Optimize a **binary-classification decision threshold** to maximize an evaluation metric on a validation set, a common step in `ml_evaluation` when converting predicted probabilities into hard labels.

Given predicted probabilities $p_i$ and a threshold $t$, the predicted label is $\hat{y}_i = \mathbb{1}[p_i \ge t]$, and you should choose $t$ that maximizes the F1 score:
$$
F1(t)=\frac{2\cdot \text{Precision}(t)\cdot \text{Recall}(t)}{\text{Precision}(t)+\text{Recall}(t)}
$$

## Requirements

Implement the function
```python
import numpy as np

def best_threshold_f1(y_true, y_prob):
    \"""
    Finds the decision threshold t in [0, 1] that maximizes the F1 score.

    Args:
        y_true (np.ndarray): Ground-truth binary labels (0 or 1).
        y_prob (np.ndarray): Predicted probabilities for the positive class.

    Returns:
        tuple[float, float]: (best_threshold, best_f1) where best_threshold is the
        threshold achieving the highest F1, and best_f1 is that F1 value.
    \"""
    # Your solution below
```

**Rules:**
- Use thresholds drawn from the unique values in `y_prob` (plus 0.0 and 1.0 if you want), and pick the one with the highest F1.
- If multiple thresholds tie for best F1, return the **smallest** threshold.
- Do not use any prebuilt metric/threshold utilities (e.g., `sklearn.metrics`).
- Return `(best_threshold, best_f1)` as Python floats.
- Use only NumPy and Python built-in libraries.

## Example

```python
y_true = [0, 1, 1, 0, 1]
y_prob = [0.10, 0.40, 0.35, 0.80, 0.70]

best_threshold_f1(y_true, y_prob)
```

Output:
```python
(0.35, 0.8)
```

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Threshold optimization

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1378. Threshold optimization

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Similar Questions

Argument	Type
y_prob	np.ndarray
y_true	np.ndarray