Update 0039.组合总和.md

problems/0039.组合总和.md

@@ -271,75 +271,101 @@ class Solution {
 
 ## Python
 
-**回溯**
+回溯（版本一）
 
 ```python
 class Solution:
-    def __init__(self):
-        self.path = []
-        self.paths = []
 
-    def combinationSum(self, candidates: List[int], target: int) -> List[List[int]]:
-        '''
-        因为本题没有组合数量限制，所以只要元素总和大于target就算结束
-        '''
-        self.path.clear()
-        self.paths.clear()
-        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[:]) # 因为是shallow copy，所以不能直接传入self.path
+    def backtracking(self, candidates, target, total, startIndex, path, result):
+        if total > target:
             return
-        if sum_ > target:
+        if total == target:
+            result.append(path[:])
             return
 
-        # 单层递归逻辑
-        for i in range(start_index, len(candidates)):
-            sum_ += candidates[i]
-            self.path.append(candidates[i])
-            self.backtracking(candidates, target, sum_, i)  # 因为无限制重复选取，所以不是i+1
-            sum_ -= candidates[i]   # 回溯
-            self.path.pop()        # 回溯
+        for i in range(startIndex, len(candidates)):
+            total += candidates[i]
+            path.append(candidates[i])
+            self.backtracking(candidates, target, total, i, path, result)  # 不用i+1了，表示可以重复读取当前的数
+            total -= candidates[i]
+            path.pop()
+
+    def combinationSum(self, candidates, target):
+        result = []
+        self.backtracking(candidates, target, 0, 0, [], result)
+        return result
+
 ```
 
-**剪枝回溯**
+回溯剪枝（版本一）
 
 ```python
 class Solution:
-    def __init__(self):
-        self.path = []
-        self.paths = []
 
-    def combinationSum(self, candidates: List[int], target: int) -> List[List[int]]:
-        '''
-        因为本题没有组合数量限制，所以只要元素总和大于target就算结束
-        '''
-        self.path.clear()
-        self.paths.clear()
-
-        # 为了剪枝需要提前进行排序
-        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[:]) # 因为是shallow copy，所以不能直接传入self.path
+    def backtracking(self, candidates, target, total, startIndex, path, result):
+        if total == target:
+            result.append(path[:])
             return
-        # 单层递归逻辑
-        # 如果本层 sum + condidates[i] > target，就提前结束遍历，剪枝
-        for i in range(start_index, len(candidates)):
-            if sum_ + candidates[i] > target:
-                return
-            sum_ += candidates[i]
-            self.path.append(candidates[i])
-            self.backtracking(candidates, target, sum_, i)  # 因为无限制重复选取，所以不是i-1
-            sum_ -= candidates[i]   # 回溯
-            self.path.pop()        # 回溯
+
+        for i in range(startIndex, len(candidates)):
+            if total + candidates[i] > target:
+                break
+            total += candidates[i]
+            path.append(candidates[i])
+            self.backtracking(candidates, target, total, i, path, result)
+            total -= candidates[i]
+            path.pop()
+
+    def combinationSum(self, candidates, target):
+        result = []
+        candidates.sort()  # 需要排序
+        self.backtracking(candidates, target, 0, 0, [], result)
+        return result
+
+```
+
+回溯（版本二）
+
+```python
+class Solution:
+    def combinationSum(self, candidates: List[int], target: int) -> List[List[int]]:
+        result =[]
+        self.backtracking(candidates, target, 0, [], result)
+        return result
+    def backtracking(self, candidates, target, startIndex, path, result):
+        if target == 0:
+            result.append(path[:])
+            return
+        if target < 0:
+            return
+        for i in range(startIndex, len(candidates)):
+            path.append(candidates[i])
+            self.backtracking(candidates, target - candidates[i], i, path, result)
+            path.pop()
+
+```
+
+回溯剪枝（版本二）
+
+```python
+class Solution:
+    def combinationSum(self, candidates: List[int], target: int) -> List[List[int]]:
+        result =[]
+        candidates.sort()
+        self.backtracking(candidates, target, 0, [], result)
+        return result
+    def backtracking(self, candidates, target, startIndex, path, result):
+        if target == 0:
+            result.append(path[:])
+            return
+
+        for i in range(startIndex, len(candidates)):
+            if target - candidates[i]  < 0:
+                break
+            path.append(candidates[i])
+            self.backtracking(candidates, target - candidates[i], i, path, result)
+            path.pop()
+
 ```
 
 ## Go