
    In a bank's fraud detection system, write a function to determine if a specific transaction amount represents a dominant pattern in a sequence of sorted transaction values. Given a sorted array of transaction amounts, the total number of transactions, and a target transaction value, determine if this specific amount appears in more than half of all transactions within the monitoring window. This pattern recognition is crucial for identifying potential coordinated fraudulent activities across multiple accounts.
    

    
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 bank's fraud detection system, write a function to determine if a specific transaction amount represents a dominant pattern in a sequence of sorted transaction values. Given a sorted array of transaction amounts, the total number of transactions, and a target transaction value, determine if this specific amount appears in more than half of all transactions within the monitoring window. This pattern recognition is crucial for identifying potential coordinated fraudulent activities across multiple accounts.
    

    """
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 bank's fraud detection system, write a function to determine if a specific transaction amount represents a dominant pattern in a sequence of sorted transaction values. Given a sorted array of transaction amounts, the total number of transactions, and a target transaction value, determine if this specific amount appears in more than half of all transactions within the monitoring window. This pattern recognition is crucial for identifying potential coordinated fraudulent activities across multiple accounts.
    

    """
    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