Hello everyone, I found this problem a while ago and I'm still stuck on it (there's no OJ to submit it as far as I know):
You are given a permutation of the integers from 1 to N. In this case, moving an element from i to j is defined as removing the element from position i, and inserting it at position j. For example, in this array: [4,5,2,1,3]
, moving the element from 2 to 5 gives us the array [4,2,1,3,5]
. The cost of moving an element from i to j is defined as i + j (1-indexed). What is the minimum total cost needed to sort the permutation?
Example: [1,3,4,5,2]
-> [1,2,3,4,5]
with total cost 5 + 2 = 7.
1 ≤ N ≤ 1000, however solutions with any reasonable complexity are welcome.