2. Inductive Formulation of the Grid Path
The chapter focuses on dynamic programming and its application in solving grid path problems. It explains how paths from the origin to various points can be calculated using recursive relations, while also addressing the concepts of memoization and the significance of handling obstacles or holes in the paths. The distinction between recursive calculations and dynamic programming is highlighted alongside practical examples.
Enroll to start learning
You've not yet enrolled in this course. Please enroll for free to listen to audio lessons, classroom podcasts and take practice test.
Sections
Navigate through the learning materials and practice exercises.
What we have learnt
- Paths to any point in a grid can be computed using the sum of paths from its left and bottom neighbors.
- Memoization avoids redundant calculations by storing previously computed results, while dynamic programming computes all subproblems systematically.
- Handling obstacles in a path requires setting values to zero at the respective grid points, thereby affecting subsequent calculations.
Key Concepts
- -- Paths in a Grid
- The number of different ways to navigate from the origin (0,0) to a target point (i,j), based on valid moves (right and up).
- -- Dynamic Programming
- An algorithmic technique that solves problems by breaking them down into simpler subproblems, solving each subproblem once, and storing their solutions.
- -- Memoization
- An optimization technique that involves storing results of expensive function calls and returning the cached result when the same inputs occur again.
- -- DAG (Directed Acyclic Graph)
- A finite directed graph with no directed cycles, used here to represent dependencies between subproblems.
Additional Learning Materials
Supplementary resources to enhance your learning experience.