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1150. Check If a Number Is Majority Element in a Sorted Array

Description

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.

 

Example 1:

Input: nums = [2,4,5,5,5,5,5,6,6], target = 5
Output: true
Explanation: The value 5 appears 5 times and the length of the array is 9.
Thus, 5 is a majority element because 5 > 9/2 is true.

Example 2:

Input: nums = [10,100,101,101], target = 101
Output: false
Explanation: The value 101 appears 2 times and the length of the array is 4.
Thus, 101 is not a majority element because 2 > 4/2 is false.

 

Constraints:

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

Solutions

Solution 1: Binary Search

We notice that the elements in the array $nums$ are non-decreasing, that is, the elements in the array $nums$ are monotonically increasing. Therefore, we can use the method of binary search to find the index $left$ of the first element in the array $nums$ that is greater than or equal to $target$, and the index $right$ of the first element in the array $nums$ that is greater than $target$. If $right - left > \frac{n}{2}$, it means that the number of occurrences of the element $target$ in the array $nums$ exceeds half of the length of the array, so return $true$, otherwise return $false$.

The time complexity is $O(\log n)$, and the space complexity is $O(1)$. Here, $n$ is the length of the array $nums$.

Solution 2: Binary Search (Optimized)

In Solution 1, we used binary search twice to find the index $left$ of the first element in the array $nums$ that is greater than or equal to $target$, and the index $right$ of the first element in the array $nums$ that is greater than $target$. However, we can use binary search once to find the index $left$ of the first element in the array $nums$ that is greater than or equal to $target$, and then judge whether $nums[left + \frac{n}{2}]$ is equal to $target$. If they are equal, it means that the number of occurrences of the element $target$ in the array $nums$ exceeds half of the length of the array, so return $true$, otherwise return $false$.

The time complexity is $O(\log n)$, and the space complexity is $O(1)$. Here, $n$ is the length of the array $nums$.

  • class Solution {
    public boolean isMajorityElement(int[] nums, int target) {
        int left = search(nums, target);
        int right = search(nums, target + 1);
        return right - left > nums.length / 2;
    }

    private int search(int[] nums, int x) {
        int left = 0, right = nums.length;
        while (left < right) {
            int mid = (left + right) >> 1;
            if (nums[mid] >= x) {
                right = mid;
            } else {
                left = mid + 1;
            }
        }
        return left;
    }
}

  • class Solution {
public:
    bool isMajorityElement(vector<int>& nums, int target) {
        auto left = lower_bound(nums.begin(), nums.end(), target);
        auto right = upper_bound(nums.begin(), nums.end(), target);
        return right - left > nums.size() / 2;
    }
};

  • class Solution:
    def isMajorityElement(self, nums: List[int], target: int) -> bool:
        left = bisect_left(nums, target)
        right = bisect_right(nums, target)
        return right - left > len(nums) // 2


  • func isMajorityElement(nums []int, target int) bool {
	left := sort.SearchInts(nums, target)
	right := sort.SearchInts(nums, target+1)
	return right-left > len(nums)/2
}

  • function isMajorityElement(nums: number[], target: number): boolean {
    const search = (x: number) => {
        let left = 0;
        let right = nums.length;
        while (left < right) {
            const mid = (left + right) >> 1;
            if (nums[mid] >= x) {
                right = mid;
            } else {
                left = mid + 1;
            }
        }
        return left;
    };
    const left = search(target);
    const right = search(target + 1);
    return right - left > nums.length >> 1;
}

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