What is the time complexity of Sum of Matrix After Queries?

The optimal solution has a time complexity of O(q).

What data structures are used to solve Sum of Matrix After Queries?

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

What are the key insights for solving Sum of Matrix After Queries?

Insight 1: Processing queries in reverse order simplifies the logic. The last query affecting a row or column determines its final value. Insight 2: Using boolean arrays to track which rows and columns have been set avoids unnecessary recalculations and ensures that we only consider the effect of the 'last' query.

Which companies ask LeetCode 2718. Sum of Matrix After Queries in interviews?

This problem is frequently asked at Sprinklr.

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Sum of Matrix After Queries - LeetCode 2718 Solution

Sum of Matrix After Queries - Complete Solution Guide

Sum of Matrix After Queries is LeetCode problem 2718, 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 an integer n and a 0-indexed 2D array queries where queries[i] = [type i , index i , val i ] . Initially, there is a 0-indexed n x n matrix filled with 0 's. For each query, you must apply one of the following changes: if type i == 0 , set the values in the row with index i to val i , overwriting any previous values. if type i == 1 , set the values in the column with index i to val i , overwriting any previous values. Return the sum of integers in the matrix after all queries are a

Detailed Explanation

The problem presents an n x n matrix initially filled with zeros. We are given a series of queries. Each query instructs us to either set all values in a specific row to a given value or set all values in a specific column to a given value. The task is to determine the sum of all elements in the matrix after applying all queries.

Solution Approach

The solution processes the queries in reverse order. This approach is crucial because the last query that modifies a row or column determines its final value. For each query, the algorithm checks if the corresponding row or column has already been processed (i.e., set by a later query). If not, it adds the contribution of that query to the total sum. The contribution is calculated by multiplying the query value by the number of cells in the row/column that have not been set by any later query.

Step-by-Step Algorithm

Step 1: Initialize `total_sum` to 0. This variable will store the final sum of the matrix.
Step 2: Create two boolean arrays, `seen_rows` and `seen_cols`, of size 'n'. Initialize all elements to `False`. These arrays will track whether a row or column has been set by a later query.
Step 3: Initialize `num_rows_set` and `num_cols_set` to 0. These variables will keep track of the number of rows and columns that have been set.
Step 4: Iterate through the `queries` array in reverse order.
Step 5: For each query, determine the `query_type`, `index`, and `val`.
Step 6: If `query_type` is 0 (row query), check if `seen_rows[index]` is `False`. If it is, it means this is the last time this row is being set. Update `total_sum` by adding `val * (n - num_cols_set)`. Set `seen_rows[index]` to `True` and increment `num_rows_set`.
Step 7: If `query_type` is 1 (column query), check if `seen_cols[index]` is `False`. If it is, it means this is the last time this column is being set. Update `total_sum` by adding `val * (n - num_rows_set)`. Set `seen_cols[index]` to `True` and increment `num_cols_set`.
Step 8: After iterating through all the queries, return `total_sum`.

Key Insights

Insight 1: Processing queries in reverse order simplifies the logic. The last query affecting a row or column determines its final value.
Insight 2: Using boolean arrays to track which rows and columns have been set avoids unnecessary recalculations and ensures that we only consider the effect of the 'last' query.
Insight 3: Optimization is achieved by only updating the sum based on the unset rows/columns at the time of processing a particular query.

Complexity Analysis

Time Complexity: O(q)

Space Complexity: O(n)

Topics

This problem involves: Array, Hash Table.

Companies

Asked at: Sprinklr.

Sum of Matrix After Queries | LeetCode 2718

Medium

Array Hash Table

Time: O(q)Space: O(n)

Solution Code

Available in:

class Solution {
    public long matrixSumQueries(int n, int[][] queries) {
        long total_sum = 0;
        
        boolean[] seen_rows = new boolean[n];
        boolean[] seen_cols = new boolean[n];
        
        int num_rows_set = 0;
        int num_cols_set = 0;
        
        // Process queries in reverse order because the last query for a
        // given row or column determines its final values.
        for (int i = queries.length - 1; i >= 0; i--) {
            int query_type = queries[i][0];
            int index = queries[i][1];
            int val = queries[i][2];
            
            if (query_type == 0) {  // Row query
                if (!seen_rows[index]) {
                    // This is the last time this row is being set.
                    // It will affect all columns that have not been set by a later query.
                    total_sum += (long)val * (n - num_cols_set);
                    seen_rows[index] = true;
                    num_rows_set++;
                }
            } else {  // Column query
                if (!seen_cols[index]) {
                    // This is the last time this column is being set.
                    // It will affect all rows that have not been set by a later query.
                    total_sum += (long)val * (n - num_rows_set);
                    seen_cols[index] = true;
                    num_cols_set++;
                }
            }
        }
        
        return total_sum;
    }
}

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Problem Info

Description

Problem 2718: Sum of Matrix After Queries - Detailed explanation and solution approaches.

Topics

Array Hash Table

Companies

Sprinklr

Stats

Difficulty:Medium

Languages:4

Companies:1

Problem #:2718

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

8 steps

1
Step 1: Initialize `total_sum` to 0. This variable will store the final sum of the matrix.
2
Step 2: Create two boolean arrays, `seen_rows` and `seen_cols`, of size 'n'. Initialize all elements to `False`. These arrays will track whether a row or column has been set by a later query.
3
Step 3: Initialize `num_rows_set` and `num_cols_set` to 0. These variables will keep track of the number of rows and columns that have been set.
4
Step 4: Iterate through the `queries` array in reverse order.
5
Step 5: For each query, determine the `query_type`, `index`, and `val`.
6
Step 6: If `query_type` is 0 (row query), check if `seen_rows[index]` is `False`. If it is, it means this is the last time this row is being set. Update `total_sum` by adding `val * (n - num_cols_set)`. Set `seen_rows[index]` to `True` and increment `num_rows_set`.
7
Step 7: If `query_type` is 1 (column query), check if `seen_cols[index]` is `False`. If it is, it means this is the last time this column is being set. Update `total_sum` by adding `val * (n - num_rows_set)`. Set `seen_cols[index]` to `True` and increment `num_cols_set`.
8
Step 8: After iterating through all the queries, return `total_sum`.

💡

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(q)

💾

Space Complexity

O(n)

📦 Linear space - Memory grows with input size.

📝

Why?

The time complexity is determined by the single loop that iterates through the queries array. The space complexity is determined by the auxiliary arrays used to store the state of the rows and columns, which are proportional to the size 'n' of the matrix.

📖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

Brute Force Approach

Simulate the matrix and update its values according to each query. After processing all queries, sum up the values in the matrix.

Time: O(q * n), where 'q' is the number of queries and 'n' is the size of the matrix. Each query potentially requires updating 'n' elements in the matrix.Space: O(n^2), to store the matrix itself.

Trade-offs: The brute force approach is simpler to understand but less efficient than the optimized solution. It's suitable for smaller input sizes but becomes inefficient for larger matrices and a large number of queries.

✨

Key Insights

1Insight 1: Processing queries in reverse order simplifies the logic. The last query affecting a row or column determines its final value.
2Insight 2: Using boolean arrays to track which rows and columns have been set avoids unnecessary recalculations and ensures that we only consider the effect of the 'last' query.
3Insight 3: Optimization is achieved by only updating the sum based on the unset rows/columns at the time of processing a particular query.

📚

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: When 'n' is 1. The algorithm handles this case correctly as the loops and calculations are still valid. Only one row and column exists and the calculation uses n-number of rows/columns set, which is 1-0=1 or 1-1 =0 when processed.
Edge case 2: When the queries array is empty. The algorithm correctly returns 0 since the initial total_sum is 0 and there are no updates.

⚠️

Common Mistakes to Avoid

✗Common mistake 1: Processing the queries in the original order. This leads to incorrect results because the final value of a cell is determined by the last query that affects it. Without extra tracking data structures, processing from the front results in an inability to determine prior set values without quadratic lookup.

✗Common mistake 2: Not accounting for previously set rows/columns when calculating the contribution of a query to the total sum. This results in overcounting the values in the matrix.

✅

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: Database updates. Imagine updating a database table where each query represents a batch update to either rows or columns. This pattern can be used to efficiently track the latest updates and calculate the final state of the table.

🏦Real-world scenario 2: Image processing. This technique could be adapted to efficiently perform image transformations where modifications are applied to entire rows or columns of pixels. Applying transformations in reverse order with tracking can optimize the final image output.

💡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 19, 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

❓

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 "Sum of Matrix After Queries"?

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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