Update 0040.组合总和II.md

problems/0040.组合总和II.md

@@ -354,93 +354,92 @@ class Solution {
 ```
 
 ## Python 
-**回溯+巧妙去重(省去使用used**
+回溯
 ```python
 class Solution:
-    def __init__(self):
-        self.paths = []
-        self.path = []
 
-    def combinationSum2(self, candidates: List[int], target: int) -> List[List[int]]:
-        '''
-        类似于求三数之和，求四数之和，为了避免重复组合，需要提前进行数组排序
-        '''
-        self.paths.clear()
-        self.path.clear()
-        # 必须提前进行数组排序，避免重复
-        candidates.sort()
-        self.backtracking(candidates, target, 0, 0)
-        return self.paths
 
-    def backtracking(self, candidates: List[int], target: int, sum_: int, start_index: int) -> None:
-        # Base Case
-        if sum_ == target:
-            self.paths.append(self.path[:])
+    def backtracking(self, candidates, target, total, startIndex, path, result):
+        if total == target:
+            result.append(path[:])
             return
-        
-        # 单层递归逻辑
-        for i in range(start_index, len(candidates)):
-            # 剪枝，同39.组合总和
-            if sum_ + candidates[i] > target:
-                return
-            
-            # 跳过同一树层使用过的元素
-            if i > start_index and candidates[i] == candidates[i-1]:
+
+        for i in range(startIndex, len(candidates)):
+            if i > startIndex and candidates[i] == candidates[i - 1]:
                 continue
-            
-            sum_ += candidates[i]
-            self.path.append(candidates[i])
-            self.backtracking(candidates, target, sum_, i+1)
-            self.path.pop()             # 回溯，为了下一轮for loop
-            sum_ -= candidates[i]       # 回溯，为了下一轮for loop
+
+            if total + candidates[i] > target:
+                break
+
+            total += candidates[i]
+            path.append(candidates[i])
+            self.backtracking(candidates, target, total, i + 1, path, result)
+            total -= candidates[i]
+            path.pop()
+
+    def combinationSum2(self, candidates, target):
+        result = []
+        candidates.sort()
+        self.backtracking(candidates, target, 0, 0, [], result)
+        return result
+
 ```
-**回溯+去重（使用used）**
+回溯+去重（使用used）
 ```python
 class Solution:
-    def __init__(self):
-        self.paths = []
-        self.path = []
-        self.used = []
 
-    def combinationSum2(self, candidates: List[int], target: int) -> List[List[int]]:
-        '''
-        类似于求三数之和，求四数之和，为了避免重复组合，需要提前进行数组排序
-        本题需要使用used，用来标记区别同一树层的元素使用重复情况：注意区分递归纵向遍历遇到的重复元素，和for循环遇到的重复元素，这两者的区别
-        '''
-        self.paths.clear()
-        self.path.clear()
-        self.usage_list = [False] * len(candidates)
-        # 必须提前进行数组排序，避免重复
-        candidates.sort()
-        self.backtracking(candidates, target, 0, 0)
-        return self.paths
 
-    def backtracking(self, candidates: List[int], target: int, sum_: int, start_index: int) -> None:
-        # Base Case
-        if sum_ == target:
-            self.paths.append(self.path[:])
+    def backtracking(self, candidates, target, total, startIndex, used, path, result):
+        if total == target:
+            result.append(path[:])
             return
-        
-        # 单层递归逻辑
-        for i in range(start_index, len(candidates)):
-            # 剪枝，同39.组合总和
-            if sum_ + candidates[i] > target:
-                return
-            
-            # 检查同一树层是否出现曾经使用过的相同元素
-            # 若数组中前后元素值相同，但前者却未被使用(used == False)，说明是for loop中的同一树层的相同元素情况
-            if i > 0 and candidates[i] == candidates[i-1] and self.usage_list[i-1] == False:
+
+        for i in range(startIndex, len(candidates)):
+            # 对于相同的数字，只选择第一个未被使用的数字，跳过其他相同数字
+            if i > startIndex and candidates[i] == candidates[i - 1] and not used[i - 1]:
                 continue
 
-            sum_ += candidates[i]
-            self.path.append(candidates[i])
-            self.usage_list[i] = True
-            self.backtracking(candidates, target, sum_, i+1)
-            self.usage_list[i] = False  # 回溯，为了下一轮for loop
-            self.path.pop()             # 回溯，为了下一轮for loop
-            sum_ -= candidates[i]       # 回溯，为了下一轮for loop
-```
+            if total + candidates[i] > target:
+                break
 
+            total += candidates[i]
+            path.append(candidates[i])
+            used[i] = True
+            self.backtracking(candidates, target, total, i + 1, used, path, result)
+            used[i] = False
+            total -= candidates[i]
+            path.pop()
+
+    def combinationSum2(self, candidates, target):
+        used = [False] * len(candidates)
+        result = []
+        candidates.sort()
+        self.backtracking(candidates, target, 0, 0, used, [], result)
+        return result
+
+```
+回溯优化
+```python
+class Solution:
+    def combinationSum2(self, candidates: List[int], target: int) -> List[List[int]]:
+        candidates.sort()
+        results = []
+        self.combinationSumHelper(candidates, target, 0, [], results)
+        return results
+
+    def combinationSumHelper(self, candidates, target, index, path, results):
+        if target == 0:
+            results.append(path[:])
+            return
+        for i in range(index, len(candidates)):
+            if i > index and candidates[i] == candidates[i - 1]:
+                continue  
+            if candidates[i] > target:
+                break  
+            path.append(candidates[i])
+            self.combinationSumHelper(candidates, target - candidates[i], i + 1, path, results)
+            path.pop()
+```
 ## Go
 主要在于如何在回溯中去重