Efficient algorithm to solve IMO 2023/5

Revision en1, by DottedCalculator, 2023-07-16 13:57:59

Problem:

Let n be a positive integer. A Japanese triangle consists of 1+2++n circles arranged in an equilateral triangular shape such that for each i=1, 2, , n, the ith row contains exactly i circles, exactly one of which is coloured red. A ninja path in a Japanese triangle is a sequence of n circles obtained by starting in the top row, then repeatedly going from a circle to one of the two circles immediately below it and finishing in the bottom row. Here is an example of a Japanese triangle with n=6, along with a ninja path in that triangle containing two red circles.

Given a Japanese triangle, find the maximum number of red circles in a ninja path.

I found an algorithm using DP that can solve this problem in O(n2). Is there a more efficient solution?

History

 
 
 
 
Revisions
 
 
  Rev. Lang. By When Δ Comment
en1 English DottedCalculator 2023-07-16 13:57:59 931 Initial revision (published)