1287. Element Appearing More Than 25% In Sorted Array

Time: O(n)

Space: O(1)

Intuition

In a sorted array, the element appearing more than 25% of the time must be among the elements at indices n/4, n/2, 3n/4. Check those candidates.

Algorithm

1Candidates: arr[n/4], arr[n/2], arr[3n/4].
2For each candidate: count occurrences using binary search. If count > n/4, return it.

Common Pitfalls

•Array is sorted so binary search works. The dominant element must appear at one of those three index positions.

1287.cs

// Approach: In a sorted array the element appearing > 25% must equal its neighbor at index+n/4; check each candidate.
// Time: O(n) Space: O(1)

public class Solution
{
    public int FindSpecialInteger(int[] arr)
    {
        int n = arr.Length;
        int quarter = n / 4;

        for (int i = 0; i < n - quarter; ++i)
        {
            if (arr[i] == arr[i + quarter])
                return arr[i];
        }

        throw new ArgumentException();
    }
}

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