The provided code is a C++ function that computes the...

The provided code is a C++ function that computes the floor and ceil of a given integer x from a given array arr. However, the implementation has errors and does not work correctly as intended. Here's what the provided code attempts to do:

Function Explanation

• Inputs:

  • x: An integer for which we want to find the floor and ceiling values.
  • arr: A reference to a vector of integers, representing the array to search.

• Outputs:

  • Returns a vector of two integers: {floor, ceil}.
    • floor: The largest element in arr that is less than or equal to x.
    • ceil: The smallest element in arr that is greater than or equal to x.

• Logic:

  • The code initializes two variables:
    • ans1 (for the floor) as INT_MIN (the smallest possible integer value).
    • ans2 (for the ceiling) as INT_MAX (the largest possible integer value).
  • Iterates through all elements of the array arr:
    • If the current element is less than or equal to x, it updates ans1 (floor) to the current value.
    • If the current element is greater than x, it updates ans2 (ceiling) to the current value.
  • Finally, the function returns {ans1, ans2}.

Issues in the Code

1. The floor and ceil calculations are incomplete:

   • For the floor (ans1), to get the largest value less than or equal to x, you need an additional condition to check whether the current value improves upon the existing ans1 (i.e., arr[i] > ans1).
   • Similarly, for the ceiling (ans2), to find the smallest element greater than or equal to x, you need to check whether the current value improves upon the existing ans2 (i.e., arr[i] < ans2).

2. The function does not handle cases where there is no valid floor or ceiling:

   • For instance, if x is smaller than all elements in the array, the floor should not exist (e.g., it might need to return INT_MIN or some sentinel value).
   • Similarly, if x is larger than all elements, the ceiling should not exist.

3. Logic bug in ceiling update:

   • The ceiling update only checks for values greater than x (if (arr[i] > x)), but it should also account for values equal to x.

Fixed Code

class Solution {
  public:
    vector<int> getFloorAndCeil(int x, vector<int> &arr) {
        int ans1 = INT_MIN; // Floor
        int ans2 = INT_MAX; // Ceiling

        for (int i = 0; i < arr.size(); i++) {
            // Update floor if the element is <= x and closer to x
            if (arr[i] <= x && arr[i] > ans1) {
                ans1 = arr[i];
            }

            // Update ceiling if the element is >= x and closer to x
            if (arr[i] >= x && arr[i] < ans2) {
                ans2 = arr[i];
            }
        }

        // Handle cases where floor or ceiling does not exist
        if (ans1 == INT_MIN) ans1 = -1; // No floor
        if (ans2 == INT_MAX) ans2 = -1; // No ceiling

        return {ans1, ans2}; // Return floor and ceiling
    }
};

Explanation of Changes

1. Added conditions to ensure ans1 (floor) and ans2 (ceiling) are updated correctly based on the requirements of being closer to x.
2. Handled cases where no valid floor or ceiling is found by returning -1 (or an alternative value).

Example

Input:

x = 5;
arr = {1, 3, 6, 8, 10};

Output:

Floor = 3
Ceiling = 6
Result = {3, 6}

Input:

x = 4;
arr = {1, 2, 3};

Output:

Floor = 3
Ceiling = -1 (no element >= 4)
Result = {3, -1}