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

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of floor and ceil search for a value in a sorted array

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

DSA Java

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

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

    public static void main(String[] args) {
        int[] arr = {1, 3, 5, 6, 8, 9};
        int x = 7;
        System.out.println("Floor: " + floor(arr, x));
        System.out.println("Ceil: " + ceil(arr, x));
    }
}

A {"Floor":6,"Ceil":8}

B {"Floor":5,"Ceil":6}

C {"Floor":7,"Ceil":7}

D {"Floor":8,"Ceil":9}

💡 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 in the array is 6 (largest number less than 7), and the ceil is 8 (smallest number greater than 7).

🧠 Conceptual

intermediate

Understanding floor and ceil in sorted arrays

In a sorted array, what does the 'floor' of a value x represent?

A The smallest element greater than x

B The average of all elements less than x

C The exact element x if present, otherwise -1

D The largest element less than or equal to x

💡 Hint

Floor is about the closest smaller or equal value to x.

Floor of x is the greatest element in the array that is less than or equal to x.

🔧 Debug

advanced

Identify the error in floor function implementation

What error will occur when running this floor function on array {2,4,6,8} with x=1?

DSA Java

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

A Throws ArrayIndexOutOfBoundsException

B Returns -1 indicating no floor found

C Returns 2 incorrectly as floor

D Infinite loop occurs

💡 Hint

Check what happens if x is smaller than all elements.

Since 1 is smaller than all elements, no floor exists, so function returns -1.

❓ Predict Output

advanced

Output of floor and ceil for value present in array

What is the output of the following code for x=5 in array {1,3,5,7,9}?

DSA Java

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

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

    public static void main(String[] args) {
        int[] arr = {1, 3, 5, 7, 9};
        int x = 5;
        System.out.println("Floor: " + floor(arr, x));
        System.out.println("Ceil: " + ceil(arr, x));
    }
}

A {"Floor":5,"Ceil":5}

B {"Floor":3,"Ceil":7}

C {"Floor":1,"Ceil":9}

D {"Floor":-1,"Ceil":-1}

💡 Hint

If x is present, floor and ceil should be x itself.

Since 5 is in the array, both floor and ceil return 5.

🚀 Application

expert

Find number of elements within a range using floor and ceil

Given a sorted array, how can you find the count of elements between two values low and high (inclusive) using floor and ceil functions?

A Count = index of ceil(high) - index of floor(low) + 1

B Count = index of ceil(high) - index of ceil(low) + 1

C Count = index of floor(high) - index of ceil(low) + 1

D Count = index of floor(high) - index of floor(low) + 1

💡 Hint

Think about the positions of floor and ceil relative to the range boundaries.

The count of elements in [low, high] is the difference between indices of floor(high) and ceil(low) plus one.

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