"""Линейная интерполяция (аналог FRAC в методичке)."""

from __future__ import annotations


def frac(numerator: float, denominator: float) -> float:
    if denominator == 0:
        return 0.0
    return numerator / denominator


def lerp(x: float, x1: float, n1: float, x2: float, n2: float) -> float:
    """Norma = n1 + frac(n2 - n1, x2 - x1) * (x - x1)."""
    if x2 == x1:
        return n1
    return n1 + frac(n2 - n1, x2 - x1) * (x - x1)


def popr_index(udoy: float, boundaries: list[float]) -> int:
    """1-based индекс столбца POPR_K по суточному удою."""
    idx = 1
    for i, bound in enumerate(boundaries, start=1):
        if udoy >= bound:
            idx = i + 1
    return min(idx, len(boundaries) + 1)