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import sys from fractions import Fraction from math import ceil from typing import cast, List, Optional, Sequence if sys.version_info >= (3, 8): from typing import Protocol else: from typing_extensions import Protocol # pragma: no cover class Edge(Protocol): """Any object that defines an edge (such as Layout).""" size: Optional[int] = None ratio: int = 1 minimum_size: int = 1 def ratio_resolve(total: int, edges: Sequence[Edge]) -> List[int]: """Divide total space to satisfy size, ratio, and minimum_size, constraints. The returned list of integers should add up to total in most cases, unless it is impossible to satisfy all the constraints. For instance, if there are two edges with a minimum size of 20 each and `total` is 30 then the returned list will be greater than total. In practice, this would mean that a Layout object would clip the rows that would overflow the screen height. Args: total (int): Total number of characters. edges (List[Edge]): Edges within total space. Returns: List[int]: Number of characters for each edge. """ # Size of edge or None for yet to be determined sizes = [(edge.size or None) for edge in edges] _Fraction = Fraction # While any edges haven't been calculated while None in sizes: # Get flexible edges and index to map these back on to sizes list flexible_edges = [ (index, edge) for index, (size, edge) in enumerate(zip(sizes, edges)) if size is None ] # Remaining space in total remaining = total - sum(size or 0 for size in sizes) if remaining <= 0: # No room for flexible edges return [ ((edge.minimum_size or 1) if size is None else size) for size, edge in zip(sizes, edges) ] # Calculate number of characters in a ratio portion portion = _Fraction( remaining, sum((edge.ratio or 1) for _, edge in flexible_edges) ) # If any edges will be less than their minimum, replace size with the minimum for index, edge in flexible_edges: if portion * edge.ratio <= edge.minimum_size: sizes[index] = edge.minimum_size # New fixed size will invalidate calculations, so we need to repeat the process break else: # Distribute flexible space and compensate for rounding error # Since edge sizes can only be integers we need to add the remainder # to the following line remainder = _Fraction(0) for index, edge in flexible_edges: size, remainder = divmod(portion * edge.ratio + remainder, 1) sizes[index] = size break # Sizes now contains integers only return cast(List[int], sizes) def ratio_reduce( total: int, ratios: List[int], maximums: List[int], values: List[int] ) -> List[int]: """Divide an integer total in to parts based on ratios. Args: total (int): The total to divide. ratios (List[int]): A list of integer ratios. maximums (List[int]): List of maximums values for each slot. values (List[int]): List of values Returns: List[int]: A list of integers guaranteed to sum to total. """ ratios = [ratio if _max else 0 for ratio, _max in zip(ratios, maximums)] total_ratio = sum(ratios) if not total_ratio: return values[:] total_remaining = total result: List[int] = [] append = result.append for ratio, maximum, value in zip(ratios, maximums, values): if ratio and total_ratio > 0: distributed = min(maximum, round(ratio * total_remaining / total_ratio)) append(value - distributed) total_remaining -= distributed total_ratio -= ratio else: append(value) return result def ratio_distribute( total: int, ratios: List[int], minimums: Optional[List[int]] = None ) -> List[int]: """Distribute an integer total in to parts based on ratios. Args: total (int): The total to divide. ratios (List[int]): A list of integer ratios. minimums (List[int]): List of minimum values for each slot. Returns: List[int]: A list of integers guaranteed to sum to total. """ if minimums: ratios = [ratio if _min else 0 for ratio, _min in zip(ratios, minimums)] total_ratio = sum(ratios) assert total_ratio > 0, "Sum of ratios must be > 0" total_remaining = total distributed_total: List[int] = [] append = distributed_total.append if minimums is None: _minimums = [0] * len(ratios) else: _minimums = minimums for ratio, minimum in zip(ratios, _minimums): if total_ratio > 0: distributed = max(minimum, ceil(ratio * total_remaining / total_ratio)) else: distributed = total_remaining append(distributed) total_ratio -= ratio total_remaining -= distributed return distributed_total if __name__ == "__main__": from dataclasses import dataclass @dataclass class E: size: Optional[int] = None ratio: int = 1 minimum_size: int = 1 resolved = ratio_resolve(110, [E(None, 1, 1), E(None, 1, 1), E(None, 1, 1)]) print(sum(resolved))