Leetcode #2761: Prime Pairs With Target Sum
In this guide, we solve Leetcode #2761 Prime Pairs With Target Sum 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 an integer n. We say that two integers x and y form a prime number pair if: 1 <= x <= y <= n x + y == n x and y are prime numbers Return the 2D sorted list of prime number pairs [xi, yi].
Quick Facts
- Difficulty: Medium
- Premium: No
- Tags: Array, Math, Enumeration, 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: n = 10
Output: [[3,7],[5,5]]
Explanation: In this example, there are two prime pairs that satisfy the criteria.
These pairs are [3,7] and [5,5], and we return them in the sorted order as described in the problem statement.
Python Solution
class Solution:
def findPrimePairs(self, n: int) -> List[List[int]]:
primes = [True] * n
for i in range(2, n):
if primes[i]:
for j in range(i + i, n, i):
primes[j] = False
ans = []
for x in range(2, n // 2 + 1):
y = n - x
if primes[x] and primes[y]:
ans.append([x, y])
return ans
Complexity
The time complexity is and the space complexity is , where is the number given in the problem. The space complexity is , where is the number given in the problem.
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.