#3242

Easy

auto_awesomeArray scanning plus hash lookup

LeetCode Problem Workspace

Design Neighbor Sum Service

Design a service that computes sums for adjacent and diagonal elements in a 2D grid.

array hash table design matrix simulation

Problem Statement

You are tasked with designing a service called NeighborSum for a 2D grid, where the grid contains distinct elements in the range from 0 to n² - 1. The grid is n x n in size. Your job is to implement methods that compute sums of adjacent and diagonal elements given a specific grid position, such as for adjacentSum or diagonalSum.

The NeighborSum service has several methods. The adjacentSum method calculates the sum of directly adjacent cells (left, right, up, and down), while the diagonalSum method computes the sum of diagonal cells (top-left, top-right, bottom-left, and bottom-right). Given these two methods, the goal is to handle multiple queries efficiently by leveraging the grid's structure with array scanning and hash lookup.

Examples

Example 1

Input: ["NeighborSum", "adjacentSum", "adjacentSum", "diagonalSum", "diagonalSum"] [[[[0, 1, 2], [3, 4, 5], [6, 7, 8]]], [1], [4], [4], [8]]

Output: [null, 6, 16, 16, 4]

Example 2

Input: ["NeighborSum", "adjacentSum", "diagonalSum"] [[[[1, 2, 0, 3], [4, 7, 15, 6], [8, 9, 10, 11], [12, 13, 14, 5]]], [15], [9]]

Output: [null, 23, 45]

Constraints

3 <= n == grid.length == grid[0].length <= 10
0 <= grid[i][j] <= n2 - 1
All grid[i][j] are distinct.
value in adjacentSum and diagonalSum will be in the range [0, n2 - 1].
At most 2 * n2 calls will be made to adjacentSum and diagonalSum.

Solution Approach

Use Array Scanning

The first step is scanning the grid to locate the target element's position. This involves iterating over the grid to find the row and column index of the element in question. Once located, calculating the sums is easy as the problem involves direct neighbors and diagonals.

Hash Lookup for Efficient Querying

After identifying the target element in the grid, use a hash map or dictionary to store precomputed sums of adjacent and diagonal cells. This allows for O(1) time complexity for each query after an initial scan.

Optimized Updates and Query Handling

To efficiently handle updates and queries, make sure to keep track of all the neighbors and diagonals in a single pass. This ensures each query can be answered in constant time by simply looking up the precomputed sums.

Complexity Analysis

Metric	Value
Time	Depends on the final approach
Space	Depends on the final approach

Time complexity depends on how the grid is scanned and how the sums are computed. An O(n²) scan is necessary to set up the grid, but after that, queries can be answered in constant time. Space complexity depends on the size of the precomputed hash map for storing the sums, which can also be O(n²).

What Interviewers Usually Probe

Efficient use of hashing to reduce lookup time
Clear implementation of array scanning to locate elements
Accurate handling of edge cases in the grid, such as boundaries or missing neighbors

Common Pitfalls or Variants

Common pitfalls

Incorrectly indexing out-of-bounds neighbors
Inefficient re-scanning of the grid for each query
Failure to handle grid boundaries properly, leading to errors when computing diagonal sums

Follow-up variants

Handling larger grids with more complex queries
Extending the problem to support dynamic grid updates
Optimizing for cases where grid size changes over time

FAQ

How does the design of NeighborSum help with efficient querying?

By using array scanning to locate the element and a hash lookup to store precomputed sums, NeighborSum ensures that each query is answered in constant time after the initial setup.

What is the time complexity of solving the NeighborSum problem?

The time complexity is O(n²) for the initial grid scan, but after that, each query is answered in O(1) due to the hash lookup.

How do I handle edge cases for diagonal sums?

Ensure that the grid boundaries are checked before accessing diagonal neighbors. If an element is on the edge, some diagonals will not exist and should be excluded from the sum.

What is the primary pattern used in the NeighborSum problem?

The problem uses array scanning combined with hash lookup to efficiently compute sums of adjacent and diagonal cells.

Can NeighborSum be optimized for larger grids?

Yes, the approach can be extended to handle larger grids by focusing on efficient lookup and possibly parallelizing the grid scanning step for very large data sets.

terminal

Solution

Solution 1: Hash Table

We can use a hash table $\textit{d}$ to store the coordinates of each element. Then, according to the problem description, we separately calculate the sum of adjacent elements and diagonally adjacent elements.

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class NeighborSum:

    def __init__(self, grid: List[List[int]]):
        self.grid = grid
        self.d = {}
        self.dirs = ((-1, 0, 1, 0, -1), (-1, 1, 1, -1, -1))
        for i, row in enumerate(grid):
            for j, x in enumerate(row):
                self.d[x] = (i, j)

    def adjacentSum(self, value: int) -> int:
        return self.cal(value, 0)

    def cal(self, value: int, k: int):
        i, j = self.d[value]
        s = 0
        for a, b in pairwise(self.dirs[k]):
            x, y = i + a, j + b
            if 0 <= x < len(self.grid) and 0 <= y < len(self.grid[0]):
                s += self.grid[x][y]
        return s

    def diagonalSum(self, value: int) -> int:
        return self.cal(value, 1)


# Your NeighborSum object will be instantiated and called as such:
# obj = NeighborSum(grid)
# param_1 = obj.adjacentSum(value)
# param_2 = obj.diagonalSum(value)

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