Create Tree-DynamicSegmentTree.py

Templates/07.Tree/Tree-DynamicSegmentTree.py

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+# 线段树的节点类
+class TreeNode:
+    def __init__(self, left=-1, right=-1, val=0):
+        self.left = left                            # 区间左边界
+        self.right = right                          # 区间右边界
+        self.mid = left + (right - left) // 2
+        self.leftNode = None                        # 区间左节点
+        self.rightNode = None                       # 区间右节点
+        self.val = val                              # 节点值（区间值）
+        self.lazy_tag = None                        # 区间问题的延迟更新标记
+
+
+# 线段树类
+class SegmentTree:
+    def __init__(self, function):
+        self.tree = TreeNode(0, int(1e9))
+        self.function = function                    # function 是一个函数，左右区间的聚合方法
+
+    # 向上更新 node 节点区间值，节点的区间值等于该节点左右子节点元素值的聚合计算结果
+    def __pushup(self, node):
+        leftNode = node.leftNode
+        rightNode = node.rightNode
+        if leftNode and rightNode:
+            node.val = self.function(leftNode.val, rightNode.val)
+
+    # 单点更新，将 nums[i] 更改为 val
+    def update_point(self, i, val):
+        self.__update_point(i, val, self.tree)
+
+    # 单点更新，将 nums[i] 更改为 val。node 节点的区间为 [node.left, node.right]
+    def __update_point(self, i, val, node):
+        if node.left == node.right:
+            node.val = val                          # 叶子节点，节点值修改为 val
+            return
+
+        if i <= node.mid:                           # 在左子树中更新节点值
+            if not node.leftNode:
+                node.leftNode = TreeNode(node.left, node.mid)
+            self.__update_point(i, val, node.leftNode)
+        else:                                       # 在右子树中更新节点值
+            if not node.rightNode:
+                node.rightNode = TreeNode(node.mid + 1, node.right)
+            self.__update_point(i, val, node.rightNode)
+        self.__pushup(node)                         # 向上更新节点的区间值
+
+    # 区间查询，查询区间为 [q_left, q_right] 的区间值
+    def query_interval(self, q_left, q_right):
+        return self.__query_interval(q_left, q_right, self.tree)
+
+    # 区间查询，在线段树的 [left, right] 区间范围中搜索区间为 [q_left, q_right] 的区间值
+    def __query_interval(self, q_left, q_right, node):
+        if node.left >= q_left and node.right <= q_right:   # 节点所在区间被 [q_left, q_right] 所覆盖
+            return node.val                         # 直接返回节点值
+        if node.right < q_left or node.left > q_right:  # 节点所在区间与 [q_left, q_right] 无关
+            return 0
+
+        self.__pushdown(node)                       # 向下更新节点所在区间的左右子节点的值和懒惰标记
+
+        res_left = 0                                # 左子树查询结果
+        res_right = 0                               # 右子树查询结果
+        if q_left <= node.mid:                      # 在左子树中查询
+            if not node.leftNode:
+                node.leftNode = TreeNode(node.left, node.mid)
+            res_left = self.__query_interval(q_left, q_right, node.leftNode)
+        if q_right > node.mid:                      # 在右子树中查询
+            if not node.rightNode:
+                node.rightNode = TreeNode(node.mid + 1, node.right)
+            res_right = self.__query_interval(q_left, q_right, node.rightNode)
+        return self.function(res_left, res_right)   # 返回左右子树元素值的聚合计算结果
+
+    # 区间更新，将区间为 [q_left, q_right] 上的元素值修改为 val
+    def update_interval(self, q_left, q_right, val):
+        self.__update_interval(q_left, q_right, val, self.tree)
+
+    # 区间更新
+    def __update_interval(self, q_left, q_right, val, node):
+        if node.left >= q_left and node.right <= q_right:  # 节点所在区间被 [q_left, q_right] 所覆盖
+            if node.lazy_tag:
+                node.lazy_tag += val                # 将当前节点的延迟标记增加 val
+            else:
+                node.lazy_tag = val                 # 将当前节点的延迟标记增加 val
+            interval_size = (node.right - node.left + 1)    # 当前节点所在区间大小
+            node.val += val * interval_size         # 当前节点所在区间每个元素值增加 val
+            return
+        if node.right < q_left or node.left > q_right:  # 节点所在区间与 [q_left, q_right] 无关
+            return 0
+
+        self.__pushdown(node)                       # 向下更新节点所在区间的左右子节点的值和懒惰标记
+
+        if q_left <= node.mid:                      # 在左子树中更新区间值
+            if not node.leftNode:
+                node.leftNode = TreeNode(node.left, node.mid)
+            self.__update_interval(q_left, q_right, val, node.leftNode)
+        if q_right > node.mid:                      # 在右子树中更新区间值
+            if not node.rightNode:
+                node.rightNode = TreeNode(node.mid + 1, node.right)
+            self.__update_interval(q_left, q_right, val, node.rightNode)
+
+        self.__pushup(node)
+
+    # 向下更新 node 节点所在区间的左右子节点的值和懒惰标记
+    def __pushdown(self, node):
+        lazy_tag = node.lazy_tag
+        if not node.lazy_tag:
+            return
+
+        if not node.leftNode:
+            node.leftNode = TreeNode(node.left, node.mid)
+        if not node.rightNode:
+            node.rightNode = TreeNode(node.mid + 1, node.right)
+
+        if node.leftNode.lazy_tag:
+            node.leftNode.lazy_tag += lazy_tag      # 更新左子节点懒惰标记
+        else:
+            node.leftNode.lazy_tag = lazy_tag       # 更新左子节点懒惰标记
+        left_size = (node.leftNode.right - node.leftNode.left + 1)
+        node.leftNode.val += lazy_tag * left_size   # 左子节点每个元素值增加 lazy_tag
+
+        if node.rightNode.lazy_tag:
+            node.rightNode.lazy_tag += lazy_tag     # 更新右子节点懒惰标记
+        else:
+            node.rightNode.lazy_tag = lazy_tag      # 更新右子节点懒惰标记
+        right_size = (node.rightNode.right - node.rightNode.left + 1)
+        node.rightNode.val += lazy_tag * right_size # 右子节点每个元素值增加 lazy_tag
+
+        node.lazy_tag = None                        # 更新当前节点的懒惰标记
+
+    def get_nums(self, length):
+        nums = [0 for _ in range(length)]
+        for i in range(length):
+            nums[i] = self.query_interval(i, i)
+        return nums