Google Software Engineer Coding Questions

In managing large datasets, Google Cloud’s BigQuery requires efficient computations to determine the largest rectangular area defined by 1s in a binary matrix.
Problem statement: Given a m x n binary matrix filled with 0s and 1s, your task is to return the area of the largest rectangle containing only 1s. You must implement maximalRectangle(matrix: List[List[int]]) -> int.Example 1:
Input: matrix = [[1,0,1,0,0],[1,0,1,1,1],[1,1,1,1,1],[1,0,0,1,0]]
Output: 6
Explanation: The largest rectangle has an area of 6.Example 2:
Input: matrix = [[0,0,0],[0,0,0]]
Output: 0
Explanation: There are no 1s in the matrix.Constraints:
- m == matrix.length
- n == matrix[i].length
- Area must be computed in O(m*n) time.

In Google's Maps, real-time navigation requires efficient pathfinding over large graphs representing cities and road networks. Your task is to implement the A* search algorithm to find the shortest path between two points.
Problem statement: You need to implement the method findShortestPath(start: Point, end: Point) -> List[Point], which returns the shortest path as a list of Points from the start to the end. Assumptions include that the environment is represented as a 2D grid where passable and non-passable terrains are indicated.
- Point: A representation of a coordinate with x and y attributes.Example 1:
Input: start = (0, 0), end = (3, 3)
Output: [(0, 0), (1, 1), (2, 2), (3, 3)]
Explanation: The algorithm finds an optimal path through the grid.Example 2:
Input: start = (1, 1), end = (4, 4)
Output: [(1, 1), (2, 2), (3, 3), (4, 4)]
Explanation: Another optimal path is provided based on proximity.Constraints:
- The grid size will be at most N x N with N ≤ 1000.
- Points coordinates will be between 0 and N-1.