import math
from abc import ABC


class ParameterSchedule(ABC):
    def compute(self, t):
        raise NotImplementedError


class ExponentialInterpolation(ParameterSchedule):
    def __init__(self, start, end, alpha):
        self.start = start
        self.end = end
        self.alpha = alpha

    def compute(self, t):
        if self.alpha != 0:
            return self.start + (self.end - self.start) * (
                math.exp(self.alpha * t) - 1
            ) / (math.exp(self.alpha) - 1)
        else:
            return self.start + (self.end - self.start) * t


class PiecewiseStepFunction(ParameterSchedule):
    def __init__(self, thresholds, values):
        self.thresholds = thresholds
        self.values = values

    def compute(self, t):
        assert len(self.thresholds) > 0
        assert len(self.values) == len(self.thresholds) + 1

        idx = 0
        while idx < len(self.thresholds) and t > self.thresholds[idx]:
            idx += 1
        return self.values[idx]