Largest Rectangle in Histogram

heights lists the bars of a histogram from left to right, each bar one unit wide. Return the area of the biggest rectangle that fits entirely inside the bars.

Example:

• Input: [2, 1, 5, 6, 2, 3]
• Output: 10 (The rectangle from index 2 to 3 with height 5 has area 5 * 2 = 10).

We use a Monotonic Increasing Stack.

Core Idea:
For each bar h at index i, if we know the first bar to the left that is smaller (left_limit) and the first bar to the right that is smaller (right_limit), then the maximum width for a rectangle with height h is right_limit - left_limit - 1.

One-Pass Logic:

1. Maintain a stack of indices with increasing heights.
2. When we encounter a bar h[i] smaller than h[stack.top()], it means h[i] is the Right Limit for h[stack.top()].
3. Pop top. Now the New Top of the stack is the Left Limit for the popped bar.
4. Calc Area: height * (i - stack.top() - 1).
5. Repeat until stack rule is satisfied, then push i.

Visualize how we pop bars when a shorter one appears, calculating potential areas.