class Tdigest(object): def __init__(self, delta=0.01, K=25, CX=1.1): self.delta = delta self.K = K self.CX = CX self.centroids = RBTree() self.nreset = 0 self.reset() def reset(self): self.centroids.clear() self.n = 0 self.nreset += 1 self.last_cumulate = 0 self.compressing = False def push(self, x, n=1): if not isinstance(x, list): x = [x] for item in x: self._digest(item, n) def percentile(self, p): if self.size() == 0: return None self._cumulate(True) cumn = self.n * p lower = self.centroids.min_item()[1] upper = self.centroids.max_item()[1] for c in self.centroids.values(): if c.cumn <= cumn: lower = c else: upper = c break if lower == upper: return lower.mean return lower.mean + (cumn - lower.cumn) * (upper.mean - lower.mean) / \ (upper.cumn - lower.cumn) def serialize(self): result = '%s~%s~%s~' % (self.delta, self.K, self.size()) if self.size() == 0: return result self._cumulate(True) means = [] counts = [] for c in self.centroids.values(): means.append(str(c.mean)) counts.append(str(c.n)) return '%s%s~%s' % (result, '~'.join(means), '~'.join(counts)) @classmethod def deserialize(cls, serialized_str): if not isinstance(serialized_str, basestring): raise Exception(u'serialized_str must be str') data = serialized_str.split('~') t = Tdigest(delta=float(data[0]), K=int(data[1])) size = int(data[2]) for i in xrange(size): t.push(float(data[i + 3]), int(data[size + i + 3])) t._cumulate(True) return t def _digest(self, x, n): if self.size() == 0: self._new_centroid(x, n, 0) else: _min = self.centroids.min_item()[1] _max = self.centroids.max_item()[1] nearest = self.find_nearest(x) if nearest and nearest.mean == x: self._addweight(nearest, x, n) elif nearest == _min: self._new_centroid(x, n, 0) elif nearest == _max: self._new_centroid(x, n, self.n) else: p = (nearest.cumn + nearest.n / 2.0) / self.n max_n = int(4 * self.n * self.delta * p * (1 - p)) if max_n >= nearest.n + n: self._addweight(nearest, x, n) else: self._new_centroid(x, n, nearest.cumn) self._cumulate(False) if self.K and self.size() > self.K / self.delta: self.compress() def find_nearest(self, x): if self.size() == 0: return None try: lower = self.centroids.ceiling_item(x)[1] except KeyError: lower = None if lower and lower.mean == x: return lower try: prev = self.centroids.floor_item(x)[1] except KeyError: prev = None if not lower: return prev if not prev: return lower if abs(prev.mean - x) < abs(lower.mean - x): return prev else: return lower def size(self): return len(self.centroids) def compress(self): if self.compressing: return points = self.toList() self.reset() self.compressing = True for point in sorted(points, key=lambda x: random()): self.push(point['mean'], point['n']) self._cumulate(True) self.compressing = False def _cumulate(self, exact): if self.n == self.last_cumulate: return if not exact and self.CX and self.last_cumulate and \ self.CX > (self.n / self.last_cumulate): return cumn = 0 for c in self.centroids.values(): cumn = c.cumn = cumn + c.n self.n = self.last_cumulate = cumn def toList(self): return [dict(mean=c.mean, n=c.n, cumn=c.cumn) for c in self.centroids.values()] def _addweight(self, nearest, x, n): if x != nearest.mean: nearest.mean += n * (x - nearest.mean) / (nearest.n + n) nearest.cumn += n nearest.n += n self.n += n def _new_centroid(self, x, n, cumn): c = Centroid(x, n, cumn) self.centroids.insert(x, c) self.n += n return c
class SparseArray(object): def __init__(self): self.tree = FastRBTree() def __len__(self): try: k, v = self.tree.max_item() except KeyError: return 0 return k + len(v) def __getitem__(self, ndx): try: base, chunk = self.tree.floor_item(ndx) except KeyError: return None offset = ndx - base if offset < len(chunk): return chunk[offset] else: return None def __setitem__(self, ndx, item): try: base, chunk = self.tree.floor_item(ndx) except KeyError: try: base, chunk = self.tree.ceiling_item(ndx) except KeyError: self.tree[ndx] = [item] return if ndx + 1 == base: chunk.insert(0, item) del self.tree[base] self.tree[ndx] = chunk return if base > ndx: self.tree[ndx] = [item] return offset = ndx - base if offset < len(chunk): chunk[offset] = item else: nextbase, nextchunk = (None, None) try: nextbase, nextchunk = self.tree.succ_item(base) except KeyError: pass if offset == len(chunk): chunk.append(item) if offset + 1 == nextbase: chunk += nextchunk del self.tree[nextbase] elif offset + 1 == nextbase: nextchunk.insert(0, item) del self.tree[nextbase] self.tree[ndx] = nextchunk else: self.tree[ndx] = [item] def __delitem__(self, ndx): base, chunk = self.tree.floor_item(ndx) offset = ndx - base if offset < len(chunk): before = chunk[:offset] after = chunk[offset + 1:] if len(before): self.tree[base] = before else: del self.tree[base] if len(after): self.tree[ndx + 1] = after def items(self): for k, vs in self.tree.items(): for n, v in enumerate(vs): yield (k + n, v) def runs(self): return self.tree.items() def run_count(self): return len(self.tree) def __repr__(self): arep = [] for k, v in self.tree.items(): arep.append('[%r]=%s' % (k, ', '.join([repr(item) for item in v]))) return 'SparseArray(%s)' % ', '.join(arep)
class ExclusiveRangeDict(object): """A class like dict whose key is a range [begin, end) of integers. It has an attribute for each range of integers, for example: [10, 20) => Attribute(0), [20, 40) => Attribute(1), [40, 50) => Attribute(2), ... An instance of this class is accessed only via iter_range(begin, end). The instance is accessed as follows: 1) If the given range [begin, end) is not covered by the instance, the range is newly created and iterated. 2) If the given range [begin, end) exactly covers ranges in the instance, the ranges are iterated. (See test_set() in tests/range_dict_tests.py.) 3) If the given range [begin, end) starts at and/or ends at a mid-point of an existing range, the existing range is split by the given range, and ranges in the given range are iterated. For example, consider a case that [25, 45) is given to an instance of [20, 30), [30, 40), [40, 50). In this case, [20, 30) is split into [20, 25) and [25, 30), and [40, 50) into [40, 45) and [45, 50). Then, [25, 30), [30, 40), [40, 45) are iterated. (See test_split() in tests/range_dict_tests.py.) 4) If the given range [begin, end) includes non-existing ranges in an instance, the gaps are filled with new ranges, and all ranges are iterated. For example, consider a case that [25, 50) is given to an instance of [30, 35) and [40, 45). In this case, [25, 30), [35, 40) and [45, 50) are created in the instance, and then [25, 30), [30, 35), [35, 40), [40, 45) and [45, 50) are iterated. (See test_fill() in tests/range_dict_tests.py.) """ class RangeAttribute(object): def __init__(self): pass def __str__(self): return '<RangeAttribute>' def __repr__(self): return '<RangeAttribute>' def copy(self): # pylint: disable=R0201 return ExclusiveRangeDict.RangeAttribute() def __init__(self, attr=RangeAttribute): self._tree = FastRBTree() self._attr = attr def iter_range(self, begin=None, end=None): if not begin: begin = self._tree.min_key() if not end: end = self._tree.max_item()[1][0] # Assume that self._tree has at least one element. if self._tree.is_empty(): self._tree[begin] = (end, self._attr()) # Create a beginning range (border) try: bound_begin, bound_value = self._tree.floor_item(begin) bound_end = bound_value[0] if begin >= bound_end: # Create a blank range. try: new_end, _ = self._tree.succ_item(bound_begin) except KeyError: new_end = end self._tree[begin] = (min(end, new_end), self._attr()) elif bound_begin < begin and begin < bound_end: # Split the existing range. new_end = bound_value[0] new_value = bound_value[1] self._tree[bound_begin] = (begin, new_value.copy()) self._tree[begin] = (new_end, new_value.copy()) else: # bound_begin == begin # Do nothing (just saying it clearly since this part is confusing) pass except KeyError: # begin is less than the smallest element. # Create a blank range. # Note that we can assume self._tree has at least one element. self._tree[begin] = (min(end, self._tree.min_key()), self._attr()) # Create an ending range (border) try: bound_begin, bound_value = self._tree.floor_item(end) bound_end = bound_value[0] if end > bound_end: # Create a blank range. new_begin = bound_end self._tree[new_begin] = (end, self._attr()) elif bound_begin < end and end < bound_end: # Split the existing range. new_end = bound_value[0] new_value = bound_value[1] self._tree[bound_begin] = (end, new_value.copy()) self._tree[end] = (new_end, new_value.copy()) else: # bound_begin == begin # Do nothing (just saying it clearly since this part is confusing) pass except KeyError: # end is less than the smallest element. # It must not happen. A blank range [begin,end) has already been created # even if [begin,end) is less than the smallest range. # Do nothing (just saying it clearly since this part is confusing) raise missing_ranges = [] prev_end = None for range_begin, range_value in self._tree.itemslice(begin, end): range_end = range_value[0] # Note that we can assume that we have a range beginning with |begin| # and a range ending with |end| (they may be the same range). if prev_end and prev_end != range_begin: missing_ranges.append((prev_end, range_begin)) prev_end = range_end for missing_begin, missing_end in missing_ranges: self._tree[missing_begin] = (missing_end, self._attr()) for range_begin, range_value in self._tree.itemslice(begin, end): yield range_begin, range_value[0], range_value[1] def __str__(self): return str(self._tree)
prev[ 0 ] = 0 cur = FastRBTree() cur[ 0 ] = 0 i = 0 for elem in newInput: v = elem[ 2 ] w = elem[ 1 ] #for line in fin: #info = line.split() #v = int( info[ 0 ] ) #w = int( info[ 1 ] ) #print newItems - i, (v,w), len( prev )#, len( testSet ) i += 1 for stepWeight in prev: step = [ stepWeight, prev[ stepWeight ] ] curv = cur.floor_item( step[ 0 ] )[ 1 ] maxv = max( step[ 1 ], curv ) # compare prev and cur on same weight if maxv == step[ 1 ]: cur[ step[ 0 ] ] = maxv nextw = step[ 0 ] + w # using step weight as base, compare value of # prev val( step weight ) + item val --> with current item # and prev val( step weight + item weight ) --> without current item if nextw < size and prev.floor_item( nextw )[ 1 ] < step[ 1 ] + v: cur[ nextw ] = step[ 1 ] + v prev = cur cur = FastRBTree() cur[ 0 ] = 0
class RangeSet(object): def __init__(self, ranges): self.tree = FastRBTree() for r in ranges: self.add(r) def add(self, rng): rs, re = rng ds, de = (None, None) try: ls, le = self.tree.floor_item(rs) # If we get here, ls <= rng.start if le >= rs - 1: de = ds = ls rs = ls except KeyError: pass for s, e in self.tree[rs:re + 2].items(): if ds is None: ds = s de = s if e > re: re = e if ds is not None: del self.tree[ds:de + 1] self.tree[rs] = re def remove(self, rng): rs, re = rng ds, de = (rs, re) try: ls, le = self.tree.floor_item(rs) # Truncate an initial range, if any if ls < rs and le >= rs: self.tree[ls] = rs - 1 if le > re: self.tree[re + 1] = le except KeyError: pass ins = None for s, e in self.tree[rs:re + 1].items(): de = s if e > re: self.tree[re + 1] = e del self.tree[ds:de + 1] def range_containing(self, pos): ls, le = self.tree.floor_item(pos) if ls <= pos and le >= pos: return (ls, le) return None def __repr__(self): return 'RangeSet([%s])' % ', '.join( ['(%s, %s)' % (s, e) for s, e in self.tree.items()]) def __iter__(self): return iter(self.tree) def items(self): return self.tree.items()