ÿØÿàJFIFÿþ ÿÛC       ÿÛC ÿÀÿÄÿÄ"#QrÿÄÿÄ&1!A"2qQaáÿÚ ?Øy,æ/3JæݹÈ߲؋5êXw²±ÉyˆR”¾I0ó2—PI¾IÌÚiMö¯–þrìN&"KgX:Šíµ•nTJnLK„…@!‰-ý ùúmë;ºgµŒ&ó±hw’¯Õ@”Ü— 9ñ-ë.²1<yà‚¹ïQÐU„ہ?.’¦èûbß±©Ö«Âw*VŒ) `$‰bØԟ’ëXÖ-ËTÜíGÚ3ð«g Ÿ§¯—Jx„–’U/ÂÅv_s(Hÿ@TñJÑãõçn­‚!ÈgfbÓc­:él[ðQe 9ÀPLbÃãCµm[5¿ç'ªjglå‡Ûí_§Úõl-;"PkÞÞÁQâ¼_Ñ^¢SŸx?"¸¦ùY騐ÒOÈ q’`~~ÚtËU¹CڒêV  I1Áß_ÿÙ""" Given a list of integers, made up of (hopefully) a small number of long runs of consecutive integers, compute a representation of the form ((start1, end1), (start2, end2) ...). Then answer the question "was x present in the original list?" in time O(log(# runs)). """ import bisect def intranges_from_list(list_): """Represent a list of integers as a sequence of ranges: ((start_0, end_0), (start_1, end_1), ...), such that the original integers are exactly those x such that start_i <= x < end_i for some i. Ranges are encoded as single integers (start << 32 | end), not as tuples. """ sorted_list = sorted(list_) ranges = [] last_write = -1 for i in range(len(sorted_list)): if i+1 < len(sorted_list): if sorted_list[i] == sorted_list[i+1]-1: continue current_range = sorted_list[last_write+1:i+1] ranges.append(_encode_range(current_range[0], current_range[-1] + 1)) last_write = i return tuple(ranges) def _encode_range(start, end): return (start << 32) | end def _decode_range(r): return (r >> 32), (r & ((1 << 32) - 1)) def intranges_contain(int_, ranges): """Determine if `int_` falls into one of the ranges in `ranges`.""" tuple_ = _encode_range(int_, 0) pos = bisect.bisect_left(ranges, tuple_) # we could be immediately ahead of a tuple (start, end) # with start < int_ <= end if pos > 0: left, right = _decode_range(ranges[pos-1]) if left <= int_ < right: return True # or we could be immediately behind a tuple (int_, end) if pos < len(ranges): left, _ = _decode_range(ranges[pos]) if left == int_: return True return False