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

The optimal solution has a time complexity of O(m*n*log(m*n)).

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

The space complexity is O(m*n).

What data structures are used to solve Minimum Operations to Make a Uni-Value Grid?

This problem uses Array, Math, Sorting, Matrix. Understanding these concepts is essential for solving this Medium problem efficiently.

What are the key insights for solving Minimum Operations to Make a Uni-Value Grid?

Insight 1: All elements must have the same remainder when divided by 'x'. If they don't, it's impossible to make them equal by adding or subtracting 'x'. Insight 2: The optimal value to make all elements equal to is the median of all elements in the grid. This minimizes the sum of absolute differences.

Which companies ask LeetCode 2033. Minimum Operations to Make a Uni-Value Grid in interviews?

This problem is frequently asked at EPAM Systems.

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Minimum Operations to Make a Uni-Value Grid - LeetCode 2033 Solution

Minimum Operations to Make a Uni-Value Grid - Complete Solution Guide

Minimum Operations to Make a Uni-Value Grid is LeetCode problem 2033, a Medium level challenge. This complete guide provides step-by-step explanations, multiple solution approaches, and optimized code in python3, java, cpp, c.

Problem Statement

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. - Subtrac

Detailed Explanation

The problem requires us to find the minimum number of operations needed to make all elements in a given 2D grid equal. Each operation involves adding or subtracting a fixed value 'x' from any element in the grid. If it's impossible to make all elements equal using the given 'x', we should return -1. The input consists of a 2D integer grid and an integer 'x'. The output is the minimum number of operations or -1 if not possible.

Solution Approach

The solution first checks if it's possible to make all elements equal by verifying if all elements have the same remainder when divided by 'x'. If they don't, it returns -1. If they do, it flattens the grid into a 1D array, sorts it, and finds the median. Then, it iterates through the sorted array and calculates the number of operations needed for each element to reach the median. The total number of operations is then returned.

Step-by-Step Algorithm

Step 1: Flatten the 2D grid into a 1D array.
Step 2: Check if all elements in the 1D array have the same remainder when divided by 'x'. If not, return -1.
Step 3: Sort the 1D array in ascending order.
Step 4: Find the median of the sorted array. For an array of size n, the median is the element at index n // 2.
Step 5: Iterate through the sorted array and calculate the number of operations needed for each element to reach the median (abs(element - median) // x).
Step 6: Sum the number of operations for all elements and return the total.

Key Insights

Insight 1: All elements must have the same remainder when divided by 'x'. If they don't, it's impossible to make them equal by adding or subtracting 'x'.
Insight 2: The optimal value to make all elements equal to is the median of all elements in the grid. This minimizes the sum of absolute differences.
Insight 3: The number of operations required for each element is the absolute difference between the element and the median, divided by 'x'.

Complexity Analysis

Time Complexity: O(m*n*log(m*n))

Space Complexity: O(m*n)

Topics

This problem involves: Array, Math, Sorting, Matrix.

Companies

Asked at: EPAM Systems.

Minimum Operations to Make a Uni-Value Grid | LeetCode 2033

Medium

Array Math Sorting Matrix

Time: O(m*n*log(m*n))Space: O(m*n)

Solution Code

Available in:

import java.util.ArrayList;
import java.util.Arrays;
import java.util.List;

class Solution {
    public int minOperations(int[][] grid, int x) {
        List<Integer> nums = new ArrayList<>();
        for (int[] row : grid) {
            for (int num : row) {
                nums.add(num);
            }
        }

        int remainder = nums.get(0) % x;
        for (int num : nums) {
            if (num % x != remainder) {
                return -1;
            }
        }

        nums.sort(null);
        int n = nums.size();
        int median = nums.get(n / 2);

        int operations = 0;
        for (int num : nums) {
            operations += Math.abs(num - median) / x;
        }

        return operations;
    }
}

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Problem Info

Description

Problem 2033: Minimum Operations to Make a Uni-Value Grid - Detailed explanation and solution approaches.

Topics

Array Math Sorting Matrix

Companies

EPAM Systems

Stats

Difficulty:Medium

Languages:4

Companies:1

Problem #:2033

Problem Explanation

💡

Think Before You Code

🤔 Ask Yourself

→What is the input? What output do I need?
→Can I solve a smaller version of this problem first?
→What patterns have I seen in similar problems?

✏️ Try This First

Before looking at the solution, try to solve it on paper with a simple example!

🚀 Try on LeetCode

Solution Approach

📋

Step-by-Step Solution

6 steps

1
Step 1: Flatten the 2D grid into a 1D array.
2
Step 2: Check if all elements in the 1D array have the same remainder when divided by 'x'. If not, return -1.
3
Step 3: Sort the 1D array in ascending order.
4
Step 4: Find the median of the sorted array. For an array of size n, the median is the element at index n // 2.
5
Step 5: Iterate through the sorted array and calculate the number of operations needed for each element to reach the median (abs(element - median) // x).
6
Step 6: Sum the number of operations for all elements and return the total.

💡

Pro Tip for Students

Try tracing through each step with a small example on paper before coding. Understanding "why" each step happens is more important than memorizing the code!

⚡

Complexity Analysis

⏱️

Time Complexity

O(m*n*log(m*n))

💾

Space Complexity

O(m*n)

📝

Why?

The time complexity is dominated by the sorting step, which requires O(NlogN) where N = m*n is the total number of elements in the grid. The space complexity stems from the need to store all grid elements in a single list before sorting.

📖New to Big O? Click to learn more

Big O Notation - Quick Guide

O(1)Best - Instant

O(log n)Excellent - Binary Search

O(n)Good - One loop

O(n log n)OK - Sorting

O(n²)Slow - Nested loops

O(2ⁿ)Very Slow - Recursion

Alternative Approaches

Using nth_element (C++)

Instead of fully sorting the array, C++ allows you to use `std::nth_element` to find the median in O(N) on average.

Time: O(m*n) on average, O((m*n)^2) worst caseSpace: O(m*n)

Trade-offs: Can be faster on average than full sorting, but has a potential worst-case time complexity. This might be useful in performance-critical applications where the average case performance is more important than the worst-case.

✨

Key Insights

1Insight 1: All elements must have the same remainder when divided by 'x'. If they don't, it's impossible to make them equal by adding or subtracting 'x'.
2Insight 2: The optimal value to make all elements equal to is the median of all elements in the grid. This minimizes the sum of absolute differences.
3Insight 3: The number of operations required for each element is the absolute difference between the element and the median, divided by 'x'.

📚

Key Terms Explained

For Students

Array

A collection of items stored at contiguous memory locations. Like a row of boxes.

Sorting

Arranging elements in a specific order (ascending/descending).

Edge Cases

Edge case 1: Empty grid. While the problem states 1 <= m * n, it's good practice to consider an empty grid. The solution will likely handle this gracefully if the check of remainder is done *after* flattening.
Edge case 2: All elements are already equal. The solution correctly returns 0 operations in this case because the median will be equal to all elements.

⚠️

Common Mistakes to Avoid

✗Common mistake 1: Not checking if all elements have the same remainder when divided by 'x'. This leads to incorrect results when it's impossible to make all elements equal.

✗Common mistake 2: Using the mean (average) instead of the median. The median minimizes the sum of absolute differences, while the mean minimizes the sum of squared differences. The problem asks for the minimum number of operations, so the median is the correct choice.

✅

Learning Tip

Every mistake is a learning opportunity! When you make an error, understand why it happened before moving on.

🌍

Where is This Used in Real Life?

💼Real-world scenario 1: Manufacturing. Consider a factory producing items where each item's property should be as close as possible to the target value (e.g., length of a component). Adjustments cost time/money. The 'grid' is the properties of produced components, 'x' is the step adjustment, and the goal is to bring them as close as possible at minimal adjustment cost.

🏦Real-world scenario 2: Image processing. Adjusting pixel values in an image to homogenize the color distribution. Each pixel's value corresponds to an element in the grid. Each operation would represent an adjustment to the color. The goal would be to make a uniform color while minimizing the number of color adjustments.

💡Understanding real-world applications helps you see the "why" behind algorithms. It's not just about passing interviews—these concepts power the apps and websites you use every day!

Author's Notes

💡 Key Insight

When dealing with arrays, always consider if sorting would simplify the problem. Many array problems have O(n) solutions using hash maps or two-pointer technique.

🎯 Interview Tip

Consider multiple approaches before coding. Mentioning alternatives shows breadth of knowledge.

⚠️ Watch Out

Off-by-one errors are the most common mistake. Double-check your loop bounds and array indices.

Written by Saswata Mondal

Software Engineer • Algorithms Enthusiast • Interview Coach

👨‍💻

About the Author

👨‍💻

Saswata MondalAuthor400+ LC Problems

B.Tech CSE, IEM Kolkata | LeetCode Rating: 1672 (Top 15%)

Certified: IBM Java Developer, NPTEL Programming in Java

Last updated: July 24, 2024LeetCode Profile GitHub

This solution has been crafted based on my experience solving 400+ LeetCode problems. Each explanation is designed to help you understand the underlying concepts, not just memorize the code.

Community Tips & Insights

Try solving this without using extra space first. It's a great exercise for understanding the underlying pattern.

@CodeNinjaJul 13

In a real interview, always clarify constraints first. Ask about input size and value ranges.

@TechLeadJul 6

Don't forget to handle the edge case when the input is empty. Many candidates miss this in interviews.

@DevExpert92Jun 29

❓

Frequently Asked Questions

When should I use in-place modification vs creating a new array?

Use in-place modification when space complexity matters (O(1) space requirement) and the original array can be modified. Create a new array when you need to preserve the original data or when the problem involves significant restructuring that would complicate in-place logic.

How much time should I spend on a medium problem in interviews?

In a 45-minute interview, aim for: 5-10 minutes understanding and clarifying, 5-10 minutes discussing approach, 20-25 minutes coding, and 5-10 minutes testing. If stuck after 15 minutes of thinking, verbalize your thought process and ask for hints.

What is the importance of time and space complexity analysis?

Complexity analysis is crucial because: 1) Interviewers always ask about it, 2) It helps you choose between approaches, 3) It demonstrates CS fundamentals. Always state both time and space complexity, and be prepared to explain how you derived them.

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

For this medium-level Array problem, the key is to identify the core pattern. Analyze the input constraints to determine acceptable time complexity. Consider whether math techniques can optimize the solution. Always handle edge cases and validate your approach with examples before coding.

🤖 Need help with this problem?