Floor and Ceil in Sorted Array in DSA Java - Interactive Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to find the floor value in a sorted array.

DSA Java

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

Drag options to blanks, or click blank then click option'

Ahigh - 1

Bmid - 1

Clow + 1

Dmid + 1

Attempts:

3 left

💡 Hint

Common Mistakes

Setting low to mid - 1 causes infinite loop or wrong search direction.

When arr[mid] is less than x, we move the low pointer to mid + 1 to search the right half.

2fill in blank

medium

Complete the code to find the ceil value in a sorted array.

DSA Java

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

Drag options to blanks, or click blank then click option'

Amid - 1

Bmid + 1

Clow - 1

Dhigh + 1

Attempts:

3 left

💡 Hint

Common Mistakes

Setting high to mid + 1 causes wrong search direction.

When arr[mid] is greater than x, we update high to mid - 1 to search the left half.

3fill in blank

hard

Fix the error in the binary search loop condition to avoid infinite loops.

DSA Java

while ([1]) {
    int mid = low + (high - low) / 2;
    if (arr[mid] == x) {
        return arr[mid];
    } else if (arr[mid] < x) {
        low = mid + 1;
    } else {
        high = mid - 1;
    }
}

Drag options to blanks, or click blank then click option'

Alow <= high

Blow > high

Clow < high

Dlow == high

Attempts:

3 left

💡 Hint

Common Mistakes

Using low < high misses checking the last element.

The loop should continue while low is less than or equal to high to cover all elements.

4fill in blank

hard

Complete the code to find the floor index (largest index where arr[index] <= x) in a sorted array.

DSA Java

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

Drag options to blanks, or click blank then click option'

Alow + 1

Bmid - 1

Cmid + 1

Dhigh - 1

Attempts:

3 left

💡 Hint

Common Mistakes

Setting low = mid causes infinite loop.

Setting low = mid - 1 searches wrong direction.

When arr[mid] <= x, update ans to mid and search right half by setting low = mid + 1 to find larger index.

5fill in blank

hard

Complete the code to find the ceil index (smallest index where arr[index] >= x) in a sorted array.

DSA Java

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

Drag options to blanks, or click blank then click option'

Amid + 1

Bmid - 1

Clow - 1

Dhigh + 1

Attempts:

3 left

💡 Hint

Common Mistakes

Setting high = mid + 1 causes wrong search direction.

When arr[mid] >= x, update ans to mid and search left half by setting high = mid - 1 to find smaller index.

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