First true (lower bound)
one step at a time.
Keep the answer inside [lo, hi] and halve it: too small moves lo past mid, big enough pulls hi down to mid.
Free to use. Step forward and back at your pace, and share a link to the exact step you are stuck on.
What you actually watch.
The part a dry run on paper loses: the state, at every step.
Keep the answer inside [lo, hi] and halve it: too small moves lo past mid, big enough pulls hi down to mid. That sentence is easy to agree with and hard to hold in your head on step nine, which is where most people lose the thread.
So the visualiser keeps it in front of you: the search space halving, and the half thrown away greyed out. The line of code being executed is highlighted as the picture changes, so the drawing and the code never drift apart. Step forward, step back, or let it play.
Put your own input in. First true (lower bound) on a clean example teaches you the shape; first true (lower bound) on an empty input, a single element, or one with duplicates teaches you the thing an interviewer asks about.
How it runs, step by step.
The same order the visualiser moves in, so the list and the picture match.
- 1Keep the answer inside a range, lo to hi.
- 2Look at the middle of what is left.
- 3Decide which half cannot hold the answer and throw it away.
- 4Repeat on the half that remains until the range holds one value.
Where people get this one wrong.
These are not made up. Each one is a switch in the tool: turn it on, run the same input, and watch the state go wrong.
- Bug: hi = mid − 1Throws mid away even when nums[mid] ≥ target, so the answer itself can leave [lo, hi]. Try "Target in the middle" or "Duplicates".
Inputs worth trying.
The cases that teach something. Each one is a preset in the tool, with the reason it is there.
- Duplicates of the targetFinds the first 5, not just any 5. Run the hi = mid − 1 bug here.
- Target in the middleThe very first mid is the answer. Run the hi = mid − 1 bug and watch it leave.
- Target not in the arrayThe answer is where 7 would be inserted.
- Smaller than alllo never moves: the answer is 0.
- Larger than allhi never moves: the answer is n, past the end.
What it costs.
The two numbers an interviewer will ask for, and what they mean here.
- Time
- O(log n)counted as real operations while it runs, not quoted from a table
- Space
- O(1)what the algorithm holds besides the input itself
- Pattern
- Binary searchHalve the search space with every check.
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Watching is the first ten minutes. The pattern sticks when you solve with it.
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About first true (lower bound).
Open it in the app and the answers are easier to see than to read.
Open the visualiserWhat does the first true (lower bound) visualiser show?
Every step of the algorithm on input you choose: the search space halving, and the half thrown away greyed out, with the line of code being executed highlighted beside it. You can step forward, step back, or let it play. Spelled visualizer or visualiser, it is the same tool.
What is the time complexity of first true (lower bound)?
O(log n) time and O(1) space. The visualiser counts the real operations as it runs, so you can watch the number grow instead of taking the formula on trust.
Why does my first true (lower bound) code fail on some inputs?
Usually one of the known traps. The visualiser ships the real ones for this algorithm (hi = mid − 1), so you can switch the bug on, run it, and watch exactly where the state goes wrong.
Can I use my own input?
Yes. Type your own array, string or graph and the algorithm runs on that, including the edge cases that break a solution in an interview.
Is it free?
Yes. The app is free to start, with 100 AI credits when you sign up and 100 every month, and watching an algorithm costs no credits.