Softmax Vector

Convert a one-dimensional vector of logits into probabilities with the softmax function, computed stably by subtracting the maximum first.

Implement solve(x).

Returns. Return a float NumPy vector of the same length whose entries are positive and sum to 1.

Examples

Example 1

Input:

solve([1, 2, 3])

Output:

[0.090031, 0.244728, 0.665241]

Example 2

Input:

solve([0, 0])

Output:

[0.5, 0.5]

Example 3

Input:

solve([1000.0, 1000.0, 999.0])

Output:

[0.422319, 0.422319, 0.155362]