Colouring Book Having spent the last couple of hours grading assignments, I decide it’s time for a break. I take out my favourite colouring book, turn to a random page I haven’t coloured in yet, and lay it on my desk. I then take out all my n crayons and line them up on the desk (it’s a very long desk). The colour of the ith crayon is a string c[i] (e.g. "blue"). Many of the crayons have the same colour. In fact, no matter how many crayons I have, there are at most 30 distinct colours amongst them.
Colouring Book
Having spent the last couple of hours grading assignments, I decide it’s time for a break. I take out my favourite colouring book, turn to a random page I haven’t coloured in yet, and lay it on my desk. I then take out all my n crayons and line them up on the desk (it’s a very long desk). The colour of the ith crayon is a string c[i] (e.g. "blue"). Many of the crayons have the same colour. In fact, no matter how many crayons I have, there are at most 30 distinct colours amongst them.
To start colouring, I always take a sublist (see Q1 for a definition) of the crayons laid on the desk and put away the rest (too many options can be overwhelming and can lead to indecision).
I take a look at the line art in front of me and wonder, “How many different colours do I need to make this look great? One? Two? Maybe three?”.
Now you understand my dilemma and are fully aware of my indecision. You kindly decide to help me out by telling me for every number k, if I were to use k distinct colours, what would be the minimum number of crayons I’d need to take?
Filename
Your filename for this question must be q4.py.
Input
The input consists of a single line containing n space-separated names of colours specifying the list c.
Output
Let m be the number of distinct colours in c. Then, output m space-separated integers. The kth of them (1-based) should be the minimum number of crayons I’d need to take so that there are at least k distinct colours amongst them.
Constraints
- 1 ≤ n ≤ 5 × 104
- 1 ≤ len(c[i]) ≤ 5
- There are at most 30 distinct colours in c.
Time Limit
- Your program has to finish running within 4 seconds on any valid input.
Sample Input 1
green red red blue red red green
Sample Output 1
1 2 4
Sample 1 Explanation
- If I wanted to use only 1 colour, I could take any single crayon.
- If I wanted to use 2 distinct colours, I could take a sublist of length 2 such as the sublist red blue.
- If I wanted to use all three colours, the smallest possible sublist would have length 4. For example, I could take blue red red green.
Sample Input 2
r g z g b b r r g y g g y b
Sample Output 2
1 2 3 5 8
Hints
- There are several ways to solve this problem, but not all of them are fast enough to pass the biggest test cases within the time limit.
- For a 100% solution, here’s a starting point (not needed for the 70% solution): as you work through the colours, what if you knew the index of the most recent occurrence of each colourDefinition:
- A sublist of a list a is any list you can obtain by removing some (possibly 0) elements from the start of a and then removing some (possibly 0) elements from the end of it. (It’s like the definition of segment from lecture.)
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