[])
+        return self.res
+
+    def isPalindrome(self,s):
+        if len(s) <= 1:
+            return True
+        i = 0
+        j = len(s)-1
+        while i < j:
+            if s[i] != s[j]:
+                return False
+            i += 1
+            j -= 1
+        return True
+
+    def helper(self,pivot,s,path):
+        if pivot == len(s):
+            self.res.append(list(path))
+            return
+
+        for i in range(pivot,len(s)):
+            sub = s[pivot:i+1]
+            if self.isPalindrome(sub):
+                path.append(sub)
+                self.helper(i+1, s, path)
+                path.pop()
+
+
+
+
+
+
+
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