From 000f31297891be351e52a22c12d8d9d3871b39a1 Mon Sep 17 00:00:00 2001
From: praxpk <23168694+praxpk@users.noreply.github.com>
Date: Mon, 16 Feb 2026 01:43:08 -0800
Subject: [PATCH] Backtracking-1

---
 combination_sum.py | 28 ++++++++++++++++++++++++++++
 1 file changed, 28 insertions(+)
 create mode 100644 combination_sum.py

diff --git a/combination_sum.py b/combination_sum.py
new file mode 100644
index 00000000..0ffed707
--- /dev/null
+++ b/combination_sum.py
@@ -0,0 +1,28 @@
+"""
+time complexity: O(n*2^n) where n is the number of candidates. In the worst case, we explore all possible combinations of candidates, which can lead to 2^n combinations. Additionally, for each valid combination, we may need to copy the current list to the result, which takes O(n) time.
+space complexity: O(n) in the worst case when the recursion depth is equal to the number of candidates. 
+We use a backtracking approach to explore all possible combinations of candidates. 
+We maintain a current list of numbers and a current sum. We start from the first candidate and recursively explore two possibilities: including the current candidate in the combination or     
+skipping it. If the current sum exceeds the target, we backtrack and return. If the current sum equals the target, we add a copy of the current list to the result.
+"""
+
+class Solution:
+    def combinationSum(self, candidates: List[int], target: int) -> List[List[int]]:
+        self.result = []
+        self.target = target
+        self.candidates = candidates
+        self.helper([], 0, 0)
+        return self.result
+    
+    def helper(self, curr_list, curr_sum, index):
+        if index >= len(self.candidates) or curr_sum>self.target:
+            return
+        if curr_sum == self.target:
+            self.result.append(copy.deepcopy(curr_list))
+        for i in range(index, len(self.candidates)):
+            curr_list.append(self.candidates[i])
+            val = curr_sum + self.candidates[i]
+            self.helper(curr_list, val, i)
+            curr_list.pop()
+
+        
\ No newline at end of file