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This is a medium difficulty Coding & Algorithms question, commonly asked during Onsite rounds at Uber.

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This question is commonly asked for Software Engineer candidates at Uber during technical interviews.

Find a Bounded Subarray and Largest Square

Quick Overview

This question evaluates array manipulation and algorithmic problem-solving skills across two tasks: enforcing bounded value ranges within contiguous subarrays and identifying largest uniform square regions in binary matrices, exercising concepts such as range-tracking, efficient data structures, and dynamic programming.

Company: Uber

Role: Software Engineer

Category: Coding & Algorithms

Difficulty: medium

Interview Round: Onsite

Implement the following two independent coding tasks. ### Task A: Longest bounded-range subarray Given an integer array `nums` and an integer `limit`, return the length of the longest contiguous subarray such that the difference between the maximum and minimum values inside that subarray is at most `limit`. Example: - Input: `nums = [8, 2, 4, 7]`, `limit = 4` - Output: `2` - Explanation: The longest valid subarray is `[2, 4]` or `[4, 7]`. Constraints: - `1 <= nums.length <= 100000` - `-1000000000 <= nums[i] <= 1000000000` - `0 <= limit <= 1000000000` ### Task B: Largest square area in a binary grid Given an `m x n` binary matrix `grid` containing only `0`s and `1`s, return the area of the largest square containing only `1`s. Example: - Input: `grid = [[1,0,1,0,0],[1,0,1,1,1],[1,1,1,1,1],[1,0,0,1,0]]` - Output: `4` - Explanation: The largest all-`1` square has side length `2`, so its area is `4`. Constraints: - `1 <= m, n <= 300` - `grid[i][j]` is either `0` or `1`.

Quick Answer: This question evaluates array manipulation and algorithmic problem-solving skills across two tasks: enforcing bounded value ranges within contiguous subarrays and identifying largest uniform square regions in binary matrices, exercising concepts such as range-tracking, efficient data structures, and dynamic programming.

Part 1: Longest Bounded-Range Subarray

Given an integer array `nums` and an integer `limit`, find the length of the longest contiguous subarray such that the difference between the maximum and minimum values inside that subarray is at most `limit`. You must return only the length, not the subarray itself.

Constraints

1 <= len(nums) <= 100000
-1000000000 <= nums[i] <= 1000000000
0 <= limit <= 1000000000

Examples

Input: ([8, 2, 4, 7], 4)

Expected Output: 2

Explanation: The longest valid subarrays are `[2, 4]` and `[4, 7]`, both of length 2.

Input: ([10, 1, 2, 4, 7, 2], 5)

Expected Output: 4

Explanation: The subarray `[2, 4, 7, 2]` has max 7, min 2, and difference 5, so the answer is 4.

Input: ([4, 2, 2, 2, 4, 4, 2, 2], 0)

Expected Output: 3

Explanation: With limit 0, all values in the subarray must be equal. The longest such run is `[2, 2, 2]`.

Input: ([], 3)

Expected Output: 0

Explanation: An empty array has no subarrays, so the longest valid length is 0.

Input: ([5], 0)

Expected Output: 1

Explanation: A single-element subarray always satisfies the condition.

Input: ([-1, -5, -3, -4, -2], 3)

Expected Output: 4

Explanation: The subarray `[-5, -3, -4, -2]` has max -2 and min -5, so the difference is 3 and the length is 4.

Hints

A sliding window is a good fit because the subarray must be contiguous.
To expand and shrink the window efficiently, maintain the current minimum and maximum using monotonic deques.

Part 2: Largest Square Area in a Binary Grid

Given an `m x n` binary matrix `grid` containing only `0`s and `1`s, return the area of the largest square that contains only `1`s. The area of a square is its side length multiplied by itself.

Constraints

1 <= m, n <= 300
grid[i][j] is either 0 or 1

Examples

Input: ([[1,0,1,0,0],[1,0,1,1,1],[1,1,1,1,1],[1,0,0,1,0]],)

Expected Output: 4

Explanation: The largest all-1 square has side length 2, so its area is 2 * 2 = 4.

Input: ([[0,1],[1,0]],)

Expected Output: 1

Explanation: There is no 2x2 square of 1s, but there are individual 1 cells, so the largest area is 1.

Input: ([[0,0,0],[0,0,0]],)

Expected Output: 0

Explanation: There are no 1s in the grid, so no valid square exists.

Input: ([],)

Expected Output: 0

Explanation: An empty grid contains no square of 1s.

Input: ([[1,1,1],[1,1,1],[1,1,1]],)

Expected Output: 9

Explanation: The entire 3x3 grid is filled with 1s, so the largest square has area 3 * 3 = 9.

Hints

Think about the largest square that can end at each cell.
If a cell contains 1, its square size depends on the top, left, and top-left neighboring cells.

Quick Overview