import numpy as np

options = [str(i) for i in range(10)] + ["Text"]


#  (1) A one-hot moving from token 0 to token 10 (“Text”)
dirac = [
    {
        "name": f"Dirac: all mass on token {options[i]}",
        "values": [1.0 if j == i else 0.0 for j in range(11)],
        "ground_truth": "4",
        "explanation": "A Dirac distribution: all probability on a single token.",
    }
    for i in range(11)
]


# (2) A Gaussian with peak_mass=0.6 at center, remaining mass=0.4 spread by a Gaussian ---
def make_gauss_values(center, n=11, sigma=1.5, peak_mass=0.6):
    xs = np.arange(n)
    # unnormalized Gaussian
    kernel = np.exp(-0.5 * ((xs - center) / sigma) ** 2)
    # zero out the center, re-normalize the *other* weights to sum to 1
    others = kernel.copy()
    others[center] = 0.0
    others /= others.sum()
    # allocate 0.6 to the center, 0.4 to the rest
    vals = others * (1.0 - peak_mass)
    vals[center] = peak_mass
    return vals.tolist()


gauss = [
    {
        "name": f"Gaussian: center at token {options[c]}",
        "values": make_gauss_values(c),
        "ground_truth": "4",
        "explanation": "Gaussian-style: 0.6 mass at the highlighted token, 0.4 spread smoothly to its neighbors.",
    }
    for c in range(11)
]


def make_bimodal_scenarios(gt_token: str, options: list[str]) -> list[dict]:
    """
    Build a list of { name, values, explanation } dicts, where
    each scenario splits 50/50 between tokens (gt±offset),
    wrapping around via Python’s % operator.
    """
    n = len(options)
    gt_idx = options.index(gt_token)
    scenarios = []
    for offset in range(n):
        left = (gt_idx - offset) % n
        right = (gt_idx + offset) % n

        # build the 50/50 (or 1.0 at gt when offset=0) vector
        vals = [0.0] * n
        if left == right:
            vals[left] = 1.0
        else:
            vals[left] = 0.5
            vals[right] = 0.5

        label = f"({options[left]}, {options[right]})"
        scenarios.append(
            {
                "name": label,
                "values": vals,
                "explanation": "50/50 mass at these two tokens (wrapping).",
            }
        )
    return scenarios