#1260

Easy

LeetCode Problem Workspace

Shift 2D Grid

Shift 2D Grid requires shifting elements of a matrix by a given number of times, simulating step-by-step movement.

Problem Statement

You are given a 2D grid with dimensions m x n and an integer k, which represents how many times you need to shift the grid. Each shift operation involves moving the elements in the grid to the right, and the last element of the last row wraps around to the first position.

Your task is to return the 2D grid after applying the shift operation exactly k times. Ensure the solution efficiently handles the grid's movement and the wrapping of elements, especially when dealing with multiple shifts or edge cases.

Examples

Example 1

Input: grid = [[1,2,3],[4,5,6],[7,8,9]], k = 1

Output: [[9,1,2],[3,4,5],[6,7,8]]

Example details omitted.

Example 2

Input: grid = [[3,8,1,9],[19,7,2,5],[4,6,11,10],[12,0,21,13]], k = 4

Output: [[12,0,21,13],[3,8,1,9],[19,7,2,5],[4,6,11,10]]

Example details omitted.

Example 3

Input: grid = [[1,2,3],[4,5,6],[7,8,9]], k = 9

Output: [[1,2,3],[4,5,6],[7,8,9]]

Example details omitted.

Constraints

m == grid.length
n == grid[i].length
1 <= m <= 50
1 <= n <= 50
-1000 <= grid[i][j] <= 1000
0 <= k <= 100

Solution Approach

Simulate the Shift Step by Step

To solve this problem, simulate each shift operation. For each step, move the elements of the grid to the right, handling the wraparound for the last element in the grid. Repeat this process k times.

Optimized Approach with Modular Arithmetic

Instead of performing k shifts individually, calculate the effective number of shifts using modular arithmetic (k % totalElements). This approach reduces unnecessary full rotations and speeds up the solution for large values of k.

Matrix Transformation

View the grid as a linear array and perform the shifts in a more efficient way by treating it as a 1D array for the shifting operation. Once the transformation is complete, convert the array back into the grid format.

Complexity Analysis

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

The time complexity of the brute-force approach is O(k * m * n), where k is the number of shifts, and m and n are the dimensions of the grid. The optimized approach using modular arithmetic reduces this to O(m * n), as only the necessary shifts are performed. The space complexity is O(m * n) for storing the grid during transformations.

What Interviewers Usually Probe

Tests candidate’s ability to simulate a matrix transformation with a step-by-step approach.
Looks for efficient use of modular arithmetic to reduce redundant operations.
Assesses the candidate’s understanding of handling grid dimensions and shifting elements.

Common Pitfalls or Variants

Common pitfalls

Over-complicating the solution by applying unnecessary shifts when k is large. Use modular arithmetic to optimize the number of shifts.
Not correctly handling the wraparound of elements when shifting the last column of the grid.
Misunderstanding the problem by not simulating each shift step-by-step or incorrectly handling edge cases.

Follow-up variants

Shift 2D grid in multiple directions, not just to the right.
Shift the grid only for specific rows or columns instead of the entire grid.
Perform the shift operation in a circular or spiral pattern.

FAQ

How does modular arithmetic optimize the Shift 2D Grid solution?

Modular arithmetic helps calculate the effective number of shifts by using k % totalElements, reducing redundant rotations and speeding up the solution.

What is the primary approach for solving the Shift 2D Grid problem?

The primary approach is simulating the shift step by step, moving elements of the grid to the right and wrapping the last element to the start.

What common mistake should I avoid in the Shift 2D Grid problem?

A common mistake is not using modular arithmetic for large k, resulting in unnecessary shifts and inefficiency.

How can GhostInterview assist with Shift 2D Grid?

GhostInterview provides tailored solutions and feedback, focusing on matrix manipulation and optimizing shift operations using modular arithmetic.

Can the Shift 2D Grid problem be solved without simulating each shift?

Yes, you can optimize the solution by using modular arithmetic and viewing the grid as a linear array, reducing the need for repeated shifts.

terminal

Solution

Solution 1: Flattening the 2D Array

According to the problem description, if we flatten the 2D array into a 1D array, then each shift operation is to move the elements in the array one position to the right, with the last element moving to the first position of the array.

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class Solution:
    def shiftGrid(self, grid: List[List[int]], k: int) -> List[List[int]]:
        m, n = len(grid), len(grid[0])
        ans = [[0] * n for _ in range(m)]
        for i, row in enumerate(grid):
            for j, v in enumerate(row):
                x, y = divmod((i * n + j + k) % (m * n), n)
                ans[x][y] = v
        return ans

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