When to Use Monotonic Stack

Use monotonic stack when:

$1.$ You need the next/previous greater or smaller element for each position

$2.$ You're computing contribution of each element as min/max of subarrays

$3.$ You see histogram-like problems with heights and widths

$4.$ You need to track "visible" elements or blocking relationships

Here's what matters: when an element gets popped, the new top is its previous greater/smaller, and the pushing element is its next greater/smaller.