Introduction

In this blog post, we will explore how to solve the LeetCode problem "650" using AI. LeetCode is a popular platform for preparing for coding interviews, and with the help of AI tools like Chatmagic, we can generate solutions quickly and efficiently - helping you pass the interviews and get the job offer without having to study for months.

Problem Statement

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: Input: n = 1 Output: 0 Constraints: 1 <= n <= 1000

Explanation

Here's the breakdown of the solution:

• Prime Factorization: The core idea is to decompose n into its prime factors. Each prime factor represents a sequence of copy-paste operations.
• Optimal Strategy: The most efficient way to generate n 'A's is to repeatedly copy the existing 'A's and paste them until you reach the desired number.

• Accumulate Operations: For each prime factor p, we need p operations (1 copy and p-1 pastes). We sum these operations for all prime factors to get the minimum operations.

• Runtime & Storage Complexity: O(sqrt(n)) runtime, O(1) storage.

Code

    def minSteps(n: int) -> int:
    """
    Calculates the minimum number of operations to obtain n 'A's starting with one 'A'.
    Operations: Copy All, Paste.
    """

    if n == 1:
        return 0

    ans = 0
    d = 2
    while d * d <= n:
        while n % d == 0:
            ans += d
            n //= d
        d += 1

    if n > 1:
        ans += n

    return ans