Find the Largest Rectangle Under Histogram Bars
Company: Google
Role: Software Engineer
Category: Coding & Algorithms
Difficulty: hard
Interview Round: Other
### Problem
The array `bars` gives the heights of adjacent histogram bars, each of width one. Return the greatest area of a rectangle that fits inside this histogram.
The rectangle spans a contiguous group of bars, has horizontal and vertical sides, and cannot extend above any bar it spans. Return only its area.
### Examples
**Example 1**
```text
Input: bars = [3,3,1,4,4]
Output: 8
```
The final two bars support a rectangle of width `2` and height `4`.
**Example 2**
```text
Input: bars = [0,2,0]
Output: 2
```
The middle bar alone supports the largest rectangle.
### Constraints
- `1 <= bars.length <= 10^5`
- `0 <= bars[i] <= 10^4`
Overview: Find the maximum rectangle area inside a histogram of unit-width bars, returning only the area across a contiguous bar range.