Check That a String of Three Bracket Types Is Properly Nested
Company: Oracle
Role: Software Engineer
Category: Coding & Algorithms
Difficulty: medium
Interview Round: Technical Screen
Given a string made only of the six bracket characters `(`, `)`, `[`, `]`, `{` and `}`, decide whether its brackets are properly nested.
### Function Signature
```python
def is_properly_nested(s: str) -> bool:
```
### Rules
- `(` pairs only with `)`, `[` only with `]`, and `{` only with `}`.
- Every closing bracket must close the most recently opened bracket that is still open, and that bracket must be of the same type.
- A closing bracket that appears while no bracket is open makes the string invalid.
- Every opening bracket must eventually be closed; a bracket still open at the end makes the string invalid.
- Pairs may sit side by side (`()[]`) or inside one another (`{[()]}`), but they may not cross: in `([)]` the `)` arrives while `[` is the most recently opened bracket, so the string is invalid.
- Return `True` when the string is properly nested and `False` otherwise.
### Constraints
- `1 <= len(s) <= 10^4`
- Every character of `s` is one of `(`, `)`, `[`, `]`, `{`, `}`.
### Examples
**Example 1**
```text
Input: s = "{[()]}()"
Output: True
```
The first six characters nest three pairs inside one another, and the final `()` sits beside them.
**Example 2**
```text
Input: s = "([)]"
Output: False
```
The `)` at index 2 must close the most recently opened bracket, which is `[`, so the types do not match.
**Example 3**
```text
Input: s = "[]{"
Output: False
```
The `{` at the end is never closed.
Overview: Decide whether a string made of round, square and curly brackets is properly nested, meaning every closing bracket matches the most recently opened bracket of the same type and nothing is left open. Tests careful handling of nesting order, crossing pairs and unmatched brackets at either end.