Introduction

In this blog post, we will explore how to solve the LeetCode problem "3145" using AI. LeetCode is a popular platform for preparing for coding interviews, and with the help of AI tools like Chatmagic, we can generate solutions quickly and efficiently - helping you pass the interviews and get the job offer without having to study for months.

Problem Statement

The powerful array of a non-negative integer x is defined as the shortest sorted array of powers of two that sum up to x. The table below illustrates examples of how the powerful array is determined. It can be proven that the powerful array of x is unique. num Binary Representation powerful array 1 00001 [1] 8 01000 [8] 10 01010 [2, 8] 13 01101 [1, 4, 8] 23 10111 [1, 2, 4, 16] The array big_nums is created by concatenating the powerful arrays for every positive integer i in ascending order: 1, 2, 3, and so on. Thus, big_nums begins as [1, 2, 1, 2, 4, 1, 4, 2, 4, 1, 2, 4, 8, ...]. You are given a 2D integer matrix queries, where for queries[i] = [fromi, toi, modi] you should calculate (big_nums[fromi] big_nums[fromi + 1] ... * big_nums[toi]) % modi. Return an integer array answer such that answer[i] is the answer to the ith query. Example 1: Input: queries = [[1,3,7]] Output: [4] Explanation: There is one query. big_nums[1..3] = [2,1,2]. The product of them is 4. The result is 4 % 7 = 4. Example 2: Input: queries = [[2,5,3],[7,7,4]] Output: [2,2] Explanation: There are two queries. First query: big_nums[2..5] = [1,2,4,1]. The product of them is 8. The result is 8 % 3 = 2. Second query: big_nums[7] = 2. The result is 2 % 4 = 2. Constraints: 1 <= queries.length <= 500 queries[i].length == 3 0 <= queries[i][0] <= queries[i][1] <= 1015 1 <= queries[i][2] <= 105

Explanation

Here's the breakdown of the solution:

• Efficient Power of 2 Extraction: Determine the powers of 2 that sum up to a number without generating the entire sequence up to 10¹⁵. We do this by iterating through the bits of the number, and if the bit is set, it means that power of 2 is part of the powerful array.
• Modular Arithmetic: Apply the modulo operator after each multiplication within a query to prevent integer overflow and ensure results remain within the specified range.

• Index Handling: Adjust the indices in queries to be 0-based for consistent array access.

• Runtime Complexity: O(Q * log(T)), where Q is the number of queries and T is the largest value of toi among all queries. More precisely, the complexity is determined by the binary representation extraction, which takes O(log(n)) per number being considered.

• Storage Complexity: O(1) - constant extra space.

def solve():
    def get_powerful_array(n):
        powers = []
        power_of_2 = 1
        while n > 0:
            if n % 2 == 1:
                powers.append(power_of_2)
            n //= 2
            power_of_2 *= 2
        return powers

    def get_big_nums_element(index):
        powerful_array = get_powerful_array(index + 1)
        return powerful_array

    def process_query(from_index, to_index, mod_val):

        product = 1
        for i in range(from_index, to_index + 1):
            powerful_array = get_powerful_array(i + 1)

            for num in powerful_array:
                product = (product * num) % mod_val

        return product


    queries = [[1,3,7]]
    #queries = [[2,5,3],[7,7,4]]
    results = []
    for query in queries:
        from_index = query[0] - 1
        to_index = query[1] - 1
        mod_val = query[2]
        result = process_query(from_index, to_index, mod_val)
        results.append(result)
    print(results)

    queries = [[2,5,3],[7,7,4]]
    results = []
    for query in queries:
        from_index = query[0] - 1
        to_index = query[1] - 1
        mod_val = query[2]
        result = process_query(from_index, to_index, mod_val)
        results.append(result)
    print(results)

def powerful_array_product_queries(queries):
    def get_powerful_array(n):
        powers = []
        power_of_2 = 1
        while n > 0:
            if n % 2 == 1:
                powers.append(power_of_2)
            n //= 2
            power_of_2 *= 2
        return powers

    def process_query(from_index, to_index, mod_val):
        product = 1
        for i in range(from_index, to_index + 1):
            powerful_array = get_powerful_array(i + 1)
            for num in powerful_array:
                product = (product * num) % mod_val
        return product

    results = []
    for query in queries:
        from_index = query[0] - 1
        to_index = query[1] - 1
        mod_val = query[2]
        result = process_query(from_index, to_index, mod_val)
        results.append(result)
    return results


    # Code
    ```python
    def powerful_array_produt_queries(queries):    def get_powerful_array(n):
        powers = []
        power_of_2 = 1
        while n > 0:
            if n % 2 == 1:
                powers.append(power_of_2)
            n //= 2
            power_of_2 *= 2
        return powers

    def process_query(from_index, to_index, mod_val):
        product = 1
        for i in range(from_index, to_index + 1):
            powerful_array = get_powerful_array(i + 1)
            for num in powerful_array:
                product = (product * num) % mod_val
        return product

    results = []
    for query in queries:
        from_index = query[0] - 1
        to_index = query[1] - 1
        mod_val = query[2]
        result = process_query(from_index, to_index, mod_val)
        results.append(result)
    return results