How do you solve Find Products of Elements of Big Array on LeetCode?

Find Products of Elements of Big Array (LeetCode #3145) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(q * log(n)) time complexity and O(1) space complexity. Key insight: Understanding binary representation is crucial for efficiently computing powers of two.

What is the brute force solution for Find Products of Elements of Big Array?

The brute force approach for Find Products of Elements of Big Array is Brute Force, with O(n²) time complexity and O(n) space complexity. The brute-force approach involves generating the powerful array for every number up to the maximum index needed in the queries. We then compute the product for each query by directly accessing the elements in this array. The optimal Optimal Solution approach improves this to O(q * log(n)).

What algorithm or data structure is used to solve Find Products of Elements of Big Array?

Find Products of Elements of Big Array uses the following concepts: Array, Binary Search, Bit Manipulation. The recommended patterns to study are: Bit Manipulation, Dynamic Programming.

What are the interview tips for Find Products of Elements of Big Array?

Always clarify the constraints and edge cases before diving into coding. Discuss your thought process and approach with the interviewer to get feedback. Practice explaining your code and logic clearly, as communication is key in interviews.

What are common mistakes when solving Find Products of Elements of Big Array?

Failing to recognize the uniqueness of the powerful array for each number. Not considering the modulo operation correctly while computing products.

#3145

Find Products of Elements of Big Array

Hard

ArrayBinary SearchBit ManipulationBit ManipulationDynamic Programming

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(q * log(n))
Space	O(n)	O(1)

💡

Intuition

Time O(q * log(n))Space O(1)

The optimal approach leverages the properties of binary representation and bit manipulation to directly compute the product of the powerful array elements without generating the entire array. This allows us to handle large indices efficiently.

⚙️

Algorithm

3 steps

1Step 1: For each query, calculate the product of the powerful array elements from 'from' to 'to' using bit manipulation.
2Step 2: Use a helper function to determine the contribution of each bit position for the numbers in the range.
3Step 3: Compute the product modulo the specified value.

solution.py18 lines

1# Full working Python code
2
3def count_powers(n, bit):
4    count = 0
5    for i in range(n + 1):
6        if (i & (1 << bit)):
7            count += 1
8    return count
9
10def find_products(queries):
11    results = []
12    for from_i, to_i, mod_i in queries:
13        product = 1
14        for bit in range(32):
15            count = count_powers(to_i, bit) - count_powers(from_i - 1, bit)
16            product = (product * pow(2, count, mod_i)) % mod_i
17        results.append(product)
18    return results

ℹ

Complexity note: The time complexity is O(q * log(n)) because for each query, we compute the contribution of each bit position, which requires logarithmic time relative to the maximum number in the query.

1Understanding binary representation is crucial for efficiently computing powers of two.
2Using bit manipulation can drastically reduce the time complexity of the solution.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.