2 Keys Keyboard Problem

Question

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].

Answer 1

To get the DP solution, analyse the pattern first by generating first few solutions

Number of A's	Steps
1	0
2	2
3	3
4	4
5	5
6	5
7	7
8	6
9	6

Now, check the solution.

Eg: n=6

To get 6, we need to copy 3 'A's two time. (2)

To get 3 'A's, copy the 1 'A' three times. (3)

So the answer for 6 is 5

Now, take n=9.

We need the lowest number just before 9 such that (9% number =0). So the lowest number is 3.

So 9%3=0. We need to copy 3 'A's three times to get 9. (3)

For getting 3 'A's, we need to copy 1 'A' three times. (3)

So the answer is 6

Finally to analyse the below code, take n=81.

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

Last Example, n=18

18/2 = 9 Copy 9 'A's 2 times (2)

9/3=3 Copy 3 'A's 3 times (3)

3/3=1 Copy 1'A's 3 times (3)

Answer: 2+3+3= 8

class Solution:     def minSteps(self, n: int) -> int:                  ans = 0                  for i in range(2, n + 1):             while n % i == 0:                 ans += i                 n /= i                  return ans

eg : ans = Solution()

ans.minSteps(889)

Output-

134