How do you solve Maximum Prime Difference on LeetCode?

Maximum Prime Difference (LeetCode #3115) 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: Finding the first and last occurrence of primes is more efficient than checking all pairs.

What is the brute force solution for Maximum Prime Difference?

The brute force approach for Maximum Prime Difference is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute force approach involves checking every pair of indices in the array to find the maximum distance between two prime numbers. This is straightforward but inefficient for larger arrays. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Maximum Prime Difference?

Maximum Prime Difference uses the following concepts: Array, Math, Number Theory. The recommended patterns to study are: Hash Map, Array.

What are the interview tips for Maximum Prime Difference?

Always clarify the problem requirements before diving into coding. Discuss your thought process and approach with the interviewer. Consider edge cases and how your solution handles them.

What are common mistakes when solving Maximum Prime Difference?

Not checking if the number is prime before calculating distances. Overlooking the case where there is only one prime number.

#3115

Maximum Prime Difference

Medium

ArrayMathNumber TheoryHash MapArray

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

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

💡

Intuition

Time O(n)Space O(1)

Instead of checking every pair, we can simply find the first and last occurrence of prime numbers in the array. The distance between these two indices will give us the maximum distance.

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Algorithm

3 steps

1Step 1: Initialize variables to store the first and last index of a prime number.
2Step 2: Iterate through the array to find prime numbers and update the first and last index accordingly.
3Step 3: Calculate the distance between the first and last index of prime numbers.

solution.py22 lines

1# Full working Python code
2
3def is_prime(num):
4    if num < 2:
5        return False
6    for i in range(2, int(num**0.5) + 1):
7        if num % i == 0:
8            return False
9    return True
10
11def max_prime_distance(nums):
12    first_index = -1
13    last_index = -1
14    for i in range(len(nums)):
15        if is_prime(nums[i]):
16            if first_index == -1:
17                first_index = i
18            last_index = i
19    return last_index - first_index
20
21# Example usage
22print(max_prime_distance([4, 2, 9, 5, 3]))

ℹ

Complexity note: The time complexity is O(n) because we only need to make a single pass through the array to find the first and last prime indices. The space complexity is O(1) since we are using a fixed amount of space for variables.

1Finding the first and last occurrence of primes is more efficient than checking all pairs.
2The problem can be simplified by focusing on indices instead of values.

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