Is 2 Keys Keyboard easy or hard?

2 Keys Keyboard is rated Medium on LeetCode with an acceptance rate around 60%. The dynamic programming solution is straightforward, but recognizing the prime factorization optimization requires mathematical insight.

2 Keys Keyboard Python/Java solution

Both Python and Java implementations follow the same idea: repeatedly divide n by its smallest factor and accumulate the factor values as the operation count. The logic is concise and runs in O(sqrt n) time with constant extra space.

How to solve 2 Keys Keyboard in O(n)?

A dynamic programming formulation can compute dp[i] as the minimum operations needed to reach i characters. For every i, iterate through its divisors j and update dp[i] = dp[j] + i/j. This runs in roughly O(n^2) in the naive version, though divisor-based optimizations reduce it significantly.

What is the best approach for 2 Keys Keyboard?

The most efficient approach uses prime factorization. The minimum operations required to generate n characters equals the sum of the prime factors of n. By repeatedly dividing n by the smallest possible factor, the solution runs in O(sqrt n) time with O(1) space.

Is 2 Keys Keyboard asked at Google/Amazon/Meta?

2 Keys Keyboard appears frequently in interview preparation sets and is associated with companies like Google and Amazon in several coding interview datasets. It tests reasoning about dynamic programming and mathematical optimization rather than complex data structures.

What data structure is used in 2 Keys Keyboard?

The dynamic programming solution uses an integer array dp where dp[i] stores the minimum operations required to produce i characters. The mathematical approach does not require additional data structures and relies purely on arithmetic factorization.

What is the time complexity of 2 Keys Keyboard?

The optimal mathematical solution runs in O(sqrt n) time because it checks possible factors up to the square root of n. The dynamic programming approach takes O(n^2) time and O(n) space since each state checks previous divisors.

Description Hints 1 Solution Video 17:37

650. 2 Keys Keyboard

Medium59.6% acceptance7 companies

There is only one character 'A' on the screen of a notepad. You can perform one of two operations on this notepad for each step:

Copy All: You can copy all the characters present on the screen (a partial copy is not allowed).
Paste: You can paste the characters which are copied last time.

Given an integer n, return the minimum number of operations to get the character 'A' exactly n times on the screen.

Example 1:

Input: n = 3
Output: 3
Explanation: Initially, we have one character 'A'.
In step 1, we use Copy All operation.
In step 2, we use Paste operation to get 'AA'.
In step 3, we use Paste operation to get 'AAA'.

Example 2: