How do you solve Minimum Non-Zero Product of the Array Elements on LeetCode?

Minimum Non-Zero Product of the Array Elements (LeetCode #1969) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(log n) time complexity and O(1) space complexity. Key insight: Swapping bits can help minimize products.

What is the brute force solution for Minimum Non-Zero Product of the Array Elements?

The brute force approach for Minimum Non-Zero Product of the Array Elements is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute force approach involves generating all possible combinations of the elements in the array and calculating their products. This method is straightforward but inefficient as it does not leverage the properties of bit manipulation and the range of numbers. The optimal Optimal Solution approach improves this to O(log n).

What algorithm or data structure is used to solve Minimum Non-Zero Product of the Array Elements?

Minimum Non-Zero Product of the Array Elements uses the following concepts: Math, Greedy, Recursion. The recommended patterns to study are: Bit Manipulation, Mathematical Properties.

What are the interview tips for Minimum Non-Zero Product of the Array Elements?

Explain your thought process clearly. Discuss edge cases, like p = 1. Practice bit manipulation problems.

What are common mistakes when solving Minimum Non-Zero Product of the Array Elements?

Overlooking the modulo operation. Not considering the properties of binary numbers.

#1969

Minimum Non-Zero Product of the Array Elements

Medium

MathGreedyRecursionBit ManipulationMathematical Properties

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

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

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Intuition

Time O(log n)Space O(1)

The optimal solution leverages the properties of binary numbers and the fact that we can swap bits to minimize the product. By focusing on the highest bit positions and ensuring we keep the largest numbers intact, we can achieve the minimum non-zero product efficiently.

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Algorithm

3 steps

1Step 1: Calculate the maximum number in nums, which is 2^p - 1.
2Step 2: The minimum non-zero product can be derived from the formula: ((2^p - 2)^(2^(p-1) - 1) * (2^p - 1)) % (10^9 + 7).
3Step 3: Return the result.

solution.py8 lines

1# Full working Python code
2
3def minNonZeroProduct(p):
4    mod = 10**9 + 7
5    max_num = (1 << p) - 1
6    return (pow(max_num - 1, (1 << (p - 1)) - 1, mod) * max_num) % mod
7
8print(minNonZeroProduct(3))  # Example call

ℹ

Complexity note: The time complexity is O(log n) due to the fast exponentiation method used to compute powers. The space complexity is O(1) since we are using a constant amount of space.

1Swapping bits can help minimize products.
2Understanding binary representation is crucial.

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