
    Design a fraud detection function that determines if a specific transaction amount represents a suspicious spending pattern in a user's credit card history. Given a chronologically sorted list of transaction amounts and the total number of transactions being analyzed, the function should identify if any single transaction amount occurs more frequently than half of the total transactions, which could indicate potential credit card fraud or compromise. The function should take the sorted transaction history, the number of transactions, and the suspicious transaction amount as inputs, and return whether that amount constitutes a majority pattern in the user's recent spending behavior.
    

    
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 fraud detection function that determines if a specific transaction amount represents a suspicious spending pattern in a user's credit card history. Given a chronologically sorted list of transaction amounts and the total number of transactions being analyzed, the function should identify if any single transaction amount occurs more frequently than half of the total transactions, which could indicate potential credit card fraud or compromise. The function should take the sorted transaction history, the number of transactions, and the suspicious transaction amount as inputs, and return whether that amount constitutes a majority pattern in the user's recent spending behavior.
    

    """
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 fraud detection function that determines if a specific transaction amount represents a suspicious spending pattern in a user's credit card history. Given a chronologically sorted list of transaction amounts and the total number of transactions being analyzed, the function should identify if any single transaction amount occurs more frequently than half of the total transactions, which could indicate potential credit card fraud or compromise. The function should take the sorted transaction history, the number of transactions, and the suspicious transaction amount as inputs, and return whether that amount constitutes a majority pattern in the user's recent spending behavior.
    

    """
    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