
    In a hospital's continuous patient monitoring system, determine if a specific vital sign reading represents a dominant pattern in a patient's sorted measurement history. Given a sequence of sorted vital sign measurements and a particular reading value, develop a function to identify if this value appears in more than half of all recorded measurements during the monitoring period. This analysis is crucial for detecting sustained abnormal patterns that may indicate patient deterioration.
    

    
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 hospital's continuous patient monitoring system, determine if a specific vital sign reading represents a dominant pattern in a patient's sorted measurement history. Given a sequence of sorted vital sign measurements and a particular reading value, develop a function to identify if this value appears in more than half of all recorded measurements during the monitoring period. This analysis is crucial for detecting sustained abnormal patterns that may indicate patient deterioration.
    

    """
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 hospital's continuous patient monitoring system, determine if a specific vital sign reading represents a dominant pattern in a patient's sorted measurement history. Given a sequence of sorted vital sign measurements and a particular reading value, develop a function to identify if this value appears in more than half of all recorded measurements during the monitoring period. This analysis is crucial for detecting sustained abnormal patterns that may indicate patient deterioration.
    

    """
    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