
    Write a function to determine if a specific suspicious transaction pattern dominates the bank's transaction monitoring system. Given a sorted array of transaction frequencies across different locations and a particular transaction pattern frequency under investigation, determine if this pattern appears in more than half of all monitored transactions. The function should analyze the sorted frequency data and the total number of transactions to identify if the investigated pattern represents a majority occurrence, indicating a potential systematic security concern.
    

    
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):
    """
    Write a function to determine if a specific suspicious transaction pattern dominates the bank's transaction monitoring system. Given a sorted array of transaction frequencies across different locations and a particular transaction pattern frequency under investigation, determine if this pattern appears in more than half of all monitored transactions. The function should analyze the sorted frequency data and the total number of transactions to identify if the investigated pattern represents a majority occurrence, indicating a potential systematic security concern.
    

    """
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):
    """
    Write a function to determine if a specific suspicious transaction pattern dominates the bank's transaction monitoring system. Given a sorted array of transaction frequencies across different locations and a particular transaction pattern frequency under investigation, determine if this pattern appears in more than half of all monitored transactions. The function should analyze the sorted frequency data and the total number of transactions to identify if the investigated pattern represents a majority occurrence, indicating a potential systematic security concern.
    

    """
    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