Python3 Easy || O(N)
Intuition:- Computing the product of all integers in a specified range and in a compact format, handling large numbers by using scientific notation and suppress
**Intuition:-** *Computing the product of all integers in a specified range and in a compact format, handling large numbers by using scientific notation and suppressing trailing zeros.*\n**It also provides utility functions for calculating factorials and checking if a product exceeds a given threshold.**\n\n# Approach-\n**1- Iteration Through Range:-** *Loop through all integers from left to right, calculating their cumulative product.*\n\n**2- Normalization:-** *Normalize the product to keep it within a manageable range (0.1 to <1) by continuously dividing by 10, while tracking the number of digits removed.*\n\n**3- Suffix Calculation:-** *Maintain a separate variable (suffix) to compute the product of the integers while also counting and removing trailing zeros.*\n\n**4- Abbreviation Logic:-** *Depending on the number of original digits and the count of zeros, format the final product either in scientific notation or a more condensed string if the product is too large.*\n\n**5- Utility Function:-** *Provide additional functionalities through helper functions (factorial and is_product_large) for further mathematical operations and checks related to the product calculated.*\n\n# Complexity\n**Time complexity:-**\n      *O(n) for each of the three functions.*\n\n**Space complexity:-**\n      *O(1) for each of the three functions.*\n\n# Code\n```\nclass Solution(object):  \n    def abbreviateProduct(self, left: int, right: int) -> str:  \n        product, suffix, zeros, org_digits = 1.0, 1, 0, 0  \n        for n in range(left, right + 1):  \n            product *= n  \n            while product >= 1:  \n                product /= 10  \n                org_digits += 1  \n            suffix *= n  \n            while suffix % 10 == 0:  \n                zeros += 1  \n                suffix //= 10  \n            if suffix > 10 ** 14:  \n                suffix %= 10 ** 14  \n        if org_digits - zeros <= 10:  \n            return str(int(product * (10 ** (org_digits - zeros)) + 0.5)) + \'e\' + str(zeros)  \n        else:  \n            return str(int(product * 100000)) + \'...\' + (\'0000\' + str(suffix))[-5:] + \'e\' + str(zeros)  \n\n    def factorial(self, n):  \n        """Returns the factorial of n."""  \n        if n < 0:  \n            raise ValueError("Factorial is not defined for negative numbers")  \n        if n == 0 or n == 1:  \n            return 1  \n        result = 1  \n        for i in range(2, n + 1):  \n            result *= i  \n        return result  \n\n    def is_product_large(self, left, right, threshold=10**14):  \n        """Checks if the product of the range left to right exceeds the given threshold."""  \n        product = 1  \n        for n in range(left, right + 1):  \n            product *= n  \n            if product > threshold:  \n                return True  \n        return False\n```
['Math', 'Python3']