README.md

Segment Tree with range operations

This is a general implementation of a segment tree for Python 3.

• Semigroup range operations in O(logN) time
• Built-in support for max, min, sum operations
• Extensible to support more semigroup operations
• Limited support for multidimensional trees
• Python 2 is not currently supported

Installation

pip3 install segment-tree

Segment Tree (one-dimensional)

Basic usage

    from segment_tree import *
    array = [3, 1, 5, 3, 13, 7, 2, 7, 2]
    tree = SegmentTree(array)

    t.query(1, 3, "sum") # 9
    t.update(0, 10) # [10, 1, 5, 3, 13, 7, 2, 7, 2]
    t.query(0, 8, "min") # 0
    t.update(2, -1) # [10, 1, -1, 3, 13, 7, 2, 0, 2]
    t.query(0, 2, "min") # -1

Updates on ranges

    from segment_tree import *
    array = [1, 2, 3, 4, 5]
    t = SegmentTree(array)
    t.update_range(0, 2, 6) # 6 6 6 4 5
    t.update_range(1, 4, 2) # 6 2 2 2 2
    t.query(0, 3, "min") # 2

Operations and their complexity

n is total number of elements in the array.

Function	Description	Complexity	Additional storage
SegmentTree(array)	Builds a segment tree from an array	O(n)	O(n)
update(position, value)	Updates an old value at position to value	O(log n)	O(1)
update_range(start, end, value)	Sets value on a [start, end] range	O(log n)	O(1)
query(start, end, function)	Returns function([start, end])	O(log n)	O(1)

Multidimensional Segment Tree (alpha version, might have bugs)

Basic usage

    from segment_tree import *
    a = [[[1, 2], [1, 3]], [[-1, -2], [-1, -3]]]
    tree = MultidimensionalSegmentTree(a)

    tree.query([(0, 1), (0, 0), (0, 0)], max) # 1
    tree.query([(1, 1), (0, 1), (0, 1)], sum) # -7
    tree.query([(0, 1), (1, 1), (0, 1)], min) # -3

Operations and their complexity

n is total number of elements in the array, p is the number of dimensions.

Function	Description	Complexity	Additional storage
MultidimensionalSegmentTree(array)	Builds a multidimensional segment tree from an array	O(4^p * n)	O(4^p * n)
update(position, value) (not implemented yet)	Updates an old value at position to value	O(log^p n)	O(1)
query(start, end, function)	Returns function([start, end])	O(log^p n)	O(1)

Tests

Execute python3 setup.py test to run tests.