Check If a Number Is Majority Element in a Sorted Array

Check If a Number Is Majority Element in a Sorted Array - Problem

Given an integer array nums sorted in non-decreasing order and an integer target, return true if target is a majority element, or false otherwise.

A majority element in an array nums is an element that appears more than nums.length / 2 times in the array.

Input & Output

Example 1 — Target is Majority

$ Input: nums = [2,4,5,5,5,5,5,6,6], target = 5

› Output: true

💡 Note: Target 5 appears 5 times in array of length 9. Since 5 > 9/2 (which is 4), target 5 is a majority element.

Example 2 — Target is Not Majority

$ Input: nums = [10,100,101,101], target = 101

› Output: false

💡 Note: Target 101 appears 2 times in array of length 4. Since 2 ≤ 4/2 (which is 2), target 101 is not a majority element.

Example 3 — Target Not Found

$ Input: nums = [1,1,2,2], target = 3

› Output: false

💡 Note: Target 3 does not appear in the array, so it cannot be a majority element.

Constraints

1 ≤ nums.length ≤ 1000
-10⁹ ≤ nums[i], target ≤ 10⁹
nums is sorted in non-decreasing order

Visualization

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Asked in

G Google 15 M Microsoft 12 A Amazon 8

The key insight is that since the array is sorted, we can use binary search to efficiently find the first and last occurrence of the target. Best approach is Binary Search with Time: O(log n), Space: O(1). For unsorted arrays, we'd need O(n) linear counting.

Common Approaches

✓ Optimized

⏱️ Time: N/A Space: N/A

Binary Search Bounds

⏱️ Time: O(log n) Space: O(1)

Use binary search to find the leftmost and rightmost positions of the target. The count equals (right - left + 1). This leverages the sorted property of the array.

Linear Count

⏱️ Time: O(n) Space: O(1)

Iterate through the array and count how many times the target appears. Check if count is greater than nums.length / 2.

Algorithm Steps — Algorithm Steps

Code -

solution.c — C

Time & Space Complexity

Time Complexity

⏱️

⚡ Linearithmic

Space Complexity

✓ Linear Space

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Medium Frequency

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Smart Actions

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