Search Insert Position
easyTime: O(log n)Space: O(1)
Signals to notice
sorted arrayfind insertion pointthe prompt wants you to keep cutting the search space down
Brute force first
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.
The key insight
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.
What must stay true
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.
Easy way to go wrong
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.