Floor and Ceil in Sorted Array in DSA C++ - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is the floor of a number in a sorted array?

The floor of a number is the greatest element in the array that is less than or equal to that number.

beginner

What is the ceil of a number in a sorted array?

The ceil of a number is the smallest element in the array that is greater than or equal to that number.

intermediate

Why is binary search useful for finding floor and ceil in a sorted array?

Binary search helps find floor and ceil efficiently by repeatedly dividing the search space in half, reducing time from linear to logarithmic.

intermediate

If the target number is smaller than all elements in the array, what is the floor and ceil?

Floor does not exist (no element ≤ target), ceil is the smallest element in the array.

intermediate

If the target number is larger than all elements in the array, what is the floor and ceil?

Floor is the largest element in the array, ceil does not exist (no element ≥ target).

What does the floor of a number represent in a sorted array?

A Greatest element greater than the number

B Smallest element greater than the number

C Smallest element less than the number

D Greatest element less than or equal to the number

Floor is the greatest element in the array that is less than or equal to the target number.

What is the ceil of 7 in the sorted array [1, 3, 5, 8, 10]?

A 8

B 5

C 7

D 10

8 is the smallest element greater than or equal to 7.

Which algorithm is best to find floor and ceil in a sorted array efficiently?

A Linear search

B Binary search

C Bubble sort

D Depth-first search

Binary search reduces the search time to O(log n) by dividing the array repeatedly.

If the target is smaller than all elements, what is the floor?

A Does not exist

B Largest element

C Target itself

D Smallest element

No element is less than or equal to the target, so floor does not exist.

If the target is larger than all elements, what is the ceil?

A Smallest element

B Largest element

C Does not exist

D Target itself

No element is greater than or equal to the target, so ceil does not exist.

Explain how to find the floor and ceil of a number in a sorted array using binary search.

Think about how binary search narrows down where the number fits.

Describe edge cases when finding floor and ceil in a sorted array.

Consider what happens when the target is outside the array range.