How do you solve Prime In Diagonal on LeetCode?

Prime In Diagonal (LeetCode #2614) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n) time complexity and O(n) space complexity. Key insight: Diagonal elements can be accessed using simple index calculations.

What is the brute force solution for Prime In Diagonal?

The brute force approach for Prime In Diagonal is Brute Force, with O(n²) time complexity and O(1) space complexity. We will check every element on both diagonals of the matrix to find the largest prime number. This is straightforward but may take longer for larger matrices. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Prime In Diagonal?

Prime In Diagonal uses the following concepts: Array, Math, Matrix, Number Theory. The recommended patterns to study are: Sieve of Eratosthenes for prime checking., Matrix traversal techniques..

What are the interview tips for Prime In Diagonal?

Explain your thought process clearly while coding. Consider edge cases and discuss them with the interviewer. Optimize your solution if time allows, and explain the improvements.

What are common mistakes when solving Prime In Diagonal?

Not handling edge cases where no primes exist. Forgetting to check both diagonals properly.

#2614

Prime In Diagonal

Easy

ArrayMathMatrixNumber TheorySieve of Eratosthenes for prime checking.Matrix traversal techniques.

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Approaches

Brute ForceOptimal

Complexity Comparison

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

💡

Intuition

Time O(n)Space O(n)

We can optimize the prime checking by using a sieve method to precompute all prime numbers up to the maximum possible value in the matrix, allowing for O(1) prime checks.

⚙️

Algorithm

5 steps

1Step 1: Use the Sieve of Eratosthenes to generate a list of prime numbers up to 4 * 10^6.
2Step 2: Initialize a variable to track the largest prime found.
3Step 3: Iterate through each index of the matrix to access both diagonals.
4Step 4: For each diagonal element, check if it is prime using the precomputed list. If it is and larger than the current largest prime, update the largest prime.
5Step 5: After checking all diagonal elements, return the largest prime found, or 0 if none were found.

solution.py25 lines

1# Full working Python code
2import math
3
4def sieve_of_eratosthenes(max_num):
5    is_prime = [True] * (max_num + 1)
6    is_prime[0] = is_prime[1] = False
7    for i in range(2, int(math.sqrt(max_num)) + 1):
8        if is_prime[i]:
9            for j in range(i * i, max_num + 1, i):
10                is_prime[j] = False
11    return is_prime
12
13def largest_prime_diagonal(nums):
14    max_val = 4 * 10**6
15    is_prime = sieve_of_eratosthenes(max_val)
16    largest_prime = 0
17    n = len(nums)
18    for i in range(n):
19        diag1 = nums[i][i]
20        diag2 = nums[i][n - i - 1]
21        if is_prime[diag1]:
22            largest_prime = max(largest_prime, diag1)
23        if is_prime[diag2]:
24            largest_prime = max(largest_prime, diag2)
25    return largest_prime if largest_prime > 0 else 0

ℹ

Complexity note: The time complexity is O(n) for checking the diagonals after precomputing primes, and the space complexity is O(n) for storing the prime information.

1Diagonal elements can be accessed using simple index calculations.
2Precomputing prime numbers allows for efficient prime checks.

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