> For the complete documentation index, see [llms.txt](https://mayanktyagi3111.gitbook.io/interview-prep/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://mayanktyagi3111.gitbook.io/interview-prep/dynamic-programming/2-keys-keyboard.md).

# 2 Keys Keyboard

Initially on a notepad only one character 'A' is present. You can perform two operations on this notepad for each step:

1. `Copy All`: You can copy all the characters present on the notepad (partial copy is not allowed).
2. `Paste`: You can paste the characters which are copied **last time**.

Given a number `n`. You have to get **exactly** `n` 'A' on the notepad by performing the minimum number of steps permitted. Output the minimum number of steps to get `n` 'A'.

**Example 1:**

```
Input: 3
Output: 3
Explanation:
Intitally, 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'.
```

**Note:**

1. The `n` will be in the range \[1, 1000].

```java
// DP solution
class Solution {
    public int minSteps(int n) {
        int dp[] = new int[n + 1];
        dp[1] = 0;
        for (int i = 2; i <= n; i++) {
            dp[i] = i;// because you can just paste 'A' i times to get i*A
            for (int j = i/2; j >=1; j--) {
                if (i % j == 0){
                    dp[i] = Math.min(dp[i], dp[j] + i / j);
                    break;
                }
            }
        }
        return dp[n];
    }
}

/*
To get 81 we check
if (81 % 2 ==0) No
if (81 % 3 ==0) Yes
So we need to copy 81/3 = 27 'A's three times (3)
Now to get 27 'A's, we need to copy 27/3= 9 'A's three times (3)
To get 9 'A's, we need to copy 9/3=3 'A's three times (3)
And to get 3 'A's, we need to copy 3/3=1 'A's three times (3)
Final answer is 3+3+3+3 = 12
*/
class Solution {
    public int minSteps(int n) {
        int res = 0;
        for (int i = 2; i <= n; i++) {
            while (n % i == 0) {
                res += i;
                n = n / i;
            }
        }
        return res;
    }
}
```


---

# Agent Instructions
This documentation is published with GitBook. GitBook is the documentation platform designed so that both humans and AI agents can read, navigate, and reason over technical content effectively. Learn more at gitbook.com.

## Querying This Documentation
If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question.

Perform an HTTP GET request on the current page URL with the `ask` query parameter, and the optional `goal` query parameter:

```
GET https://mayanktyagi3111.gitbook.io/interview-prep/dynamic-programming/2-keys-keyboard.md?ask=<question>&goal=<endgoal>
```

`ask` is the immediate question: it should be specific, self-contained, and written in natural language.
`goal` is optional and describes the broader end goal you are ultimately trying to accomplish on behalf of the user. GitBook uses it to tailor the answer towards what is most useful for that goal.

The response will contain a direct answer to the question and relevant excerpts and sources from the documentation.

Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.