
    Design a function for a social media content recommendation engine that determines if a specific type of user interaction dominates the engagement pattern. Given a sorted array of interaction frequencies and the total number of recorded interactions, determine if a particular interaction type accounts for more than half of all user activities. The function should help identify predominant user behaviors to optimize content recommendations and improve user experience.
    

    
def binary_search(arr, low, high, x):
    if high >= low:
        mid = (low + high) // 2
        if (mid == 0 or x > arr[mid - 1]) and arr[mid] == x:
            return mid
        elif x > arr[mid]:
            return binary_search(arr, mid + 1, high, x)
        else:
            return binary_search(arr, low, mid - 1, x)
    return -1

def is_majority(arr, n, x):
    """
    Design a function for a social media content recommendation engine that determines if a specific type of user interaction dominates the engagement pattern. Given a sorted array of interaction frequencies and the total number of recorded interactions, determine if a particular interaction type accounts for more than half of all user activities. The function should help identify predominant user behaviors to optimize content recommendations and improve user experience.
    

    """
def binary_search(arr, low, high, x):
    if high >= low:
        mid = (low + high) // 2
        if (mid == 0 or x > arr[mid - 1]) and arr[mid] == x:
            return mid
        elif x > arr[mid]:
            return binary_search(arr, mid + 1, high, x)
        else:
            return binary_search(arr, low, mid - 1, x)
    return -1

def is_majority(arr, n, x):
    """
    Design a function for a social media content recommendation engine that determines if a specific type of user interaction dominates the engagement pattern. Given a sorted array of interaction frequencies and the total number of recorded interactions, determine if a particular interaction type accounts for more than half of all user activities. The function should help identify predominant user behaviors to optimize content recommendations and improve user experience.
    

    """
    i = binary_search(arr, 0, n - 1, x)
    if i == -1:
        return False
    if i + n // 2 <= n - 1 and arr[i + n // 2] == x:
        return True
    else:
        return False