Need help with a problem ("Candy", ALPR2000)

I am trying to solve the problem
candy.My approach is that i am giving the first child 1 candy , the second child k+1 candies , the third child k+1+k candies and so on.Then by using the for formula for finding the sum of an ap series, i am calculating the minimum number of candies that is required.can anybody please point out what is wrong with my approach.

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Your Approach is wrong because if you read the problem it is written that
“difference of at least K candies between two adjacent kids.”

Lets take an example-
if n=5 and k=1

1st child will get 1 candy.

2nd child will get k+1 candies.

3rd child will get 1 candy: (At this point you are wrong!)
(we will not give k+1+k candies because k+1(2nd child) and 1(3rd child) have a difference of k candies so condition is satisfied)

4th child will get k+1 candies because the third child got 1 candy and we have to make a difference of k candies.

5th child will get k candies more than the 4th child because the 5th child is adjacent to first child(Children are sitting in circle)

so 5th child (nth child) has to make a difference atleast k candies with respect to 1st child and 4th child.

So if n is even then the formula will be

and if n is odd then formula will be:
(n-1) +( (n-1)/2)* (k) + (2*k)+1

Just draw the figure sitting 5 students in a circle and visualise what i explained!


Thank you very much…

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Welcome! :slight_smile:

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