
    In a patient's comprehensive prescription history, determine if a specific medication poses a potential overmedication risk by checking if it constitutes a majority of their prescriptions. Given a chronologically sorted list of medication IDs from all healthcare providers, the total count of prescriptions, and a specific medication ID to investigate, write a function that identifies whether this medication appears in more than half of all prescriptions. This analysis is crucial for identifying possible medication dependencies or prescription overlaps across multiple providers.
    

    
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):
    """
    In a patient's comprehensive prescription history, determine if a specific medication poses a potential overmedication risk by checking if it constitutes a majority of their prescriptions. Given a chronologically sorted list of medication IDs from all healthcare providers, the total count of prescriptions, and a specific medication ID to investigate, write a function that identifies whether this medication appears in more than half of all prescriptions. This analysis is crucial for identifying possible medication dependencies or prescription overlaps across multiple providers.
    

    """
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):
    """
    In a patient's comprehensive prescription history, determine if a specific medication poses a potential overmedication risk by checking if it constitutes a majority of their prescriptions. Given a chronologically sorted list of medication IDs from all healthcare providers, the total count of prescriptions, and a specific medication ID to investigate, write a function that identifies whether this medication appears in more than half of all prescriptions. This analysis is crucial for identifying possible medication dependencies or prescription overlaps across multiple providers.
    

    """
    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