Floor and Ceil in Sorted Array in DSA C++ - Interactive Practice

Practice - 5 Tasks

1fill in blank

easy

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

DSA C++

int floorIndex(const vector<int>& arr, int x) {
    int low = 0, high = arr.size() - 1;
    int result = -1;
    while (low <= high) {
        int mid = low + (high - low) / 2;
        if (arr[mid] == x) {
            return mid;
        } else if (arr[mid] [1] x) {
            result = mid;
            low = mid + 1;
        } else {
            high = mid - 1;
        }
    }
    return result;
}

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

A>

B>=

C<

D<=

Attempts:

3 left

💡 Hint

Common Mistakes

Using '>' instead of '<=' causes missing correct floor values.

Not updating result when arr[mid] <= x.

We want to find the floor, so if arr[mid] is less than or equal to x, we update result and move right.

2fill in blank

medium

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

DSA C++

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

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

A>

B>=

C<=

D<

Attempts:

3 left

💡 Hint

Common Mistakes

Using '<' instead of '>' causes wrong ceil index.

Not updating result when arr[mid] >= x.

For ceil, if arr[mid] is greater than or equal to x, we update result and move left. Here, '>' is used to check if arr[mid] is strictly greater than x.

3fill in blank

hard

Fix the error in the binary search condition to correctly find the floor index.

DSA C++

int floorIndex(const vector<int>& arr, int x) {
    int low = 0, high = arr.size() - 1;
    int result = -1;
    while (low <= high) {
        int mid = low + (high - low) / 2;
        if (arr[mid] == x) {
            return mid;
        } else if (arr[mid] [1] x) {
            result = mid;
            low = mid + 1;
        } else {
            high = mid - 1;
        }
    }
    return result;
}

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

A<=

B>

C<

D>=

Attempts:

3 left

💡 Hint

Common Mistakes

Using '>' causes skipping valid floor elements.

Not updating result when arr[mid] <= x.

The condition must be arr[mid] <= x to find the floor correctly.

4fill in blank

hard

Fill both blanks to complete the code that finds floor and ceil indices in a sorted array.

DSA C++

pair<int, int> floorAndCeil(const vector<int>& arr, int x) {
    int low = 0, high = arr.size() - 1;
    int floor = -1, ceil = -1;
    while (low <= high) {
        int mid = low + (high - low) / 2;
        if (arr[mid] == x) {
            floor = mid;
            ceil = mid;
            break;
        } else if (arr[mid] [1] x) {
            floor = mid;
            low = mid + 1;
        } else {
            ceil = mid;
            high = mid - 1;
        }
    }
    return {floor, ceil};
}

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

A<=

B>

C<

D>=

Attempts:

3 left

💡 Hint

Common Mistakes

Swapping floor and ceil conditions.

Not updating floor or ceil indices properly.

For floor, use '<=' to move right and update floor. For ceil, use '>' to move left and update ceil.

5fill in blank

hard

Fill all three blanks to complete the code that returns a map of floor and ceil values for each query in a sorted array.

DSA C++

map<int, pair<int, int>> floorAndCeilForQueries(const vector<int>& arr, const vector<int>& queries) {
    map<int, pair<int, int>> result;
    for (int q : queries) {
        int low = 0, high = arr.size() - 1;
        int floor = -1, ceil = -1;
        while (low <= high) {
            int mid = low + (high - low) / 2;
            if (arr[mid] == q) {
                floor = mid;
                ceil = mid;
                break;
            } else if (arr[mid] [1] q) {
                floor = mid;
                low = mid + 1;
            } else {
                ceil = mid;
                high = mid - 1;
            }
        }
        result[q] = {arr[2], arr[3];
    }
    return result;
}

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

A<=

B[floor]

C[ceil]

D>

Attempts:

3 left

💡 Hint

Common Mistakes

Using wrong comparison operators.

Accessing arr with wrong indices or missing brackets.

Use '<=' for floor condition. Use floor and ceil indices to access arr elements for values.

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 given number.

2. Step 2: Compare options with definition

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

Common Mistakes:

• Confusing floor with ceil
• Choosing smallest element greater than number
• Thinking floor is average or exact match only

2. Which of the following is the correct C++ function signature to find the floor of a number in a sorted array?

easy

A. int findFloor(int arr[], int n, int x);

B. void findFloor(int arr[], int n, int x);

C. int findFloor(int arr, int n, int x);

D. int findFloor(int arr[], int x);

Solution

1. Step 1: Analyze function parameters

   The function needs the array, its size, and the target number to find floor.

2. Step 2: Check each option's signature

   int findFloor(int arr[], int n, int x); correctly uses array pointer, size, and target number. void findFloor(int arr[], int n, int x); returns void which is incorrect. int findFloor(int arr, int n, int x); uses int arr instead of array. int findFloor(int arr[], int x); misses size parameter.

3. Final Answer:

   int findFloor(int arr[], int n, int x); -> Option A

4. Quick Check:

   Correct signature includes array, size, target [OK]

Hint: Function needs array, size, and target number [OK]

Common Mistakes:

• Omitting array size parameter
• Using wrong array type
• Returning void instead of int

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

int arr[] = {1, 3, 5, 7, 9};
int n = 5;
int x = 6;
int floor = -1;
for (int i = 0; i < n; i++) {
  if (arr[i] <= x) floor = arr[i];
  else break;
}
std::cout << floor;

medium

A. 6

B. 7

C. 5

D. -1

Solution

1. Step 1: Trace the loop and condition

   Loop checks each element ≤ 6. Elements 1, 3, 5 satisfy condition, floor updates to 5. When arr[i] = 7, condition fails and loop breaks.

2. Step 2: Determine final floor value

   Floor remains 5 after loop ends.

3. Final Answer:

   5 -> Option C

4. Quick Check:

   Floor of 6 in array = 5 [OK]

Hint: Floor is last element ≤ target before break [OK]

Common Mistakes:

• Choosing 6 which is not in array
• Choosing 7 which is > 6
• Not updating floor correctly

4. Find the error in the following code to find the ceil of a number in a sorted array:

int findCeil(int arr[], int n, int x) {
  int ceil = -1;
  for (int i = 0; i < n; i++) {
    if (arr[i] >= x) {
      ceil = arr[i];
    }
  }
  return ceil;
}

medium

A. It uses wrong comparison operator

B. It returns -1 even if ceil exists

C. It should return floor instead of ceil

D. It does not return the smallest element ≥ x

Solution

1. Step 1: Understand the loop logic

   The loop updates ceil whenever arr[i] ≥ x, but does not stop or check for smallest such element.

2. Step 2: Identify the error

   Because it keeps updating, it ends with the last element ≥ x, not the smallest. It should break or track minimum.

3. Final Answer:

   It does not return the smallest element ≥ x -> Option D

4. Quick Check:

   Ceil = smallest ≥ x, code returns largest ≥ x [OK]

Hint: Ceil must be smallest ≥ target, not last found [OK]

Common Mistakes:

• Not breaking loop after first valid ceil
• Updating ceil without checking if smaller
• Confusing floor and ceil logic

5. Given a sorted array arr = {2, 4, 6, 8, 10}, what are the floor and ceil of x = 5? Choose the correct pair.

hard

A. Floor = 5, Ceil = 6

B. Floor = 4, Ceil = 6

C. Floor = 4, Ceil = 5

D. Floor = 6, Ceil = 8

Solution

1. Step 1: Find floor of 5 in array

   Floor is greatest element ≤ 5. Elements ≤ 5 are 2 and 4, greatest is 4.

2. Step 2: Find ceil of 5 in array

   Ceil is smallest element ≥ 5. Elements ≥ 5 are 6, 8, 10, smallest is 6.

3. Final Answer:

   Floor = 4, Ceil = 6 -> Option B

4. Quick Check:

   Floor ≤ 5 = 4, Ceil ≥ 5 = 6 [OK]

Hint: Floor ≤ x, Ceil ≥ x; pick closest elements [OK]

Common Mistakes:

• Assuming floor or ceil must equal x
• Choosing elements not in array
• Mixing floor and ceil values