We need to write N same characters on a screen and each time we can insert a character, delete the last character and copy and paste all written characters i.e. after copy operation count of total written character will become twice. Now we are given time for insertion, deletion and copying. We need to output minimum time to write N characters on the screen using these operations.
Input : N = 9 insert time = 1 removal time = 2 copy time = 1 Output : 5 N character can be written on screen in 5 time units as shown below, insert a character characters = 1 total time = 1 again insert character characters = 2 total time = 2 copy characters characters = 4 total time = 3 copy characters characters = 8 total time = 4 insert character characters = 9 total time = 5
We can solve this problem using dynamic programming. We can observe a pattern after solving some examples by hand that for writing each character we have two choices either get it by inserting or get it by copying, whichever takes less time. Now writing relation accordingly,
Let dp[i] be the optimal time to write i characters on screen then,
If i is even then, dp[i] = min((dp[i-1] + insert_time), (dp[i/2] + copy_time)) Else (If i is odd) dp[i] = min(dp[i-1] + insert_time), (dp[(i+1)/2] + copy_time + removal_time)
In the case of odd, removal time is added because when (i+1)/2 characters will be copied one extra character will be on the screen which needs to be removed. Total time complexity of solution will be O(N) and auxiliary space needed will be O(N).
This article is contributed by Utkarsh Trivedi. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to firstname.lastname@example.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.
- Minimum insertions to sort an array
- Minimum number of jumps to reach end
- Space and time efficient Binomial Coefficient
- Minimum insertions to form a palindrome | DP-28
- Remove minimum elements from either side such that 2*min becomes more than max
- Minimum Cost Polygon Triangulation
- Find the minimum cost to reach destination using a train
- Find minimum number of coins that make a given value
- Minimum steps to reach a destination
- Minimum number of squares whose sum equals to given number n
- Minimum Initial Points to Reach Destination
- Find minimum possible size of array with given rules for removing elements
- Partition a set into two subsets such that the difference of subset sums is minimum
- Weighted Job Scheduling in O(n Log n) time
- Minimum time to finish tasks without skipping two consecutive