Graphs, Grids & DP

Two families share this lesson because Oracle draws from both, and together they are close to a sixth of the coding surface. The first is graph work: a grid you flood, a set of prerequisites you order. The second is dynamic programming, the table you fill one cell at a time. They look unrelated, and the room treats them as one cluster, so this lesson teaches them back to back and keeps the seam visible.

Start with the reframe that opens up the graph half. A grid cell is a node whose neighbors are the four cells around it. A course is a node whose neighbors are the courses that depend on it. Once you see the graph, the traversal follows from the question: reachability and regions want a plain flood fill, order and cycles want a topological sort. The DP half has its own reframe, which is that a hard-looking optimization is often just a small table where each entry is built from a couple of earlier ones.

The Oracle angle

Dynamic programming shows up at Oracle, so do not skip it. The loop is an easy-to-medium bar with no hard-algorithm gauntlet, which leads some candidates to bet that DP never comes. That bet loses. House Robber and the other max-non-adjacent-sum variants are among the most recurring problems in the whole loop, and two Premium questions sit right behind them. What Oracle wants is ordinary: define the state, write the transition, and set the base case cleanly on a one-dimensional table, then say why each entry only needs the ones already computed. Bring that and the DP round is a gift, because the problems stay in the standard tier.