Persistent Segment Tree by putul03 · Pull Request #12186 · TheAlgorithms/Python

putul03 · 2024-10-19T11:25:39Z

The persistent segment tree allows us to efficiently query and update an array while preserving previous versions of the array. The primary operations include:

Build Operation: Constructs the segment tree from the given array. Each node represents a range of the array and stores the sum of that range.
Update Operation: When an update is performed, a new version of the segment tree is created without modifying the existing tree. This is achieved by copying the necessary nodes and updating the affected ranges.
Query Operation: To retrieve the sum of a given range, the segment tree is traversed based on the requested indices. The operation can access multiple versions of the tree to return the correct sum for each version.

Time and Space Complexity:

Time Complexity:
- Build Operation: O(n log n), where n is the number of elements in the array. This is because we need to recursively build the tree.
- Update Operation: O(log n) per update, since we only traverse the necessary nodes to create a new version.
- Query Operation: O(log n) per query, as we traverse the segment tree to find the required sums.
Space Complexity:
- The space complexity is O(n * log n) for storing multiple versions of the segment tree, where each version contains log n nodes and there can be up to n versions depending on the number of updates.

Describe your change:

Add an algorithm?
Fix a bug or typo in an existing algorithm?
Add or change doctests? -- Note: Please avoid changing both code and tests in a single pull request.
Documentation change?

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algorithms-keeper · 2024-10-19T11:25:44Z

+        self.roots.append(new_root)
+        return len(self.roots) - 1
+
+    def _update(self, node: Node | None, start: int, end: int, index: int, value: int) -> Node:


As there is no test file in this pull request nor any test function or class in the file data_structures/persistent_segment_tree.py, please provide doctest for the function _update

algorithms-keeper · 2024-10-19T11:25:44Z

+        """
+        return self._query(self.roots[version], 0, self.n - 1, left, right)
+
+    def _query(self, node: Node | None, start: int, end: int, left: int, right: int) -> int:


As there is no test file in this pull request nor any test function or class in the file data_structures/persistent_segment_tree.py, please provide doctest for the function _query

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algorithms-keeper · 2024-10-19T11:34:10Z

+        self.roots: list[Node] = []
+        self.roots.append(self._build(arr, 0, self.n - 1))
+
+    def _build(self, arr: list[int], start: int, end: int) -> Node:


As there is no test file in this pull request nor any test function or class in the file data_structures/persistent_segment_tree.py, please provide doctest for the function _build

algorithms-keeper · 2024-10-19T11:34:10Z

+        node.value = node.left.value + node.right.value
+        return node
+
+    def update(self, version: int, index: int, value: int) -> int:


As there is no test file in this pull request nor any test function or class in the file data_structures/persistent_segment_tree.py, please provide doctest for the function update

algorithms-keeper · 2024-10-19T11:34:11Z

+        self.roots.append(new_root)
+        return len(self.roots) - 1
+
+    def _update(self, node: Node | None, start: int, end: int, index: int, value: int) -> Node:


As there is no test file in this pull request nor any test function or class in the file data_structures/persistent_segment_tree.py, please provide doctest for the function _update

algorithms-keeper · 2024-10-19T11:34:11Z

+
+        return new_node
+
+    def query(self, version: int, left: int, right: int) -> int:


As there is no test file in this pull request nor any test function or class in the file data_structures/persistent_segment_tree.py, please provide doctest for the function query

algorithms-keeper · 2024-10-19T11:34:11Z

+        """
+        return self._query(self.roots[version], 0, self.n - 1, left, right)
+
+    def _query(self, node: Node | None, start: int, end: int, left: int, right: int) -> int:


As there is no test file in this pull request nor any test function or class in the file data_structures/persistent_segment_tree.py, please provide doctest for the function _query

for more information, see https://pre-commit.ci

putul03 and others added 17 commits October 19, 2024 13:21

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Persistent Segment Tree - #12186

Persistent Segment Tree#12186
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		return new_node

		def query(self, version: int, left: int, right: int) -> int:

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putul03 commented Oct 19, 2024

Time and Space Complexity:

Describe your change:

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