Is Equal Row and Column Pairs easy or hard?

Equal Row and Column Pairs is classified as a Medium problem on LeetCode. The brute-force solution is straightforward, but identifying the hashing optimization that reduces comparisons from O(n^3) to O(n^2) is the key insight.

Equal Row and Column Pairs Python/Java solution

In Python, rows and columns are typically converted into tuples and stored in a dictionary or Counter. In Java, arrays or lists can be serialized into strings or stored using List objects in a HashMap. Both implementations follow the same hashing strategy with O(n^2) time complexity.

How to solve Equal Row and Column Pairs in O(n^2)?

Convert each row of the grid into a tuple and store it in a dictionary with its count. Then build each column as a tuple and check if it exists in the dictionary. If it does, add the stored frequency to the result. Building rows and columns each requires O(n^2) work, resulting in an overall O(n^2) solution.

What is the best approach for Equal Row and Column Pairs?

The most efficient approach uses hashing with a dictionary. Store every row of the matrix as a tuple in a hash map with its frequency. Then construct each column as a tuple and check how many times it appears in the map. This reduces the complexity from O(n^3) brute force to O(n^2) with O(n^2) additional space.

Is Equal Row and Column Pairs asked at Google/Amazon/Meta?

Matrix hashing and row-column comparison problems appear frequently in interviews at large tech companies including Amazon, Google, and Meta. Variants that require recognizing repeating patterns in rows or columns are common in data structure and algorithm interview rounds.

What data structure is used in Equal Row and Column Pairs?

The optimal solution relies on a hash table (dictionary or unordered_map). Each row is converted into a hashable sequence such as a tuple or string and stored with its frequency. Columns are constructed in the same format and checked against the map for matches.

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

The brute-force iterative comparison takes O(n^3) time because every row is compared with every column and each comparison checks n elements. The optimized hashing approach reduces the complexity to O(n^2) by storing row signatures in a dictionary and performing constant-time lookups for each column.

Description Hints 3 Solution Video 19:59

2352. Equal Row and Column Pairs

Medium70.9% acceptance6 companies

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 row and column pairs:
- (Row 0, Column 0): [3,1,2,2]
- (Row 2, Column 2): [2,4,2,2]
- (Row 3, Column 2): [2,4,2,2]

Constraints:

n == grid.length == grid[i].length
1 <= n <= 200
1 <= grid[i][j] <= 10⁵

Asked at 6 companies

D. E. Shaw

Google Amazon Microsoft Meta Bloomberg

Topics

Hints open one at a time

Hint 1

We can use nested loops to compare every row against every column.

Hint 2

Another loop is necessary to compare the row and column element by element.

Hint 3

It is also possible to hash the arrays and compare the hashed values instead.

19:59

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