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.

Practice

1. What does the floor of a number mean in a sorted array context?

easy

A. The greatest element less than or equal to the number

B. The smallest element greater than the number

C. The average of all elements less than the number

D. The smallest element less than the number

Solution

1. Step 1: Understand floor definition in sorted array

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

2. Step 2: Compare options with definition

   The greatest element less than or equal to the number matches the definition exactly. Other options describe different concepts.

3. Final Answer:

   The greatest element less than or equal to the number -> Option A

4. Quick Check:

   Floor = greatest ≤ number [OK]

Hint: Floor is always ≤ number, pick greatest such element [OK]

Common Mistakes:

• Confusing floor with ceil
• Choosing smallest element greater than number
• Thinking floor is average or exact match only

2. Which of the following is the correct C++ function signature to find the floor of a number in a sorted array?

easy

A. int findFloor(int arr[], int n, int x);

B. void findFloor(int arr[], int n, int x);

C. int findFloor(int arr, int n, int x);

D. int findFloor(int arr[], int x);

Solution

1. Step 1: Analyze function parameters

   The function needs the array, its size, and the target number to find floor.

2. Step 2: Check each option's signature

   int findFloor(int arr[], int n, int x); correctly uses array pointer, size, and target number. void findFloor(int arr[], int n, int x); returns void which is incorrect. int findFloor(int arr, int n, int x); uses int arr instead of array. int findFloor(int arr[], int x); misses size parameter.

3. Final Answer:

   int findFloor(int arr[], int n, int x); -> Option A

4. Quick Check:

   Correct signature includes array, size, target [OK]

Hint: Function needs array, size, and target number [OK]

Common Mistakes:

• Omitting array size parameter
• Using wrong array type
• Returning void instead of int

3. What is the output of the following code snippet?

int arr[] = {1, 3, 5, 7, 9};
int n = 5;
int x = 6;
int floor = -1;
for (int i = 0; i < n; i++) {
  if (arr[i] <= x) floor = arr[i];
  else break;
}
std::cout << floor;

medium

A. 6

B. 7

C. 5

D. -1

Solution

1. Step 1: Trace the loop and condition

   Loop checks each element ≤ 6. Elements 1, 3, 5 satisfy condition, floor updates to 5. When arr[i] = 7, condition fails and loop breaks.

2. Step 2: Determine final floor value

   Floor remains 5 after loop ends.

3. Final Answer:

   5 -> Option C

4. Quick Check:

   Floor of 6 in array = 5 [OK]

Hint: Floor is last element ≤ target before break [OK]

Common Mistakes:

• Choosing 6 which is not in array
• Choosing 7 which is > 6
• Not updating floor correctly

4. Find the error in the following code to find the ceil of a number in a sorted array:

int findCeil(int arr[], int n, int x) {
  int ceil = -1;
  for (int i = 0; i < n; i++) {
    if (arr[i] >= x) {
      ceil = arr[i];
    }
  }
  return ceil;
}

medium

A. It uses wrong comparison operator

B. It returns -1 even if ceil exists

C. It should return floor instead of ceil

D. It does not return the smallest element ≥ x

Solution

1. Step 1: Understand the loop logic

   The loop updates ceil whenever arr[i] ≥ x, but does not stop or check for smallest such element.

2. Step 2: Identify the error

   Because it keeps updating, it ends with the last element ≥ x, not the smallest. It should break or track minimum.

3. Final Answer:

   It does not return the smallest element ≥ x -> Option D

4. Quick Check:

   Ceil = smallest ≥ x, code returns largest ≥ x [OK]

Hint: Ceil must be smallest ≥ target, not last found [OK]

Common Mistakes:

• Not breaking loop after first valid ceil
• Updating ceil without checking if smaller
• Confusing floor and ceil logic

5. Given a sorted array arr = {2, 4, 6, 8, 10}, what are the floor and ceil of x = 5? Choose the correct pair.

hard

A. Floor = 5, Ceil = 6

B. Floor = 4, Ceil = 6

C. Floor = 4, Ceil = 5

D. Floor = 6, Ceil = 8

Solution

1. Step 1: Find floor of 5 in array

   Floor is greatest element ≤ 5. Elements ≤ 5 are 2 and 4, greatest is 4.

2. Step 2: Find ceil of 5 in array

   Ceil is smallest element ≥ 5. Elements ≥ 5 are 6, 8, 10, smallest is 6.

3. Final Answer:

   Floor = 4, Ceil = 6 -> Option B

4. Quick Check:

   Floor ≤ 5 = 4, Ceil ≥ 5 = 6 [OK]

Hint: Floor ≤ x, Ceil ≥ x; pick closest elements [OK]

Common Mistakes:

• Assuming floor or ceil must equal x
• Choosing elements not in array
• Mixing floor and ceil values