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Solution: Cherry Pickup

Explore how to solve the Cherry Pickup problem using dynamic programming by modeling two synchronized paths through a grid. Learn to apply memoization to efficiently compute and store states, maximizing cherry collection while avoiding invalid paths like thorns. Understand the complexity analysis and gain insight into a practical approach to complex pathfinding challenges.

Statement

You are given an n×nn \times n grid representing a field of cherries. Each cell in the grid can have one of three possible values:

  • 00: An empty cell that can be walked through

  • 11: A cell containing a cherry that can be picked and then passed through

  • ...