leetcode 169 Majority Element

题目描述：
Given an array of size n, 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.

找到这个数组中出现次数超过n/2次的元素，假设这个元素一定是存在的。
一个简单的方法就是排序后找中间的元素，代码如下：

class Solution {
public:
    int majorityElement(vector<int>& nums) {
        sort(nums.begin(), nums.end());
        return nums[nums.size() / 2];
    }

};

还有一种方法就是分而治之，每次将这个数组分为两半分别去找两边的主元素，若两边的主元素不同则利用count方法比较出现次数，时间复杂度略优

class Solution {
public:
    int majorityElement(vector<int>& nums) {
        return divideMajor(nums, 0, nums.size() - 1);
    }
    int divideMajor(vector<int>& nums, int begin, int end) {
        if (begin == end) {
            return nums[begin];
        }
        int leftM = divideMajor(nums, begin, (begin + end) / 2);
        int rightM = divideMajor(nums, (begin + end) / 2 + 1, end);
        if (leftM == rightM) {
            return leftM;
        }
        if (count(nums.begin() + begin, nums.begin() + end+1, leftM) < count(nums.begin() + begin, nums.begin() + end+1, rightM)) {
            return rightM;
        }
        else {
            return leftM;
        }
    }
};