First True: Predicate Binary Search
Search a monotonic yes/no boundary.
First True: Predicate Binary Search is a free Coding Interview Prep lesson on CoddyKit — lesson 3 of 4. You can read the complete lesson below for free — then practise it hands-on in the browser with a built-in code editor and a 24/7 AI tutor. It is part of the Coding Interview Prep learning path, one of 4 lessons in the course, and your progress syncs across the web and the CoddyKit app.
Search a Yes/No Boundary
Many problems hide a monotonic predicate: false, false, then true forever. Binary search can find that first true without a sorted array.
# FFFFTTTT -> find first TWhat Monotonic Means
A predicate is monotonic when once it turns true it stays true. That single property is what lets you binary-search the boundary.
def ok(x):
return x * x >= targetFrame the Answer Space
Pick a range that surely contains the boundary. Set low to the smallest candidate and high to a value where ok is certainly true.
low, high = 0, 10**9Test the Middle
Take mid and call ok(mid). The boolean result tells you which half to keep, exactly like comparing a value in plain binary search.
mid = (low + high) // 2
if ok(mid):
...True Means Maybe Smaller
If ok(mid) is true, mid is a valid answer but a smaller one might also work. Keep mid by setting high = mid, not mid - 1.
if ok(mid):
high = midFalse Means Go Higher
If ok(mid) is false, the boundary lies above mid. Discard mid and everything below it with low = mid + 1.
else:
low = mid + 1Loop While Low Is Below High
Use while low < high, not less-than-or-equal. The two pointers converge onto the first true index and then the loop stops.
while low < high:
mid = (low + high) // 2The Answer Is Low
When the loop ends, low equals high and both point at the first true value. Return low as the boundary you were hunting.
return low # first x where ok(x)Why high = mid Works
Because mid can be the answer, you must not skip it. Using high = mid keeps it in range while still shrinking, guaranteeing progress.
high = mid # mid stays a candidateInteger Square Root Example
To find the largest x with x*x at most n, search the first true of x*x > n, then step back one. The pattern reuses itself.
def ok(x):
return x * x > n
# answer is found_index - 1One Template, Many Problems
This first-true template solves countless tasks: minimum feasible value, leftmost index, smallest capacity. Learn it once, reuse it everywhere.
# low<high, ok->high=mid, else low=mid+1Quick Check
Pin down the move that keeps the candidate alive.
Recap: First True Found
You can now turn a problem into a monotonic predicate and binary-search the boundary. high = mid plus while low < high is the safe pattern. 🧭
Frequently asked questions
Is the “First True: Predicate Binary Search” lesson free?
Yes — the full text of “First True: Predicate Binary Search” is free to read here on the web, and the Coding Interview Prep course includes 4 lessons in total. To practise it interactively (a built-in code editor and a 24/7 AI tutor) and unlock the rest of the Coding Interview Prep course, upgrade to CoddyKit PRO.
What will I learn in “First True: Predicate Binary Search”?
Search a monotonic yes/no boundary. You practise Coding Interview Prep with hands-on code you run directly in the browser, and a 24/7 AI tutor answers your questions as you work through the lesson.
Do I need any experience to start Coding Interview Prep?
No prior experience is required. Coding Interview Prep on CoddyKit is structured for beginners through advanced learners; this is — lesson 3 of 4, so you can start here or from the beginning and move at your own pace.
How long does the “First True: Predicate Binary Search” lesson take?
Most CoddyKit lessons take about 5–10 minutes. Each one is bite-sized and interactive, so you make steady progress and pick up exactly where you left off across the web and the app.
Can I write and run code in this Coding Interview Prep lesson?
Yes. Every Coding Interview Prep lesson includes a built-in code editor, so you write and run real code right in your browser and get instant AI feedback — no local setup required.
All lessons in this course
- Classic Binary Search Without Bugs
- bisect_left and bisect_right
- First True: Predicate Binary Search
- Binary Search on the Answer