Leetcode #2601: Prime Subtraction Operation
In this guide, we solve Leetcode #2601 Prime Subtraction Operation 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 integer array nums of length n. You can perform the following operation as many times as you want: Pick an index i that you haven’t picked before, and pick a prime p strictly less than nums[i], then subtract p from nums[i].
Quick Facts
- Difficulty: Medium
- Premium: No
- Tags: Greedy, Array, Math, Binary Search, Number Theory
Intuition
The problem structure suggests a monotonic decision, which makes binary search a natural fit.
By halving the search space each step, we reach the answer efficiently.
Approach
Search either directly on a sorted array or on the answer space using a check function.
Each check is fast, and the logarithmic search keeps the overall runtime low.
Steps:
- Define the search bounds.
- Check the mid point condition.
- Narrow the bounds until convergence.
Example
Input: nums = [4,9,6,10]
Output: true
Explanation: In the first operation: Pick i = 0 and p = 3, and then subtract 3 from nums[0], so that nums becomes [1,9,6,10].
In the second operation: i = 1, p = 7, subtract 7 from nums[1], so nums becomes equal to [1,2,6,10].
After the second operation, nums is sorted in strictly increasing order, so the answer is true.
Python Solution
class Solution:
def primeSubOperation(self, nums: List[int]) -> bool:
p = []
for i in range(2, max(nums)):
for j in p:
if i % j == 0:
break
else:
p.append(i)
n = len(nums)
for i in range(n - 2, -1, -1):
if nums[i] < nums[i + 1]:
continue
j = bisect_right(p, nums[i] - nums[i + 1])
if j == len(p) or p[j] >= nums[i]:
return False
nums[i] -= p[j]
return True
Complexity
The time complexity is and the space complexity is . 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.