Update 0039.组合总和.md

补充python代码和注释

problems/0039.组合总和.md

@@ -264,25 +264,73 @@ class Solution {
 }
 ```
 
-## Python
+## Python  
+**回溯**
 ```python3
 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
+            return
+        if sum_ > target:
+            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
+```
+**剪枝回溯**
+```python3
+class Solution:
+    def __init__(self):
+        self.path = []
+        self.paths = []
+
     def combinationSum(self, candidates: List[int], target: int) -> List[List[int]]:
-        res = []
-        path = []
-        def backtrack(candidates,target,sum,startIndex):
-            if sum > target: return 
-            if sum == target: return res.append(path[:])
-            for i in range(startIndex,len(candidates)):
-                if sum + candidates[i] >target: return  #如果 sum + candidates[i] > target 就终止遍历
-                sum += candidates[i] 
-                path.append(candidates[i])
-                backtrack(candidates,target,sum,i)  #startIndex = i:表示可以重复读取当前的数
-                sum -= candidates[i]  #回溯
-                path.pop()  #回溯
-        candidates = sorted(candidates)  #需要排序
-        backtrack(candidates,target,0,0)
-        return res
+        '''
+        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
+            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
 ```
 
 ## Go