What is the time complexity of Subrectangle Queries?

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

What data structures are used to solve Subrectangle Queries?

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

What are the key insights for solving Subrectangle Queries?

Insight 1: The crucial part is efficiently handling the update operations and retrieving the correct value after multiple updates potentially overlap. Insight 2: Instead of directly updating the original rectangle, storing the update operations and iterating through them in reverse order during `getValue` allows us to find the latest update that affects a given cell.

Which companies ask LeetCode 1476. Subrectangle Queries in interviews?

This problem is frequently asked at Info Edge, Nuro.

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Subrectangle Queries - LeetCode 1476 Solution

Subrectangle Queries - Complete Solution Guide

Subrectangle Queries is LeetCode problem 1476, 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

Implement the class SubrectangleQueries which receives a rows x cols rectangle as a matrix of integers in the constructor and supports two methods: 1. updateSubrectangle(int row1, int col1, int row2, int col2, int newValue) Updates all values with newValue in the subrectangle whose upper left coordinate is (row1,col1) and bottom right coordinate is (row2,col2) . 2. getValue(int row, int col) Returns the current value of the coordinate (row,col) from the rectangle. Example 1: Input ["Subrectangle

Detailed Explanation

The problem asks us to implement a `SubrectangleQueries` class that can perform two operations on a given rectangle (represented as a 2D array/matrix): `updateSubrectangle` and `getValue`. The `updateSubrectangle` method takes the coordinates of the top-left and bottom-right corners of a subrectangle and a new value. It updates all cells within that subrectangle to the new value. The `getValue` method takes a row and column index and returns the current value of the rectangle at that position. The constraints specify the dimensions of the rectangle, the range of values, and the maximum number of operations.

Solution Approach

The solution maintains the original rectangle and a list of update operations. The `updateSubrectangle` method simply stores the update parameters (row1, col1, row2, col2, newValue) in a list. The `getValue` method iterates through the update list in reverse order. For each update, it checks if the given row and column fall within the update's subrectangle. If it does, the method returns the update's new value. If no update applies to the cell, the method returns the original value from the rectangle.

Step-by-Step Algorithm

Step 1: Initialize the `SubrectangleQueries` object with the given rectangle.
Step 2: Create an empty list `updates` to store the update operations.
Step 3: Implement the `updateSubrectangle` method: Append the `(row1, col1, row2, col2, newValue)` tuple to the `updates` list.
Step 4: Implement the `getValue` method: Iterate through the `updates` list in reverse order.
Step 5: For each update in `updates`, check if the given `(row, col)` falls within the rectangle defined by `(row1, col1)` and `(row2, col2)`. That is, check if `row1 <= row <= row2` and `col1 <= col <= col2`.
Step 6: If the `(row, col)` falls within the update's rectangle, return the `newValue` of that update.
Step 7: If no update applies to the given `(row, col)`, return the value at `rectangle[row][col]`.

Key Insights

Insight 1: The crucial part is efficiently handling the update operations and retrieving the correct value after multiple updates potentially overlap.
Insight 2: Instead of directly updating the original rectangle, storing the update operations and iterating through them in reverse order during `getValue` allows us to find the latest update that affects a given cell.
Insight 3: The order of checking updates in `getValue` is important because the most recent update should override older ones. Therefore, iterating in reverse ensures the correct value is returned.

Complexity Analysis

Time Complexity: O(n)

Space Complexity: O(u)

Topics

This problem involves: Array, Design, Matrix.

Companies

Asked at: Info Edge, Nuro.

Subrectangle Queries | LeetCode 1476

Medium

Array Design Matrix

Time: O(n)Space: O(u)

Solution Code

Available in:

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

class SubrectangleQueries {

    private int[][] rectangle;
    private List<int[]> updates;

    public SubrectangleQueries(int[][] rectangle) {
        this.rectangle = rectangle;
        this.updates = new ArrayList<>();
    }
    
    public void updateSubrectangle(int row1, int col1, int row2, int col2, int newValue) {
        this.updates.add(new int[]{row1, col1, row2, col2, newValue});
    }
    
    public int getValue(int row, int col) {
        for (int i = updates.size() - 1; i >= 0; i--) {
            int[] update = updates.get(i);
            int r1 = update[0];
            int c1 = update[1];
            int r2 = update[2];
            int c2 = update[3];
            int value = update[4];
            if (r1 <= row && row <= r2 && c1 <= col && col <= c2) {
                return value;
            }
        }
        return rectangle[row][col];
    }
}

/**
 * Your SubrectangleQueries object will be instantiated and called as such:
 * SubrectangleQueries obj = new SubrectangleQueries(rectangle);
 * obj.updateSubrectangle(row1,col1,row2,col2,newValue);
 * int param_2 = obj.getValue(row,col);
 */

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Problem Info

Description

Problem 1476: Subrectangle Queries - Detailed explanation and solution approaches.

Topics

Array Design Matrix

Companies

Info EdgeNuro

Stats

Difficulty:Medium

Languages:4

Companies:2

Problem #:1476

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

7 steps

1
Step 1: Initialize the `SubrectangleQueries` object with the given rectangle.
2
Step 2: Create an empty list `updates` to store the update operations.
3
Step 3: Implement the `updateSubrectangle` method: Append the `(row1, col1, row2, col2, newValue)` tuple to the `updates` list.
4
Step 4: Implement the `getValue` method: Iterate through the `updates` list in reverse order.
5
Step 5: For each update in `updates`, check if the given `(row, col)` falls within the rectangle defined by `(row1, col1)` and `(row2, col2)`. That is, check if `row1 <= row <= row2` and `col1 <= col <= col2`.
6
Step 6: If the `(row, col)` falls within the update's rectangle, return the `newValue` of that update.
7
Step 7: If no update applies to the given `(row, col)`, return the value at `rectangle[row][col]`.

💡

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)

👍 Linear - Good! Visits each element once.

💾

Space Complexity

O(u)

📝

Why?

The time complexity of `getValue` depends on how many updates have been performed. The space complexity is directly proportional to the number of updates stored.

📖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

Directly Updating the Matrix

Instead of storing update operations, we can directly modify the rectangle matrix in the `updateSubrectangle` method. This would involve iterating through each cell within the given subrectangle and updating its value.

Time: O(m*n) for updateSubrectangle, O(1) for getValue, where m and n are the dimensions of the subrectangle to be updated.Space: O(1), as the updates are done in-place

Trade-offs: This approach trades space for time. While `getValue` becomes O(1), `updateSubrectangle` could be much slower, especially for large subrectangles. The current solution is better when `getValue` is called more frequently than `updateSubrectangle` and the updated subrectangles are very large.

✨

Key Insights

1Insight 1: The crucial part is efficiently handling the update operations and retrieving the correct value after multiple updates potentially overlap.
2Insight 2: Instead of directly updating the original rectangle, storing the update operations and iterating through them in reverse order during `getValue` allows us to find the latest update that affects a given cell.
3Insight 3: The order of checking updates in `getValue` is important because the most recent update should override older ones. Therefore, iterating in reverse ensures the correct value is returned.

📚

Key Terms Explained

For Students

Array

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

Edge Cases

Edge case 1: No updates have been performed. In this case, `getValue` should return the original value from the rectangle. The solution handles this correctly as the reverse iteration will complete without finding a matching update, and the final `return rectangle[row][col]` statement will be executed.
Edge case 2: Multiple overlapping updates exist. The solution correctly handles this because `getValue` iterates through the updates in reverse order, ensuring that the most recent update is considered first.
Edge case 3: The given row and column for getValue are out of bounds. The problem description explicitly defines that `0 <= row < rows` and `0 <= col < cols` which implies the input is always valid so we do not need to check for out of bounds indices.

⚠️

Common Mistakes to Avoid

✗Common mistake 1: Iterating through the `updates` list in the wrong order in `getValue`. Iterating in forward order would give precedence to older updates, resulting in incorrect values.

✗Common mistake 2: Failing to handle the case where no updates apply to a given cell in `getValue`. The solution must return the original value from the rectangle if no update matches.

✗Common mistake 3: Not considering the space complexity when storing updates. For a large number of updates, the space used by the `updates` list can become significant.

✅

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: Implementing a game board with dynamic updates. The rectangle could represent the game board, and `updateSubrectangle` could be used to update regions of the board after player actions or events.

🏦Real-world scenario 2: Managing large datasets where sections of the data are frequently updated. For example, a spreadsheet application where users can update ranges of cells. This can also be used to implement a cache invalidation system.

💡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: July 7, 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

The key insight here is recognizing the pattern. Once you see it, the solution becomes straightforward.

@AlgoMasterJul 13

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

@InterviewProJul 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 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 "Subrectangle 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 design techniques can optimize the solution. Always handle edge cases and validate your approach with examples before coding.

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