
    Write a function to analyze a customer's sorted transaction history and determine if a specific transaction amount dominates their spending pattern. Given a sorted array of transaction values, the total number of transactions, and a target transaction amount, determine if this amount occurs in more than half of all transactions. This analysis is crucial for identifying primary spending behaviors and tailoring financial planning recommendations.
    

    
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 analyze a customer's sorted transaction history and determine if a specific transaction amount dominates their spending pattern. Given a sorted array of transaction values, the total number of transactions, and a target transaction amount, determine if this amount occurs in more than half of all transactions. This analysis is crucial for identifying primary spending behaviors and tailoring financial planning recommendations.
    

    """
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 analyze a customer's sorted transaction history and determine if a specific transaction amount dominates their spending pattern. Given a sorted array of transaction values, the total number of transactions, and a target transaction amount, determine if this amount occurs in more than half of all transactions. This analysis is crucial for identifying primary spending behaviors and tailoring financial planning recommendations.
    

    """
    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