spookywooky's blog

By spookywooky, history, 5 years ago, In English

Hello,

I am trying to solve https://cses.fi/problemset/task/1163, but got some problem to understand it. It states that "There is a street of length x whose positions are numbered 0,1,…,n. " That should be "0, 1,..., x", not n, isn't it?

Then the example:

Input:
8 3
3 6 2

Output:
5 3 3

I think output should be 5, 3, 2, not 5, 3, 3. Since obviously the longest segment without a traffic light is 2, not 3.

0 1 2 3 4 5 6 7 8
    x x     x

Can somebody explain? A lot of people solved that problem, I think I am missing something. Thanks.

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5 years ago, # |
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Found it by myself ;)

Two things one must notice:

There is an "implicit" traffic light after position 0. The length of the segment is calculated as without left bound, but including right bound.

So, the traffic lights are placed kind of "right of the positions". After adding the three lights, it looks like

0 1 2 3 4 5 6 7 8
 x   x x     x

The longest segment is the one "4,5,6", of length 3.

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    4 years ago, # ^ |
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    spookywooky Can You Explain it in simple words.I am also stuck at this problem but not able to get it.Problem Statement is not clear.

    Thanks in Advance!

    PS-Why this post is getting downvoted?I have done nothing wrong.If asking a doubt is an offense to community then why a discuss section was made on Codeforces.This discuss section is made for discussing doubts and problems.

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      4 years ago, # ^ |
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      Which part is unclear? The statement or the solution?

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        4 years ago, # ^ |
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        I am not getting the statement! i think the output should be 5 3 2 and not 5 3 3

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          4 years ago, # ^ |
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          The traffic lights are placed between the numbered segments of the street, after the given number.

          In the testcase above there are 3 lights, at positions between 2 and 3, between 3 and 4, and between 6 and 7.

          So the longest segment without a traffic light is {4,5,6} of size 3.

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            4 years ago, # ^ |
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            After adding 6 wouldn't be answer 4 Because we have 3 segments which do not contain traffic lights :

            0 1   
            
            1 2
            
            2 3
            

            and size is 4. I am sorry if its a dumb question but i can request if you can clarify this! spookywooky ?

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              4 years ago, # ^ |
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              Nah, the numbers are not the spaces between the segments, the numbers are the segments.

              There is a segment 1, a segemnt 2 etc... We place the lights between the segments.

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                4 years ago, # ^ |
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                You mean to say

                0 1 is segment 1
                
                1 2 is segment 2
                
                2 3 is segment 3
                

                and so on... spookywooky?

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                  4 years ago, # ^ |
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                  light only belongs to the left segment

                  light on 1 means 1-1 and 2-n

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5 years ago, # |
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You are right, the task statement had a typo. This has now been fixed, thanks!

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    4 years ago, # ^ |
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    Fixed? Nothing has been changed. Can you recheck?

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5 years ago, # |
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Can you please give me a hint on how to solve this problem? I am stuck in it.

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    5 years ago, # ^ |
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    Hint: Think about the number of segments that could be affected after adding a new traffic light.

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      5 years ago, # ^ |
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      Thanks for the hint man

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        5 years ago, # ^ |
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        Hey, I am still not able to figure it out, can you share your approach?

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          5 years ago, # ^ |
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          Solution
          Code
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            5 years ago, # ^ |
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            Thank you :) Hey, If you know how to approach "Throwing dice"? https://cses.fi/problemset/task/1096

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              5 years ago, # ^ |
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              it is an easy linear reccurence:
              $$$f(x) = \sum_{i=1}^{6} f(x-i)$$$ which can be solved by the matrix multiplication

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              5 years ago, # ^ |
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              Solution
              Code
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                5 years ago, # ^ |
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                Thank you very much! I did not know about the matrix multiplication part, it look's really cool.

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            3 years ago, # ^ |
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            Hey, your solution is giving TLE for some Cases.

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              3 years ago, # ^ |
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              O(N) will give TLE, he was explaining the basic idea, check the comment below it.