Candy Distribution

Give each child at least one candy and more than neighbors with minimum total candies.

greedy arrays optimization

You are given a list of non-negative integers `ratings` representing each child's rating. You must distribute candies to the children according to these rules:

1. Each child must have at least one candy.
2. Children with a higher rating than their immediate neighbor must receive more candies than that neighbor.

Write a function `minimum_candies(ratings)` that returns the **minimum** total number of candies required to satisfy the rules.

The list may be empty — return `0` in that case.

For example, for `ratings = [1, 0, 2]`, one optimal distribution is `[2, 1, 2]`, giving a total of `5`. Note that the distribution is not unique, but the minimum total is what matters.

Constraints

- `0 <= len(ratings) <= 10^5`
- `0 <= ratings[i] <= 10^5`
- Your solution should run in `O(n)` time and `O(n)` or `O(1)` extra space (beyond the output/input).

Example

```python
>>> minimum_candies([1, 0, 2])
5
>>> minimum_candies([1, 2, 2])
4
>>> minimum_candies([])
0
```

20 points ~20 min

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Hints

Try a two-pass approach: left to right, then right to left.

Think of each child's candies as needing to satisfy only the neighbor they are higher than.

An empty list should return 0 — handle that first.

The final candies for each child is the maximum of the left and right constraints, and at least 1.

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