Floor and Ceil in Sorted Array in DSA C - Practice Problems & Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Find floor and ceil for a value in a sorted array

What is the output of the following code that finds the floor and ceil of 7 in the sorted array?

DSA C

int arr[] = {1, 3, 5, 6, 8, 9};
int n = 6;
int x = 7;
int floor = -1, ceil = -1;
for (int i = 0; i < n; i++) {
    if (arr[i] <= x) floor = arr[i];
    if (arr[i] >= x && ceil == -1) ceil = arr[i];
}
printf("Floor: %d, Ceil: %d\n", floor, ceil);

A Floor: 8, Ceil: 9

B Floor: 5, Ceil: 6

C Floor: 7, Ceil: 7

D Floor: 6, Ceil: 8

💡 Hint

Remember floor is the greatest element less than or equal to x, ceil is the smallest element greater than or equal to x.

The floor of 7 is 6 because 6 is the greatest number less than or equal to 7 in the array. The ceil of 7 is 8 because 8 is the smallest number greater than or equal to 7.

❓ Predict Output

intermediate

Output when value is smaller than all elements

What is the output of the code when searching floor and ceil of 0 in the sorted array?

DSA C

int arr[] = {2, 4, 6, 8, 10};
int n = 5;
int x = 0;
int floor = -1, ceil = -1;
for (int i = 0; i < n; i++) {
    if (arr[i] <= x) floor = arr[i];
    if (arr[i] >= x && ceil == -1) ceil = arr[i];
}
printf("Floor: %d, Ceil: %d\n", floor, ceil);

A Floor: 2, Ceil: 2

B Floor: -1, Ceil: 2

C Floor: -1, Ceil: -1

D Floor: 0, Ceil: 2

💡 Hint

Floor is -1 if no element is less than or equal to x.

Since 0 is smaller than all elements, floor remains -1 (no element <= 0), ceil is the smallest element 2.

❓ Predict Output

advanced

Output when value is larger than all elements

What is the output of the code when searching floor and ceil of 15 in the sorted array?

DSA C

int arr[] = {3, 5, 7, 10, 12};
int n = 5;
int x = 15;
int floor = -1, ceil = -1;
for (int i = 0; i < n; i++) {
    if (arr[i] <= x) floor = arr[i];
    if (arr[i] >= x && ceil == -1) ceil = arr[i];
}
printf("Floor: %d, Ceil: %d\n", floor, ceil);

A Floor: 12, Ceil: -1

B Floor: -1, Ceil: 15

C Floor: 15, Ceil: 15

D Floor: 10, Ceil: 12

💡 Hint

Ceil is -1 if no element is greater than or equal to x.

Since 15 is larger than all elements, floor is the largest element 12, ceil remains -1 (no element >= 15).

🧠 Conceptual

advanced

Understanding floor and ceil definitions

Which of the following statements correctly defines floor and ceil in a sorted array?

A Floor is the smallest element less than x; Ceil is the greatest element greater than x.

B Floor is the smallest element greater than or equal to x; Ceil is the greatest element less than or equal to x.

C Floor is the greatest element less than or equal to x; Ceil is the smallest element greater than or equal to x.

D Floor and Ceil both are the closest elements to x regardless of being smaller or greater.

💡 Hint

Floor is always less than or equal to x, ceil is always greater than or equal to x.

Floor is the greatest element that does not exceed x, ceil is the smallest element that is not less than x.

❓ Predict Output

expert

Output of binary search based floor and ceil finder

What is the output of the following code that uses binary search to find floor and ceil of 4 in the sorted array?

DSA C

int arr[] = {1, 2, 4, 6, 8};
int n = 5;
int x = 4;
int floor = -1, ceil = -1;
int low = 0, high = n - 1;
while (low <= high) {
    int mid = low + (high - low) / 2;
    if (arr[mid] == x) {
        floor = arr[mid];
        ceil = arr[mid];
        break;
    } else if (arr[mid] < x) {
        floor = arr[mid];
        low = mid + 1;
    } else {
        ceil = arr[mid];
        high = mid - 1;
    }
}
printf("Floor: %d, Ceil: %d\n", floor, ceil);

A Floor: 4, Ceil: 4

B Floor: 2, Ceil: 6

C Floor: 1, Ceil: 8

D Floor: -1, Ceil: -1

💡 Hint

If the element is found, floor and ceil are both that element.

Since 4 is present in the array, both floor and ceil are 4.

Practice

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

easy

A. The smallest element strictly less than the number

B. The smallest element greater than or equal to the number

C. The average of all elements less than the number

D. The greatest element less than or equal to 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, others describe ceil or incorrect concepts.

3. Final Answer:

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

4. Quick Check:

   Floor = greatest ≤ number [OK]

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

Common Mistakes:

• Confusing floor with ceil
• Thinking floor is strictly less than number
• Mixing floor with average or median

2. Which of the following is the correct C syntax to find the middle index in binary search for array of size n?

easy

A. int mid = (0 + n) / 2;

B. int mid = 0 + n - 1 / 2;

C. int mid = (0 + (n - 1)) >> 1;

D. int mid = n / 2;

Solution

1. Step 1: Understand middle index calculation in binary search

   For array indices 0 to n-1, middle is (0 + n-1) / 2 or equivalent.

2. Step 2: Analyze options for correct syntax and efficiency

   int mid = (0 + (n - 1)) >> 1; uses bitwise right shift for division by 2, which is efficient and correct for integer mid calculation.

3. Final Answer:

   int mid = (0 + (n - 1)) >> 1; -> Option C

4. Quick Check:

   Mid = (start + end) >> 1 [OK]

Hint: Use (start + end) >> 1 for efficient mid calculation [OK]

Common Mistakes:

• Using n instead of n-1 as end index
• Forgetting parentheses causing wrong precedence
• Using floating division instead of integer

3. Given the sorted array arr = {1, 3, 5, 7, 9}, what is the floor of 6?

medium

A. 7

B. 5

C. 6

D. -1

Solution

1. Step 1: Identify elements less than or equal to 6

   Elements ≤ 6 are 1, 3, 5.

2. Step 2: Find greatest among these

   The greatest element ≤ 6 is 5.

3. Final Answer:

   5 -> Option B

4. Quick Check:

   Floor(6) = 5 [OK]

Hint: Floor is largest ≤ target in sorted array [OK]

Common Mistakes:

• Choosing 7 which is greater than 6
• Assuming floor equals the number if not present
• Returning -1 incorrectly when floor exists

4. Consider this code snippet to find ceil in a sorted array int ceil = -1; for(int i=0; i= x) { ceil = arr[i]; break; } }. What is the main issue?

medium

A. It may return wrong value if array is not sorted

B. It does not handle empty array

C. It returns first element ≥ x, which is correct for ceil

D. It finds floor instead of ceil

Solution

1. Step 1: Understand the code logic

   The code returns the first element in array ≥ x, which is correct if array is sorted.

2. Step 2: Identify assumptions and issues

   If array is not sorted, first element ≥ x may not be the smallest such element, so ceil is incorrect.

3. Final Answer:

   It may return wrong value if array is not sorted -> Option A

4. Quick Check:

   Ceil requires sorted array for correctness [OK]

Hint: Ceil logic needs sorted array to work correctly [OK]

Common Mistakes:

• Ignoring array sorting requirement
• Confusing ceil with floor
• Not checking for empty array before loop

5. You have a sorted array arr = {2, 4, 6, 8, 10}. If you want to find the ceil of 11 using binary search, what should be the returned value?

hard

A. -1

B. 11

C. 10

D. Error

Solution

1. Step 1: Understand ceil definition and array elements

   Ceil is smallest element ≥ target. Here, target is 11, which is greater than all elements.

2. Step 2: Check if any element ≥ 11 exists

   No element in array ≥ 11, so ceil does not exist, return -1.

3. Final Answer:

   -1 -> Option A

4. Quick Check:

   No element ≥ 11 means ceil = -1 [OK]

Hint: If target > max element, ceil is -1 (not found) [OK]

Common Mistakes:

• Returning last element as ceil incorrectly
• Returning target itself if not found
• Not handling no ceil case properly