Ceil the Floor Visualization & Animation

Finds both floor and ceil of a target in a single binary search pass over a sorted array.

## What is it? Find both the floor (largest element ≤ target) and ceil (smallest element ≥ target) of a target value in a sorted array in a single pass using binary search. ## How it works - Run binary search tracking two candidates: `floor` and `ceil` - If `arr[mid] == target` → floor = ceil = `arr[mid]`; done - If `arr[mid] < target` → `arr[mid]` is a floor candidate; update floor, move `low = mid + 1` - If `arr[mid] > target` → `arr[mid]` is a ceil candidate; update ceil, move `high = mid - 1` ## When to use - Finding the two closest values to a target in a sorted array - Interval queries and nearest-neighbor lookups - Prerequisite for more complex binary search problems ## Key Points - Both floor and ceil can be found in a single binary search pass - If target exists in the array, floor == ceil == target - If target is smaller than all elements, floor does not exist; if larger than all, ceil does not exist

Category: algorithms

Difficulty: beginner

Time Complexity: O(log n)

Space Complexity: O(1)

Ceil the Floor

beginner

Finds both floor and ceil of a target in a single binary search pass over a sorted array.

GFG
PhaseUpper Bound
x5
Floor—
Ceil—
Round 1 — upper_bound (Floor)
lo
mid
hi
1
[0]
2
[1]
8
[2]
10
[3]
10
[4]
12
[5]
19
[6]
mid / ceil candidate
floor candidate / result
too big / too small
search window
Round 1 — upper_bound: lo=0, hi=7. Find first index where arr[i] > x=5.