Is Minimum Operations to Make a Uni-Value Grid easy or hard?

The problem is generally classified as Medium. The main challenge is recognizing the modulo feasibility constraint and the fact that the median minimizes total absolute movement. Once these insights are clear, the implementation becomes straightforward.

Minimum Operations to Make a Uni-Value Grid Python/Java solution

In Python or Java, flatten the grid into a list, verify all values share the same remainder modulo x, then sort the list and pick the middle element as the median. The total operations are computed using abs(value - median) / x for each element. The implementation is short and typically under 20 lines.

How to solve Minimum Operations to Make a Uni-Value Grid in O(n)?

After verifying that all numbers share the same remainder modulo x, you can avoid full sorting by using a selection algorithm (like Quickselect) to find the median in O(n) average time. Once the median is known, compute the operation cost in a single linear scan. This reduces the median search from O(n log n) to O(n).

What is the best approach for Minimum Operations to Make a Uni-Value Grid?

The optimal approach flattens the grid into a single array, checks that all elements share the same remainder modulo x, then sorts the array and converts all values to the median. The median minimizes the total absolute distance, so the total operations become the sum of |value − median| / x. This solution runs in O(mn log(mn)) time due to sorting.

Is Minimum Operations to Make a Uni-Value Grid asked at Google/Amazon/Meta?

Problems involving median minimization, grid transformations, and modular feasibility checks commonly appear in interviews at companies like Google, Amazon, and Meta. Variants of this problem test understanding of sorting, absolute difference minimization, and mathematical constraints.

What data structure is used in Minimum Operations to Make a Uni-Value Grid?

The solution primarily uses arrays. The grid is flattened into a one-dimensional array so that sorting or median selection can be applied efficiently. Additional logic relies on modular arithmetic and simple iteration over the array.

What is the time complexity of Minimum Operations to Make a Uni-Value Grid?

The common optimal solution runs in O(mn log(mn)) time and O(mn) space. The grid is flattened into an array of size m*n, then sorted to locate the median. After that, a linear pass computes the number of operations required for each element.

Description Hints 3 Solution Video 29:28

2033. Minimum Operations to Make a Uni-Value Grid

Medium70.7% acceptance5 companies

You are given a 2D integer grid of size m x n and an integer x. In one operation, you can add x to or subtract x from any element in the grid.

A uni-value grid is a grid where all the elements of it are equal.

Return the minimum number of operations to make the grid uni-value. If it is not possible, return -1.

Example 1:

Input: grid = [[2,4],[6,8]], x = 2
Output: 4
Explanation: We can make every element equal to 4 by doing the following: 
- Add x to 2 once.
- Subtract x from 6 once.
- Subtract x from 8 twice.
A total of 4 operations were used.

Example 2:

Input: grid = [[1,5],[2,3]], x = 1
Output: 5
Explanation: We can make every element equal to 3.

Example 3:

Input: grid = [[1,2],[3,4]], x = 2
Output: -1
Explanation: It is impossible to make every element equal.

Constraints:

m == grid.length
n == grid[i].length
1 <= m, n <= 10⁵
1 <= m * n <= 10⁵
1 <= x, grid[i][j] <= 10⁴

Asked at 5 companies

EPAM Systems Amazon

Google Microsoft Meta

Topics

Hints open one at a time

Hint 1

Is it possible to make two integers a and b equal if they have different remainders dividing by x?

Hint 2

If it is possible, which number should you select to minimize the number of operations?

Hint 3

What if the elements are sorted?

29:28

Still stuck?Read 3 approaches, or watch a walkthrough.

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