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Solution: Cherry Pickup

Explore an advanced dynamic programming approach to solve the Cherry Pickup problem, where you calculate the maximum cherries collected by simulating two synchronized paths through a thorny grid. This lesson covers the strategy of using memoization in a 3D table to optimize state exploration and handle path dependencies. You will understand how to manage overlapping states, compute multiple move combinations, and evaluate the algorithm's time and space complexity, preparing you to tackle similar complex grid traversal problems efficiently.

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

  • ...