Special Array With X Elements Greater Than or Equal X

Problem Description

You are given an array nums of non-negative integers. nums is considered special if there exists a number x such that there are exactly x numbers in nums that are greater than or equal to x. Notice that x does not have to be an element in nums. Return x if the array is special, otherwise, return -1. It can be proven that if nums is special, the value for x is unique.

Key Insights

• The problem requires identifying a number x such that exactly x elements in the array are greater than or equal to x.
• We can utilize sorting to simplify the problem by comparing values directly.
• The maximum possible value for x is constrained by the length of the array.

Space and Time Complexity

Time Complexity: O(n log n), where n is the length of the array (due to sorting).
Space Complexity: O(1), if we ignore the space used by the input array.

Solution

To solve this problem, we can follow these steps:

1. Sort the array nums.
2. Iterate through potential values of x from 0 to the length of nums.
3. Check how many elements are greater than or equal to each potential value of x using the sorted array.
4. If we find a value of x that matches the number of elements greater than or equal to it, we return that x.
5. If no such x exists, we return -1.

The algorithm primarily utilizes sorting to facilitate the comparison of elements against potential values of x.

Code Solutions