How do you solve Check If It Is a Good Array on LeetCode?

Check If It Is a Good Array (LeetCode #1250) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n) time complexity and O(1) space complexity. Key insight: The gcd of the array elements determines if we can form the sum of 1.

What is the brute force solution for Check If It Is a Good Array?

The brute force approach for Check If It Is a Good Array is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute force approach involves checking all possible subsets of the array and their respective multiplicands to see if we can achieve a sum of 1. This is straightforward but inefficient due to the exponential number of subsets. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Check If It Is a Good Array?

Check If It Is a Good Array uses the following concepts: Array, Math, Number Theory. The recommended patterns to study are: Number Theory, GCD, Mathematical Properties.

What are the interview tips for Check If It Is a Good Array?

Always think about mathematical properties that can simplify the problem. When faced with a combinatorial problem, check if there's a way to reduce the number of combinations needed. Practice explaining your thought process clearly, as it helps in interviews.

What are common mistakes when solving Check If It Is a Good Array?

Overcomplicating the problem by trying to brute force all combinations without recognizing the gcd property. Not considering edge cases where the array has only one element.

#1250

Check If It Is a Good Array

Hard

ArrayMathNumber TheoryNumber TheoryGCDMathematical Properties

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

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

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Intuition

Time O(n)Space O(1)

The optimal approach leverages the mathematical property that a linear combination of integers can yield a specific integer (like 1) if the greatest common divisor (gcd) of the integers is 1. This is based on Bézout's lemma.

⚙️

Algorithm

2 steps

1Step 1: Compute the gcd of all elements in the array.
2Step 2: If the gcd is 1, return True; otherwise, return False.

solution.py6 lines

1# Full working Python code
2import math
3from functools import reduce
4
5def is_good_array(nums):
6    return reduce(math.gcd, nums) == 1

ℹ

Complexity note: The time complexity is O(n) because we are calculating the gcd of n numbers in a single pass. The space complexity is O(1) since we are only using a few variables.

1The gcd of the array elements determines if we can form the sum of 1.
2Using mathematical properties can significantly reduce the complexity of the solution.

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