What is the time complexity of Equal Row and Column Pairs?

The optimal solution has a time complexity of O(n^2).

What is the space complexity of Equal Row and Column Pairs?

The space complexity is O(n^2).

What data structures are used to solve Equal Row and Column Pairs?

This problem uses Array, Hash Table, Matrix, Simulation. Understanding these concepts is essential for solving this Medium problem efficiently.

What are the key insights for solving Equal Row and Column Pairs?

Insight 1: The core idea is to efficiently compare each row with every column and count the matches. Direct comparison in a naive nested loop approach will work, but it can be optimized. Insight 2: Using a hash table (or dictionary) to store the counts of each row can significantly improve the efficiency of finding matching columns. We can then iterate through the columns and check how many times each column appears as a row.

Which companies ask LeetCode 2352. Equal Row and Column Pairs in interviews?

This problem is frequently asked at DE Shaw.

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Equal Row and Column Pairs - LeetCode 2352 Solution

Q: How to solve Equal Row and Column Pairs?

The solution uses a hash table to count the occurrences of each row in the grid. Then, it iterates through each column of the grid, creates a tuple (or string representation) of the column, and checks if this column exists as a row in the hash table. If it does, the count is incremented by the number of times that row exists. This approach avoids redundant comparisons and efficiently finds the matching row-column pairs.

Equal Row and Column Pairs - Complete Solution Guide

Equal Row and Column Pairs is LeetCode problem 2352, 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

Given a 0-indexed n x n integer matrix grid , return the number of pairs (r i , c j ) such that row r i and column c j are equal . A row and column pair is considered equal if they contain the same elements in the same order (i.e., an equal array). Example 1: Input: grid = [[3,2,1],[1,7,6],[2,7,7]] Output: 1 Explanation: There is 1 equal row and column pair: - (Row 2, Column 1): [2,7,7] Example 2: Input: grid = [[3,1,2,2],[1,4,4,5],[2,4,2,2],[2,4,2,2]] Output: 3 Explanation: There are 3 equal ro

Detailed Explanation

The problem asks us to count the number of pairs (row_i, col_j) in a given n x n integer matrix 'grid' where the row row_i and the column col_j are identical as arrays. In simpler terms, we need to find how many times a row is exactly the same as a column in the grid. The input is a 2D integer array representing the grid. The output is a single integer representing the count of such row-column pairs. The constraints specify the size of the grid (1 <= n <= 200) and the range of values in the grid (1 <= grid[i][j] <= 10^5).

Solution Approach

The solution uses a hash table to count the occurrences of each row in the grid. Then, it iterates through each column of the grid, creates a tuple (or string representation) of the column, and checks if this column exists as a row in the hash table. If it does, the count is incremented by the number of times that row exists. This approach avoids redundant comparisons and efficiently finds the matching row-column pairs.

Step-by-Step Algorithm

Step 1: Create a hash table (Counter in Python, HashMap in Java, map in C++) to store the count of each row in the grid.
Step 2: Iterate through each row of the grid.
Step 3: Convert the row into a string or tuple format so it can be used as a key in the hash table.
Step 4: Update the count of the row in the hash table.
Step 5: Iterate through each column of the grid.
Step 6: Create a temporary array (or list) to store the values of the current column.
Step 7: Convert the column into a string or tuple format so it can be compared with row keys in the hash table.
Step 8: Look up the column in the hash table to find how many times it appears as a row.
Step 9: Add the count to the total number of equal row and column pairs.
Step 10: Return the total count.

Key Insights

Insight 1: The core idea is to efficiently compare each row with every column and count the matches. Direct comparison in a naive nested loop approach will work, but it can be optimized.
Insight 2: Using a hash table (or dictionary) to store the counts of each row can significantly improve the efficiency of finding matching columns. We can then iterate through the columns and check how many times each column appears as a row.
Insight 3: Converting the rows and columns to a string or tuple representation allows us to use them as keys in the hash table, since arrays themselves are not hashable in some languages.

Complexity Analysis

Time Complexity: O(n^2)

Space Complexity: O(n^2)

Topics

This problem involves: Array, Hash Table, Matrix, Simulation.

Companies

Asked at: DE Shaw.

Equal Row and Column Pairs | LeetCode 2352

Medium

Array Hash Table Matrix Simulation

Time: O(n^2)Space: O(n^2)

Solution Code

Available in:

import java.util.Arrays;
import java.util.HashMap;
import java.util.Map;

class Solution {
    public int equalPairs(int[][] grid) {
        Map<String, Integer> rowCounts = new HashMap<>();
        int count = 0;
        
        for (int[] row : grid) {
            String rowStr = Arrays.toString(row);
            rowCounts.put(rowStr, rowCounts.getOrDefault(rowStr, 0) + 1);
        }
        
        int n = grid.length;
        for (int j = 0; j < n; j++) {
            int[] col = new int[n];
            for (int i = 0; i < n; i++) {
                col[i] = grid[i][j];
            }
            String colStr = Arrays.toString(col);
            count += rowCounts.getOrDefault(colStr, 0);
        }
        
        return count;
    }
}

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Problem Info

Description

Problem 2352: Equal Row and Column Pairs - Detailed explanation and solution approaches.

Topics

Array Hash Table Matrix Simulation

Companies

DE Shaw

Stats

Difficulty:Medium

Languages:4

Companies:1

Problem #:2352

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

10 steps

1
Step 1: Create a hash table (Counter in Python, HashMap in Java, map in C++) to store the count of each row in the grid.
2
Step 2: Iterate through each row of the grid.
3
Step 3: Convert the row into a string or tuple format so it can be used as a key in the hash table.
4
Step 4: Update the count of the row in the hash table.
5
Step 5: Iterate through each column of the grid.
6
Step 6: Create a temporary array (or list) to store the values of the current column.
7
Step 7: Convert the column into a string or tuple format so it can be compared with row keys in the hash table.
8
Step 8: Look up the column in the hash table to find how many times it appears as a row.
9
Step 9: Add the count to the total number of equal row and column pairs.
10
Step 10: Return the total count.

💡

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(n^2)

🐢 Quadratic - Gets slow with large inputs. Consider optimization!

💾

Space Complexity

O(n^2)

📚 Quadratic space - Uses lots of memory!

📝

Why?

The outer loops iterate n times (rows and columns). Inside these loops, the operations are dominated by converting the row/column to string/tuple which takes O(n) time. The hash table operations (insertion/lookup) take O(1) on average. Thus, the complexity is n*n * O(1) = O(n^2) time. Space is determined by the space used by hashmap. In the worst case, all the rows/columns are different, so we end up storing n rows with n values in the hashmap, giving O(n^2).

📖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

Naive comparison

Compare each row with each column using nested loops. In each inner loop, compare the elements of the row and column element by element. If they are equal, increment the counter.

Time: O(n^3), where n is the size of the grid. This is because we have two nested loops iterating through rows and columns (O(n^2)) and another inner loop that compares the elements of the row and column (O(n)).Space: O(1). No extra space is used other than a constant number of variables.

Trade-offs: This is simpler to implement but less efficient for larger grids. Use this if space is severely constrained and n is very small.

✨

Key Insights

1Insight 1: The core idea is to efficiently compare each row with every column and count the matches. Direct comparison in a naive nested loop approach will work, but it can be optimized.
2Insight 2: Using a hash table (or dictionary) to store the counts of each row can significantly improve the efficiency of finding matching columns. We can then iterate through the columns and check how many times each column appears as a row.
3Insight 3: Converting the rows and columns to a string or tuple representation allows us to use them as keys in the hash table, since arrays themselves are not hashable in some languages.

📚

Key Terms Explained

For Students

Array

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

Hash Table

A data structure that maps keys to values for quick lookup. Like a dictionary!

Edge Cases

Edge case 1: Grid with only one element. The algorithm correctly identifies the single row and column as equal and returns 1.
Edge case 2: Grid with all identical rows. The algorithm correctly counts n equal row-column pairs for each column. The row_counts will store the single row, and for each column, the count will be n.
Edge case 3: Grid with all distinct rows and columns. The algorithm correctly returns 0 as there are no equal pairs. The counts will be stored, and looking up columns in the map won't find a match.

⚠️

Common Mistakes to Avoid

✗Common mistake 1: Forgetting to convert the row or column to a hashable type (like a tuple or string) before using it as a key in the hash table (Python) or HashMap (Java). Arrays cannot be directly used as keys.

✗Common mistake 2: Failing to handle the case where a column does not exist as a row in the hash table. Using `getOrDefault` (Java) or `collections.Counter` (Python) simplifies this.

✗Common mistake 3: Incorrectly comparing rows and columns element by element in the naive approach, leading to wrong results. Ensure a complete comparison is done for each pair.

✅

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: Data analysis where you need to find identical patterns in rows and columns of a dataset. This is useful when dealing with tabular data where features (columns) might mirror samples (rows).

🏦Real-world scenario 2: Image processing where you might need to find symmetrical patterns or identical structures in rows and columns of a pixel matrix. This can be useful for object detection or image compression.

💡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

Medium problems are the bread and butter of technical interviews. Practice explaining your approach before coding.

⚠️ 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: June 13, 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

I was asked this exact problem at my Google interview. The interviewer wanted me to optimize space complexity.

@InterviewProJul 14

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

@CodeNinjaJul 7

❓

Frequently Asked Questions

What is the most efficient way to solve array problems?

Most array problems can be solved efficiently using techniques like two-pointer approach, sliding window, or hash maps. The key is identifying whether the array is sorted (enabling binary search) or if tracking seen elements (using hash maps) can help achieve O(n) time complexity.

What are the trade-offs of using a hash table?

Hash tables provide O(1) average-case lookup, insertion, and deletion, making them ideal for frequency counting and duplicate detection. However, they use O(n) extra space and may degrade to O(n) time in worst-case scenarios with hash collisions. Always consider if the space trade-off is acceptable.

What techniques are commonly tested in medium-difficulty problems?

Medium problems often require combining multiple techniques: two-pointer with hash maps, BFS/DFS with state tracking, dynamic programming with optimization, or divide-and-conquer approaches. They test your ability to recognize patterns and choose the right combination of techniques.

How should I practice algorithm problems effectively?

Focus on understanding patterns rather than memorizing solutions. After solving a problem, review optimal solutions and understand the intuition. Group similar problems to recognize patterns. Practice explaining your approach out loud. Review problems after a few days to test retention.

What is the optimal approach for "Equal Row and Column Pairs"?

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 hash table techniques can optimize the solution. Always handle edge cases and validate your approach with examples before coding.

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