Search Insert Position
Recognize the pattern
Brute force idea
The naive version of Search Insert Position sounds like this: Scan linearly to find the position. That direct path helps you understand the question, but it tends to treat every possibility as brand new instead of learning from earlier steps.
Better approach
A calmer way to see Search Insert Position is this: Binary search: narrow the range by half each step. The goal is not to be clever for its own sake, but to remember the one relationship that keeps the solution grounded as you move forward.
Key invariant
The truth you want to protect throughout Search Insert Position is this: The left pointer always points to the correct insertion position when search ends. If that remains true after every update, the rest of the reasoning has a stable place to stand.
Watch out for
The trap in Search Insert Position usually looks like this: Off-by-one in the return value — return left, not mid, when the target isn't found. When the code becomes mechanical before the idea is clear, small edge cases start breaking the whole story.