Racing Gems
From charlesreid1
Problem Description
This problem is an ICPC programming competition problem.
In this problem, we have a race track of width x = 0 to x = w, height y = 0 to y = h. We have a character that begins at the x-axis (y=0) and moves toward the finish line (y=h) with a steady velocity v.
You control the character's horizontal velocity, -v/r to +v/r, and your goal is to obtain as many gems as possible.
The location of gems are given by (x,y) integer pairs on the grid. Determine the maximum number of gems that can be obtained by the character.
Git repo has solution explanation: https://git.charlesreid1.com/cs/java/src/master/dynamic-programming/racing-gems
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Combinatorics
Combinatorial Structures - Order Does Not Matter Ordinary generating functions
Labelled Structures - Order Matters Enumerating Permutations: String Permutations Generating Permutations: Cool · Algorithm M (add-one) · Algorithm G (Gray binary code)
Combinatorics Problems Longest Increasing Subsequence · Maximum Value Contiguous Subsequence · Racing Gems Cards (poker hands with a deck of 52 playing cards)
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