int find_max_recursive(const vector<int>& nums, int left, int right) {
    if (left == right) {
        return nums[left];
    }

    int mid = left + (right - left) / 2;
    int left_max = find_max_recursive(nums, left, mid);
    int right_max = find_max_recursive(nums, mid + 1, right);

    return max(left_max, right_max);
}

int find_max(const vector<int>& nums) {
    if (nums.empty()) {
        throw invalid_argument("输入数组不能为空");
    }
    return find_max_recursive(nums, 0, nums.size() - 1);
}