# Majority Element

`Array`

Easy

Given an array of sizen, find the majority element. The majority element is the element that appears **more than** `⌊ n/2 ⌋`times.

You may assume that the array is non-empty and the majority element always exist in the array.

**Example 1:**

```
Input:
 [3,2,3]

Output:
 3
```

**Example 2:**

```
Input:
 [2,2,1,1,1,2,2]

Output:
 2
```

## Solution

### Approach 1: HashMap <a href="#approach-2-hashmap" id="approach-2-hashmap"></a>

We can use a HashMap that maps elements to counts in order to count occurrences in linear time by looping over nums. Then, we simply return the key with maximum value.

* Time complexity: O(n)
* Space complexity : O(n)

```java
class Solution {
    private Map<Integer, Integer> countNums(int[] nums) {
        Map<Integer, Integer> counts = new HashMap<Integer, Integer>();
        for (int num : nums) {
            if (!counts.containsKey(num)) {
                counts.put(num, 1);
            }
            else {
                counts.put(num, counts.get(num)+1);
            }
        }
        return counts;
    }

    public int majorityElement(int[] nums) {
        Map<Integer, Integer> counts = countNums(nums);

        Map.Entry<Integer, Integer> majorityEntry = null;
        for (Map.Entry<Integer, Integer> entry : counts.entrySet()) {
            if (majorityEntry == null || entry.getValue() > majorityEntry.getValue()) {
                majorityEntry = entry;
            }
        }

        return majorityEntry.getKey();
    }
}
```

### Approach 2: Sorting <a href="#approach-3-sorting" id="approach-3-sorting"></a>

If the elements are sorted in monotonically increasing (or decreasing) order, the majority element can be found at index ⌊ n / 2 ⌋ (and ⌊ n / 2 ⌋ + 1, incidentally, if n is even).

* Time complexity :  O(nlgn)  Sorting the array costs O(nlgn) time in Python and Java, so it dominates the overall runtime.&#x20;
* Space complexity :  O(1) or (O(n))  We sorted nums in place here - if that is not allowed, then we must spend linear additional space on a copy of nums and sort the copy instead.&#x20;

```java
class Solution {
    public int majorityElement(int[] nums) {
        Arrays.sort(nums);
        return nums[nums.length/2];
    }
}
```

### Approach 3: Boyer-Moore Voting Algorithm

> If we had some way of counting instances of the majority element as +1 and instances of any other element as −1, summing them would make it obvious that the majority element is indeed the majority element.

**Complexity Analysis**

* Time complexity :O(n)

  Boyer-Moore performs constant work exactlynntimes, so the algorithm runs in linear time.
* Space complexity :O(1)

  Boyer-Moore allocates only constant additional memory.

```java
class Solution {
    public int majorityElement(int[] nums) {
        int count = 0;
        Integer candidate = null;

        for (int num : nums) {
            if (count == 0) {
                candidate = num;
            }
            count += (num == candidate) ? 1 : -1;
        }

        return candidate;
    }
}
```

## Reference

<https://leetcode.com/problems/majority-element/solution/>