Floor and Ceil in Sorted Array in DSA Java - 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 complexity to O(log n).

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 The greatest element less than or equal to the number

B The first element in the array

C The average of all elements less than the number

D The smallest element greater than or equal to the number

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

What is the time complexity of finding floor or ceil using binary search in a sorted array?

A O(log n)

B O(n log n)

C O(n)

D O(1)

Binary search reduces the search space by half each step, resulting in O(log n) time.

If the target number is exactly equal to an element in the array, what are floor and ceil?

A Floor is smaller element, ceil is larger element

B Both floor and ceil are that element

C Floor and ceil do not exist

D Floor is the first element, ceil is the last element

When the target matches an element, floor and ceil are that element itself.

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

A The smallest element

B The largest element

C No floor exists

D The middle element

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

Which search method is best to find floor and ceil in a sorted array?

A Linear search

B Bubble sort

C Depth-first search

D Binary search

Binary search efficiently finds floor and ceil in O(log n) time.

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

Think about how to move left or right in the array to find closest smaller or larger elements.

Describe what happens when the target number is outside the range of the sorted array elements for floor and ceil.

Consider the smallest and largest elements in the array.

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 number.

2. Step 2: Compare options with definition

   The greatest element less than or equal to the number matches the definition exactly, others 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 ≤ target, pick greatest such element [OK]

Common Mistakes:

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

2. Which of the following is the correct Java method signature to find the floor of a number in a sorted integer array?

easy

A. int findFloor(int arr[], target)

B. public int findFloor(int[] arr, int target, int size)

C. static int findFloor(int[] arr, int target) throws Exception

D. public static int findFloor(int[] arr, int target)

Solution

1. Step 1: Check Java method signature syntax

   Java methods must specify access modifier, return type, method name, and parameter types.

2. Step 2: Validate each option

   public static int findFloor(int[] arr, int target) is correct: public static int findFloor(int[] arr, int target). int findFloor(int arr[], target) misses access modifier and parameter type for target. static int findFloor(int[] arr, int target) throws Exception unnecessarily throws Exception. public int findFloor(int[] arr, int target, int size) has extra parameter 'size' not needed.

3. Final Answer:

   public static int findFloor(int[] arr, int target) -> Option D

4. Quick Check:

   Correct Java method signature = public static int findFloor(int[] arr, int target) [OK]

Hint: Java method needs access modifier, return type, parameters [OK]

Common Mistakes:

• Omitting access modifier
• Missing parameter types
• Adding unnecessary throws clause

3. Given the sorted array int[] arr = {1, 3, 5, 7, 9} and target = 6, what is the floor and ceil of 6?

medium

A. Floor = 7, Ceil = 9

B. Floor = 3, Ceil = 5

C. Floor = 5, Ceil = 7

D. Floor = 6, Ceil = 6

Solution

1. Step 1: Identify floor of 6 in array

   Floor is greatest element ≤ 6. Elements ≤ 6 are 1, 3, 5. Greatest is 5.

2. Step 2: Identify ceil of 6 in array

   Ceil is smallest element ≥ 6. Elements ≥ 6 are 7, 9. Smallest is 7.

3. Final Answer:

   Floor = 5, Ceil = 7 -> Option C

4. Quick Check:

   Floor ≤ 6 = 5, Ceil ≥ 6 = 7 [OK]

Hint: Floor ≤ target, ceil ≥ target; pick closest values [OK]

Common Mistakes:

• Choosing floor greater than target
• Choosing ceil less than target
• Assuming target must be in array

4. Consider this Java method to find floor in a sorted array:

public static int findFloor(int[] arr, int target) {
    int low = 0, high = arr.length - 1;
    int floor = -1;
    while (low <= high) {
        int mid = (low + high) / 2;
        if (arr[mid] == target) return arr[mid];
        else if (arr[mid] < target) {
            floor = arr[mid];
            low = mid + 1;
        } else {
            high = mid - 1;
        }
    }
    return floor;
}

What is the bug if the array is empty?

medium

A. Returns -1 correctly as floor does not exist

B. Throws ArrayIndexOutOfBoundsException at mid calculation

C. Returns 0 incorrectly as floor

D. Infinite loop occurs

Solution

1. Step 1: Analyze behavior with empty array

   If array is empty, arr.length = 0, so high = -1. Condition low <= high is false initially, so loop never runs.

2. Step 2: Check return value when loop doesn't run

   Variable floor initialized to -1 and returned as is, indicating no floor found.

3. Final Answer:

   Returns -1 correctly as floor does not exist -> Option A

4. Quick Check:

   Empty array returns -1 floor [OK]

Hint: Check loop condition before accessing array [OK]

Common Mistakes:

• Assuming mid calculation causes error on empty array
• Expecting exception instead of -1 return
• Missing initialization of floor variable

5. You have a sorted array int[] arr = {2, 4, 6, 8, 10}. You want to find the floor and ceil for target = 1 and target = 11. What are the correct floor and ceil values for these targets?

hard

A. For 1: Floor = -1, Ceil = 2; For 11: Floor = -1, Ceil = -1

B. For 1: Floor = -1, Ceil = 2; For 11: Floor = 10, Ceil = -1

C. For 1: Floor = -1, Ceil = -1; For 11: Floor = 10, Ceil = 10

D. For 1: Floor = 2, Ceil = -1; For 11: Floor = -1, Ceil = 10

Solution

1. Step 1: Find floor and ceil for target = 1

   Floor is greatest element ≤ 1. No elements ≤ 1, so floor = -1 (not found). Ceil is smallest element ≥ 1, which is 2.

2. Step 2: Find floor and ceil for target = 11

   Floor is greatest element ≤ 11, which is 10. Ceil is smallest element ≥ 11, none exists, so ceil = -1.

3. Final Answer:

   For 1: Floor = -1, Ceil = 2; For 11: Floor = 10, Ceil = -1 -> Option B

4. Quick Check:

   Floor and ceil outside array bounds handled with -1 [OK]

Hint: Floor or ceil missing means return -1 for that value [OK]

Common Mistakes:

• Returning array ends incorrectly as floor or ceil
• Confusing floor and ceil for out-of-bound targets
• Assuming floor or ceil always exists