Leetcode #2614: Prime In Diagonal
In this guide, we solve Leetcode #2614 Prime In Diagonal in Python and focus on the core idea that makes the solution efficient.
You will see the intuition, the step-by-step method, and a clean Python implementation you can use in interviews.
Problem Statement
You are given a 0-indexed two-dimensional integer array nums. Return the largest prime number that lies on at least one of the diagonals of nums.
Quick Facts
- Difficulty: Easy
- Premium: No
- Tags: Array, Math, Matrix, Number Theory
Intuition
There is a mathematical invariant or formula that directly leads to the result.
Using math avoids unnecessary loops and reduces complexity.
Approach
Derive the formula or update rule, then compute the answer directly.
Handle edge cases like overflow or zero carefully.
Steps:
- Identify the math relationship.
- Compute the result with a loop or formula.
- Handle edge cases.
Example
Input: nums = [[1,2,3],[5,6,7],[9,10,11]]
Output: 11
Explanation: The numbers 1, 3, 6, 9, and 11 are the only numbers present on at least one of the diagonals. Since 11 is the largest prime, we return 11.
Python Solution
class Solution:
def diagonalPrime(self, nums: List[List[int]]) -> int:
def is_prime(x: int) -> bool:
if x < 2:
return False
return all(x % i for i in range(2, int(sqrt(x)) + 1))
n = len(nums)
ans = 0
for i, row in enumerate(nums):
if is_prime(row[i]):
ans = max(ans, row[i])
if is_prime(row[n - i - 1]):
ans = max(ans, row[n - i - 1])
return ans
Complexity
The time complexity is , where and are the number of rows of the array and the maximum value in the array, respectively. The space complexity is .
Edge Cases and Pitfalls
Watch for boundary values, empty inputs, and duplicate values where applicable. If the problem involves ordering or constraints, confirm the invariant is preserved at every step.
Summary
This Python solution focuses on the essential structure of the problem and keeps the implementation interview-friendly while meeting the constraints.