Completed Backtracking-1

combination_sum.py

@@ -0,0 +1,18 @@
+# Time Complexity: exponential
+# Space Complexity: O(T/M)
+class Solution:
+    def combinationSum(self, candidates: list[int], target: int) -> list[list[int]]:
+        result = []
+        self.combinationSumHelper([], 0, result, 0, target, candidates)
+        return result
+
+    def combinationSumHelper(self, current: list[int], start: int, result: list[list[int]], sum_val: int, target: int, candidates: list[int]):
+        if sum_val > target:
+            return
+        if sum_val == target:
+            result.append(current[:])
+            return
+        for i in range(start, len(candidates)):
+            current.append(candidates[i])
+            self.combinationSumHelper(current, i, result, sum_val + candidates[i], target, candidates)
+            current.pop()

expression.py

@@ -0,0 +1,35 @@
+# Time Complexity: O(3^N * N)
+# Space Complexity: O(N)
+
+class Solution:
+    def addOperators(self, num: str, target: int) -> list[str]:
+        result = []
+        num_length = len(num)
+
+        def helper(start: int, expression: list[str], current_value: int, previous_value: int):
+            # Base case: if we've processed the entire number
+            if start >= num_length:
+                if current_value == target:
+                    result.append("".join(expression))
+                return
+
+            # Handle the first number
+            if start == 0:
+                if num[start] == '0':
+                    helper(start + 1, expression + ['0'], 0, 0)
+                else:
+                    for i in range(start, num_length):
+                        helper(i + 1, expression + [num[start:i + 1]], int(num[start:i + 1]), int(num[start:i + 1]))
+
+            # Handle subsequent numbers
+            else:
+                if num[start] == '0':
+                    helper(start + 1, expression + ['+'] + ['0'], current_value, 0)
+                    helper(start + 1, expression + ['-'] + ['0'], current_value, 0)
+                    helper(start + 1, expression + ['*'] + ['0'], current_value - previous_value, 0)
+                else:
+                    for i in range(start, num_length):
+                        current_num = int(num[start:i + 1])
+                        helper(i + 1, expression + ['+'] + [num[start:i + 1]], current_value + current_num, current_num)
+                        helper(i + 1, expression + ['-'] + [num[start:i + 1]], current_value - current_num, -current_num)
+                        helper(i + 1, expression + ['*'] + [num[start:i + 1]], current_value - previous_value + previous_value * current_num, previous_value