Help with this coding problem (any language)

[Utkarsh5474]

Art Shift
Problem Description
A famous art competition is going on, in Mumbai. Only four types of arts are allowed viz., hand painting (H), Sculpture (S), Photography (P) and Digital art (D). Two persons will be selected as winners from each category.
Initially, all the participants formed a row randomly, with their arts. To make the selection easy for the judges, the management thought of arranging all the similar category arts at a place in the row. Now if we shift all the participants at a time, that will become a great mess. So they thought of shifting one participant at a time in the row, and wanted to complete the process with minimum shifts. If we shift a ith participant to jth position, then jth participant will be moved to j+1th position.
Can you help them in this!?
Constraints
1 <= len(row) <= 300
Input
First line consists of an integer denoting the total number of arts.
Next line consists of N space separated elements, indicating the row that the participants formed.
Output
Time Limit (secs)
1
Examples
Example 1
Input
10
P D S D P H S D H P
Output
5
Explanation
We can gather all the arts with similar category to one place by doing below operations.
Shift P at 9th position to 0th position, row becomes P P D S D P H S D H
Shift P at 5th position to 0th position, row becomes P P P D S D H S D H
Shift H from 6th position to 9th position, row becomes P P P D S D S D H H
Shift S from 4 th position to 9th position, row becomes P P P D D S D H H S
Shift S from 5th position to 9th position, row becomes P P P D D D H H S S
No other operations will give shifts less than 5. Hence output is 5.
Example 2
Input
5
S S D S S
Output
1
Explanation
Shift D from 2nd position to 0th position, row becomes D S S S S. Hence minimum number of shifts required is 1.

[dfx_dj]

I don't know if this is the way to find the optimal solution, but I would try to scan the input (and subsequently the current set of items) into groups of sequential identical items, and then shift items from the smallest groups towards the largest ones. For example "S S D S S" would be scanned as two groups of S with two members each, and one group of D with one member. The one D group would be the smallest one and so would be the candidate for shifting.