mirror of
https://github.com/vale981/ray
synced 2025-03-06 10:31:39 -05:00
143 lines
4.8 KiB
Python
143 lines
4.8 KiB
Python
import operator
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class OldSegmentTree(object):
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def __init__(self, capacity, operation, neutral_element):
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"""Build a Segment Tree data structure.
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https://en.wikipedia.org/wiki/Segment_tree
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Can be used as regular array, but with two
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important differences:
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a) setting item's value is slightly slower.
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It is O(lg capacity) instead of O(1).
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b) user has access to an efficient `reduce`
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operation which reduces `operation` over
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a contiguous subsequence of items in the
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array.
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Paramters
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---------
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capacity: int
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Total size of the array - must be a power of two.
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operation: lambda obj, obj -> obj
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and operation for combining elements (eg. sum, max)
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must for a mathematical group together with the set of
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possible values for array elements.
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neutral_element: obj
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neutral element for the operation above. eg. float('-inf')
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for max and 0 for sum.
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"""
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assert capacity > 0 and capacity & (capacity - 1) == 0, \
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"capacity must be positive and a power of 2."
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self._capacity = capacity
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self._value = [neutral_element for _ in range(2 * capacity)]
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self._operation = operation
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def _reduce_helper(self, start, end, node, node_start, node_end):
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if start == node_start and end == node_end:
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return self._value[node]
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mid = (node_start + node_end) // 2
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if end <= mid:
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return self._reduce_helper(start, end, 2 * node, node_start, mid)
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else:
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if mid + 1 <= start:
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return self._reduce_helper(start, end, 2 * node + 1, mid + 1,
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node_end)
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else:
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return self._operation(
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self._reduce_helper(start, mid, 2 * node, node_start, mid),
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self._reduce_helper(mid + 1, end, 2 * node + 1, mid + 1,
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node_end))
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def reduce(self, start=0, end=None):
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"""Returns result of applying `self.operation`
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to a contiguous subsequence of the array.
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self.operation(
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arr[start], operation(arr[start+1], operation(... arr[end])))
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Parameters
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----------
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start: int
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beginning of the subsequence
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end: int
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end of the subsequences
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Returns
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-------
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reduced: obj
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result of reducing self.operation over the specified range of array
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elements.
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"""
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if end is None:
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end = self._capacity
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if end < 0:
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end += self._capacity
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end -= 1
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return self._reduce_helper(start, end, 1, 0, self._capacity - 1)
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def __setitem__(self, idx, val):
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# index of the leaf
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idx += self._capacity
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self._value[idx] = val
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idx //= 2
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while idx >= 1:
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self._value[idx] = self._operation(self._value[2 * idx],
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self._value[2 * idx + 1])
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idx //= 2
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def __getitem__(self, idx):
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assert 0 <= idx < self._capacity
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return self._value[self._capacity + idx]
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class OldSumSegmentTree(OldSegmentTree):
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def __init__(self, capacity):
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super(OldSumSegmentTree, self).__init__(
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capacity=capacity, operation=operator.add, neutral_element=0.0)
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def sum(self, start=0, end=None):
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"""Returns arr[start] + ... + arr[end]"""
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return super(OldSumSegmentTree, self).reduce(start, end)
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def find_prefixsum_idx(self, prefixsum):
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"""Find the highest index `i` in the array such that
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sum(arr[0] + arr[1] + ... + arr[i - i]) <= prefixsum
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if array values are probabilities, this function
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allows to sample indexes according to the discrete
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probability efficiently.
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Parameters
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----------
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perfixsum: float
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upperbound on the sum of array prefix
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Returns
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-------
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idx: int
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highest index satisfying the prefixsum constraint
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"""
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assert 0 <= prefixsum <= self.sum() + 1e-5
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idx = 1
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while idx < self._capacity: # while non-leaf
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if self._value[2 * idx] > prefixsum:
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idx = 2 * idx
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else:
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prefixsum -= self._value[2 * idx]
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idx = 2 * idx + 1
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return idx - self._capacity
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class OldMinSegmentTree(OldSegmentTree):
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def __init__(self, capacity):
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super(OldMinSegmentTree, self).__init__(
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capacity=capacity, operation=min, neutral_element=float("inf"))
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def min(self, start=0, end=None):
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"""Returns min(arr[start], ..., arr[end])"""
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return super(OldMinSegmentTree, self).reduce(start, end)
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