Design Neighbor Sum Service - Solution & Explanation

This approach directly finds the position of the element in the grid and checks its adjacent or diagonal cells. Using the element's coordinates, it sums up the appropriate neighbors by checking boundary conditions. This approach has a guaranteed complexity due to the small size limits of the grid (n ≤ 10).

The NeighborSum class is initialized with the grid and populates a dictionary to map each value to its coordinates. For adjacentSum and diagonalSum, the stored references allow fast lookup of neighbors by iterating over potential offsets.

In this approach, we construct precomputed lists for each element that contain all potential adjacent and diagonal sums. These lists are cached, allowing for rapid retrieval of sums without the need to recompute directions dynamically.

The preprocessing step compiles possible sums of neighbors during initialization, effectively converting neighbor sum requests into dictionary lookups for constant time retrieval.