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

Challenge - 5 Problems

❓ Predict Output

intermediate

Find floor and ceil of 7 in a sorted array

What is the output of the following code that finds the floor and ceil of 7 in the sorted array [1, 3, 5, 7, 9, 11]?

DSA Javascript

function floorAndCeil(arr, x) {
  let floor = -1, ceil = -1;
  let left = 0, right = arr.length - 1;
  while (left <= right) {
    let mid = Math.floor((left + right) / 2);
    if (arr[mid] === x) {
      floor = arr[mid];
      ceil = arr[mid];
      break;
    } else if (arr[mid] < x) {
      floor = arr[mid];
      left = mid + 1;
    } else {
      ceil = arr[mid];
      right = mid - 1;
    }
  }
  return { floor, ceil };
}

console.log(floorAndCeil([1, 3, 5, 7, 9, 11], 7));

A {"floor":7,"ceil":7}

B {"floor":5,"ceil":9}

C {"floor":6,"ceil":8}

D {"floor":-1,"ceil":-1}

💡 Hint

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

Since 7 is present in the array, both floor and ceil are 7.

❓ Predict Output

intermediate

Floor and ceil for 8 in a sorted array

What is the output of the code that finds floor and ceil of 8 in the sorted array [2, 4, 6, 10, 12]?

DSA Javascript

function floorAndCeil(arr, x) {
  let floor = -1, ceil = -1;
  let left = 0, right = arr.length - 1;
  while (left <= right) {
    let mid = Math.floor((left + right) / 2);
    if (arr[mid] === x) {
      floor = arr[mid];
      ceil = arr[mid];
      break;
    } else if (arr[mid] < x) {
      floor = arr[mid];
      left = mid + 1;
    } else {
      ceil = arr[mid];
      right = mid - 1;
    }
  }
  return { floor, ceil };
}

console.log(floorAndCeil([2, 4, 6, 10, 12], 8));

A {"floor":6,"ceil":10}

B {"floor":10,"ceil":12}

C {"floor":8,"ceil":8}

D {"floor":4,"ceil":6}

💡 Hint

8 is not in the array, so floor and ceil are neighbors around 8.

Floor is the greatest element less than 8, which is 6. Ceil is the smallest element greater than 8, which is 10.

🧠 Conceptual

advanced

Floor and Ceil when element is smaller than all array elements

If you search for floor and ceil of 1 in the sorted array [3, 5, 7, 9], what will be the floor and ceil values?

A {"floor":3,"ceil":5}

B {"floor":1,"ceil":3}

C {"floor":-1,"ceil":3}

D {"floor":-1,"ceil":-1}

💡 Hint

Floor is the greatest element less than or equal to x. If none exists, floor is -1.

Since 1 is less than all elements, floor is -1 (no smaller or equal element), ceil is the smallest element 3.

🧠 Conceptual

advanced

Floor and Ceil when element is greater than all array elements

What are the floor and ceil of 20 in the sorted array [2, 4, 6, 8, 10]?

A {"floor":20,"ceil":20}

B {"floor":-1,"ceil":10}

C {"floor":8,"ceil":10}

D {"floor":10,"ceil":-1}

💡 Hint

Ceil is the smallest element greater than or equal to x. If none exists, ceil is -1.

20 is greater than all elements, so floor is the greatest element 10, ceil is -1 (no greater or equal element).

🔧 Debug

expert

Identify the error in floor and ceil implementation

What error will the following code produce when finding floor and ceil of 5 in [1, 2, 3, 4]?

DSA Javascript

function floorAndCeil(arr, x) {
  let floor = -1, ceil = -1;
  let left = 0, right = arr.length - 1;
  while (left < right) {
    let mid = Math.floor((left + right) / 2);
    if (arr[mid] === x) {
      floor = arr[mid];
      ceil = arr[mid];
      break;
    } else if (arr[mid] < x) {
      floor = arr[mid];
      left = mid + 1;
    } else {
      ceil = arr[mid];
      right = mid - 1;
    }
  }
  return { floor, ceil };
}

console.log(floorAndCeil([1, 2, 3, 4], 5));

A The code runs and returns { floor: -1, ceil: -1 }

B The code runs infinitely (infinite loop)

C The code runs and returns { floor: 3, ceil: 4 }

D The code runs and returns { floor: 4, ceil: -1 }

💡 Hint

Check the loop condition and how left and right pointers move.

The loop condition 'left < right' causes infinite loop when searching for a value greater than all elements because left and right pointers do not converge properly.

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 or equal to the number

C. The average of all elements less than the number

D. The smallest element strictly 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 with options

   The greatest element less than or equal to the number matches this definition exactly, while others describe ceil or incorrect 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
• Thinking floor must be strictly less than number
• Mixing floor with average or median

2. Which of the following is the correct JavaScript syntax to find the floor of a number x in a sorted array arr using binary search?

easy

A. Use Math.floor(x) directly on array

B. Use a for loop from 0 to arr.length and return first element greater than x

C. Use arr.indexOf(x) to find floor

D. Use a while loop with start = 0, end = arr.length - 1, update mid and check arr[mid] <= x

Solution

1. Step 1: Understand binary search for floor

   Binary search uses start and end pointers, calculates mid, and checks if arr[mid] <= x to move start or end accordingly.

2. Step 2: Evaluate options

   Use a while loop with start = 0, end = arr.length - 1, update mid and check arr[mid] <= x correctly describes binary search logic for floor. Options A, B, and C are incorrect or irrelevant.

3. Final Answer:

   Use a while loop with start=0, end=arr.length-1, update mid and check arr[mid] ≤ x -> Option D

4. Quick Check:

   Binary search with arr[mid] ≤ x finds floor [OK]

Hint: Binary search with arr[mid] ≤ x finds floor efficiently [OK]

Common Mistakes:

• Using linear search instead of binary search
• Using indexOf which only finds exact matches
• Misusing Math.floor which works on numbers, not arrays

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

const arr = [1, 3, 5, 7, 9];
function findFloor(arr, x) {
  let start = 0, end = arr.length - 1, floor = -1;
  while (start <= end) {
    let mid = Math.floor((start + end) / 2);
    if (arr[mid] <= x) {
      floor = arr[mid];
      start = mid + 1;
    } else {
      end = mid - 1;
    }
  }
  return floor;
}
console.log(findFloor(arr, 6));

medium

A. 6

B. 5

C. 7

D. -1

Solution

1. Step 1: Trace binary search for floor of 6

   Initial start=0, end=4, floor=-1. mid=2 (arr[2]=5) ≤ 6, floor=5, start=3. mid=3 (arr[3]=7) > 6, end=2. Loop ends.

2. Step 2: Return floor value

   Floor found is 5, which is the greatest element ≤ 6.

3. Final Answer:

   5 -> Option B

4. Quick Check:

   Floor of 6 in [1,3,5,7,9] is 5 [OK]

Hint: Floor is last arr[mid] ≤ x during binary search [OK]

Common Mistakes:

• Returning mid index instead of value
• Confusing floor with ceil
• Not updating floor variable correctly

4. Identify the bug in this JavaScript function to find the ceil of a number x in a sorted array arr:

function findCeil(arr, x) {
  let start = 0, end = arr.length - 1, ceil = -1;
  while (start <= end) {
    let mid = Math.floor((start + end) / 2);
    if (arr[mid] >= x) {
      ceil = arr[mid];
      end = mid + 1;
    } else {
      start = mid + 1;
    }
  }
  return ceil;
}

medium

A. The line end = mid + 1; should be end = mid - 1;

B. The line start = mid + 1; should be start = mid - 1;

C. The initial value of ceil should be 0 instead of -1

D. The while loop condition should be start < end instead of start <= end

Solution

1. Step 1: Analyze binary search update for ceil

   When arr[mid] ≥ x, we update ceil and must move end to mid - 1 to search left side for smaller ceil.

2. Step 2: Identify incorrect update

   The code incorrectly sets end = mid + 1, which moves end right, causing infinite loop or wrong result.

3. Final Answer:

   The line end = mid + 1; should be end = mid - 1; -> Option A

4. Quick Check:

   For ceil, move end left with end = mid - 1 [OK]

Hint: For ceil, move end left; for floor, move start right [OK]

Common Mistakes:

• Moving end pointer in wrong direction
• Confusing ceil logic with floor
• Incorrect initial ceil value

5. Given a sorted array arr = [2, 4, 6, 8, 10], write a function to find both floor and ceil of a number x. What will be the floor and ceil of x = 5?

hard

A. Floor = 5, Ceil = 5

B. Floor = 6, Ceil = 4

C. Floor = 4, Ceil = 6

D. Floor = 2, Ceil = 10

Solution

1. Step 1: Understand floor and ceil definitions

   Floor is greatest element ≤ x, ceil is smallest element ≥ x.

2. Step 2: Find floor and ceil for x=5 in arr

   Elements ≤ 5 are 2 and 4; greatest is 4 (floor). Elements ≥ 5 are 6, 8, 10; smallest is 6 (ceil).

3. Final Answer:

   Floor = 4, Ceil = 6 -> Option C

4. Quick Check:

   Floor ≤ 5 = 4, Ceil ≥ 5 = 6 [OK]

Hint: Floor ≤ x max, Ceil ≥ x min in sorted array [OK]

Common Mistakes:

• Swapping floor and ceil values
• Assuming floor or ceil equals x if not present
• Choosing wrong boundary elements