How to implement lazy segment tree lazy segment tree algorithm in python

Introduction to lazy segment tree lazy segment tree algorithm

The Lazy Segment Tree algorithm is an efficient data structure used to handle interval query and interval update operations.

It improves the efficiency of the algorithm by introducing latency update technology (Lazy Propagation) to perform actual update operations when needed.

Here are some key points about the Lazy Segment Tree algorithm:

Basic concepts

Data structure: Lazy Segment Tree is a tree-shaped data structure that represents an array as a binary tree, and each node represents a continuous interval in the array. The root node of a tree represents the entire array, while the leaf node represents a single element in the array.
Interval query: Lazy Segment Tree can quickly process interval query operations, such as summing, maximum value, minimum value, etc.
Interval update: When it is necessary to update all elements in an interval in an array, the Lazy Segment Tree temporarily stores the update operation in the node (i.e., lazy mark), and performs the actual update operation when querying or updating to a specific interval.

How it works

Creation: Start from the root node, recursively build left and right subtrees until the leaf node. During the construction process, the value of the parent node is calculated based on the value of the child node.
Query: Starting from the root node, based on the query interval and the interval position of the current node, decide whether to continue querying the left subtree and right subtree, or directly return the value of the current node. If the query interval is completely contained in the interval of a node and the node has lazy marks, the lazy marks will be processed first and then the query will be conducted.
Update: When it is necessary to update elements within a certain interval, start from the root node, find all nodes containing the interval, and store the update operation in these nodes as lazy tags. The actual update operation is executed when querying or further updates to a specific interval.

advantage

Efficiency: Through delayed update operations, Lazy Segment Tree can perform actual updates when needed, thereby improving the efficiency of the algorithm.
High spatial efficiency: The space complexity of the Lazy Segment Tree is O(n), where n is the size of the array.

Things to note

When implementing Lazy Segment Tree, the pass and update of lazy tags need to be carefully handled to ensure the accuracy of query results.
The introduction of lazy tags may increase the complexity of the code and therefore requires careful design and implementation.

in conclusion:

Lazy Segment Tree is a powerful data structure that can efficiently handle interval query and interval update operations.

It significantly improves the efficiency of the algorithm by introducing delay update technology. However, when implementing, you need to pay attention to the passing and update of lazy tags to ensure the correctness and efficiency of the algorithm.

lazy segment tree lazy segment tree algorithm python implementation example

Here is an example of a lazy segment tree algorithm implemented by python:

class LazySegmentTree:
    def __init__(self, arr):
         = arr
         = [0] * (4 * len(arr))
         = [0] * (4 * len(arr))
        self.build_tree(1, 0, len(arr) - 1)

    def build_tree(self, node, start, end):
        if start == end:
            [node] = [start]
        else:
            mid = (start + end) // 2
            self.build_tree(2 * node, start, mid)
            self.build_tree(2 * node + 1, mid + 1, end)
            [node] = [2 * node] + [2 * node + 1]

    def update(self, node, start, end, l, r, val):
        if [node] != 0:
            [node] += (end - start + 1) * [node]
            if start != end:
                [2 * node] += [node]
                [2 * node + 1] += [node]
            [node] = 0

        if start &gt; end or start &gt; r or end &lt; l:
            return

        if start &gt;= l and end &lt;= r:
            [node] += (end - start + 1) * val
            if start != end:
                [2 * node] += val
                [2 * node + 1] += val
            return

        mid = (start + end) // 2
        (2 * node, start, mid, l, r, val)
        (2 * node + 1, mid + 1, end, l, r, val)
        [node] = [2 * node] + [2 * node + 1]

    def query(self, node, start, end, l, r):
        if start &gt; end or start &gt; r or end &lt; l:
            return 0

        if [node] != 0:
            [node] += (end - start + 1) * [node]
            if start != end:
                [2 * node] += [node]
                [2 * node + 1] += [node]
            [node] = 0

        if start &gt;= l and end &lt;= r:
            return [node]

        mid = (start + end) // 2
        left_query = (2 * node, start, mid, l, r)
        right_query = (2 * node + 1, mid + 1, end, l, r)
        return left_query + right_query

# Example usagearr = [1, 2, 3, 4, 5]
seg_tree = LazySegmentTree(arr)

print(seg_tree.query(1, 0, len(arr) - 1, 1, 3)) # Output 9
seg_tree.update(1, 0, len(arr) - 1, 1, 3, 2)

print(seg_tree.query(1, 0, len(arr) - 1, 1, 3)) # Output 15

This example implements a class of lazy segment treeLazySegmentTree。

It includes the following methods:

__init__(self, arr): Initialize the segment tree and build the tree structure.
build_tree(self, node, start, end): Functions that recursively build segment tree.
update(self, node, start, end, l, r, val): Update the value of the element in the range [l, r] toval。
query(self, node, start, end, l, r): Query the sum of elements within the range [l, r].

In the example, an array of length 5 is createdarr, and passLazySegmentTreeThe class builds the corresponding lazy segment tree. Then query and update operations are performed and the results are output.

Summarize

The above is personal experience. I hope you can give you a reference and I hope you can support me more.