o $i@sJddlZddlmZmZGdddZGdddeZGdddeZdS) N)AnyOptionalc@seZdZdZ ddededeefddZdd ed eed efd d Zdede d dfddZ ded efddZ ddZ ddZ dS) SegmentTreeamA Segment Tree data structure. https://en.wikipedia.org/wiki/Segment_tree Can be used as regular array, but with two important differences: a) Setting an item's value is slightly slower. It is O(lg capacity), instead of O(1). b) Offers efficient `reduce` operation which reduces the tree's values over some specified contiguous subsequence of items in the array. Operation could be e.g. min/max/sum. The data is stored in a list, where the length is 2 * capacity. The second half of the list stores the actual values for each index, so if capacity=8, values are stored at indices 8 to 15. The first half of the array contains the reduced-values of the different (binary divided) segments, e.g. (capacity=4): 0=not used 1=reduced-value over all elements (array indices 4 to 7). 2=reduced-value over array indices (4 and 5). 3=reduced-value over array indices (6 and 7). 4-7: values of the tree. NOTE that the values of the tree are accessed by indices starting at 0, so `tree[0]` accesses `internal_array[4]` in the above example. Ncapacity operationneutral_elementcs|dkr ||d@dksJd|_|dur*|tjurdn |tur&tdntd}|_fdd td |D_|_dS) a>Initializes a Segment Tree object. Args: capacity: Total size of the array - must be a power of two. operation: Lambda obj, obj -> obj The operation for combining elements (eg. sum, max). Must be a mathematical group together with the set of possible values for array elements. neutral_element (Optional[obj]): The neutral element for `operation`. Use None for automatically finding a value: max: float("-inf"), min: float("inf"), sum: 0.0. rz+Capacity must be positive and a power of 2!Ngz-infinfcsg|]}jqS)r).0_selfr ]/home/ubuntu/veenaModal/venv/lib/python3.10/site-packages/ray/rllib/execution/segment_tree.py =sz(SegmentTree.__init__..) roperatoraddmaxfloatrrangevaluer)rrrrr r r__init__ s  zSegmentTree.__init__rstartendreturncCs|dur|j}n |dkr||j7}|j}||j7}||j7}||krP|d@r3|||j|}|d7}|d@rD|d8}|||j|}|d}|d}||ks"|S)aApplies `self.operation` to subsequence of our values. Subsequence is contiguous, includes `start` and excludes `end`. self.operation( arr[start], operation(arr[start+1], operation(... arr[end]))) Args: start: Start index to apply reduction to. end (Optional[int]): End index to apply reduction to (excluded). Returns: any: The result of reducing self.operation over the specified range of `self._value` elements. Nrrr)rrrr)rrrresultr r rreduce@s$   zSegmentTree.reduceidxvalcCsd|kr |jksnJd|d|j||j7}||j|<|d?}|dkrHd|}||j||j|d|j|<|d?}|dks)dSdS)z Inserts/overwrites a value in/into the tree. Args: idx: The index to insert to. Must be in [0, `self.capacity`) val: The value to insert. rzidx=z capacity=rrN)rrr)rrr update_idxr r r __setitem__s.   zSegmentTree.__setitem__cCs.d|kr |jksJJ|j||jS)Nr)rr)rrr r r __getitem__szSegmentTree.__getitem__cCs|jSN)rr r r r get_stateszSegmentTree.get_statecCs t||jdks J||_dS)Nr)lenrr)rstater r r set_states zSegmentTree.set_stater#rN)__name__ __module__ __qualname____doc__intrrrrrr!r"r$r'r r r rrs  F rcsTeZdZdZdeffdd Zddedeed efd d Zd e d efd dZ Z S)SumSegmentTreez:A SegmentTree with the reduction `operation`=operator.add.rcstt|j|tjddSN)rr)superr.rrrrr __class__r rrszSumSegmentTree.__init__rNrrrcC |||S)z/Returns the sum over a sub-segment of the tree.rrrrr r rsum zSumSegmentTree.sum prefixsumcCsd|kr|dksJJd}||j|kr"|j|d}||jkrEd|}|j||kr5|}n ||j|8}|d}||jks'||jS)zFinds highest i, for which: sum(arr[0]+..+arr[i - i]) <= prefixsum. Args: prefixsum: `prefixsum` upper bound in above constraint. Returns: int: Largest possible index (i) satisfying above constraint. rgh㈵>rr)r7rr)rr9rr r r rfind_prefixsum_idxs$   z!SumSegmentTree.find_prefixsum_idxr() r)r*r+r,r-rrrr7rr: __classcell__r r r2rr.s r.cs>eZdZdeffdd Zd dedeedefd d ZZS) MinSegmentTreercstt|j|tddSr/)r0r<rminr1r2r rrszMinSegmentTree.__init__rNrrrcCr4)z'Returns min(arr[start], ..., arr[end])r5r6r r rr=r8zMinSegmentTree.minr() r)r*r+r-rrrr=r;r r r2rr<s$r<)rtypingrrrr.r<r r r rs ('