Importance of Dynamic Programming (DP) on Grids
Grid problems often exhibit overlapping subproblems. This means that the optimal solution for a larger problem depends on the solutions to smaller subproblems within the grid. A naive approach would involve calculating the solutions for each cell independently, leading to significant redundancy and inefficiency. Whereas DP uses the overlapping subproblems property by storing solutions to previously encountered subproblems, significantly reducing the number of repeated calculations and leading to a more efficient solution.
Dynamic Programming (DP) on Grids
Grid problems involve a 2D grid of cells, often representing a map or graph. We can apply Dynamic Programming on Grids when the solution for a cell is dependent on solutions of previously traversed cells like to find a path or count number of paths or solve an optimization problem across the grid, with certain constraints on movement or cost. In this article we are going to discuss about the idea behind Dynamic Programming on Grids with their importance, use cases and some practice problems.
Table of Content
- Idea behind Dynamic Programming (DP) on Grids
- Importance of Dynamic Programming (DP) on Grids
- Use Cases of Dynamic Programming (DP) on Grids
- Practice Problems on Dynamic Programming (DP) on Grids