1598738400

# Final Matrix after incrementing submatrices by K in range given by Q queries

Given a 2D matrix mat[][] of size N*M and Q queries of the form {x1, y1, x2, y2, K}. For each query, the task is to add the value K to submatrix from cell (x1, y1) to (x2, y2). Print the matrix after all the queries performed.

Examples:

Input:_ N = 3, M = 4, mat[][] = {{1, 0, 1, 2}, {0, 2, 4, 1}, {1, 2, 1, 0}}, Q = 1, Queries[][] = {{0, 0, 1, 1, 2}}_

Output:

3 2 1 2

2 4 4 1

1 2 1 0

Explanation:

There is only one query i.e., updating the submatrix from cell mat[0][0] to mat[1][1] by increment of 2, the matrix becomes:

3 2 1 2

2 4 4 1

1 2 1 0

Input:_ N = 2, M = 3, mat[][] = {{3, 2, 1}, {2, 4, 4}}, Q = 1, Queries[][] = { {0, 1, 1, 2, -1}, {0, 0, 1, 1, 5}}_

Output:

8 6 0

7 8 3

Explanation:

For query 1, i.e., updating the submatrix from cell mat[0][1] to mat[1][2] by increment of (-1), the matrix becomes:

3 1 0

2 3 3

For query 2, i.e., updating the submatrix from cell mat[0][0] to mat[2][2] by increment of 5, the matrix becomes:

8 6 0

7 8 3

### Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Naive Approach: The simplest approach is to iterate over the submatrix and add K to all elements from mat[x1][y1] to mat[x2][y2] for each query. Print the matrix after the above operations.

Time Complexity:_ O(NMQ)_

Auxiliary Space:_ O(1)_

Efficient Approach: The idea is to use an auxiliary matrix to perform the update operations on the corners of the submatrix cells and then find the prefix sum of the matrix to get the resultant matrix. Below are the steps:

1. Initialize all elements of the auxiliary matrix say aux[][] to 0.
2. For each query {x1, y1, x2, y2, K} update the auxiliary matrix as:
• aux[x1][y1] += K
• if(x2 + 1 < N) then aux[x2 + 1][y1] -= K
• if(x2 + 1 < N && y2 + 1 < N) then aux[x2 + 1][y2 + 1] += K
• if(y2 + 1 < N) then aux[x1][y2 + 1] -= K
1. Find the prefix sum of each row of the auxiliary matrix.
2. Find the prefix sum of each column of the auxiliary matrix.
3. Now, update the auxiliary matrix as sum of elements at each respective cell of the auxiliary and the given matrix.
4. Print the auxiliary matrix after all the above operations.

Below is the illustration for how auxiliary matrix is created and updated for query[][] = {{0, 0, 1, 1, 2}, {0, 1, 2, 3, -1}}:

Below is the implementation of the above approach:

### C++

// C++ program for the above approach

#include <bits/stdc++.h>

**using** **namespace** std;

#define N 3

#define M 4

// Query data type

**struct** query {

**int** x1, x2, y1, y2, K;

};

// Function to update the given query

**void** updateQuery(``**int** from_x, **int** from_y,

**int** to_x, **int** to_y,

**int** k, **int** aux[][M])

{

// Update top cell

aux[from_x][from_y] += k;

// Update bottom left cell

**if** (to_x + 1 < N)

aux[to_x + 1][from_y] -= k;

// Update bottom right cell

**if** (to_x + 1 < N && to_y + 1 < M)

aux[to_x + 1][to_y + 1] += k;

// Update top right cell

**if** (to_y + 1 < M)

aux[from_x][to_y + 1] -= k;

}

// Function that updates the matrix

// mat[][] by adding elements of aux[][]

**void** updateMatrix(``**int** mat[][M], **int** aux[][M])

{

// Compute the prefix sum of all columns

**for** (``**int** i = 0; i < N; i++) {

**for** (``**int** j = 1; j < M; j++) {

aux[i][j] += aux[i][j - 1];

}

}

// Compute the prefix sum of all rows

**for** (``**int** i = 0; i < M; i++) {

**for** (``**int** j = 1; j < N; j++) {

aux[j][i] += aux[j - 1][i];

}

}

// Get the final matrix by adding

// mat and aux matrix at each cell

**for** (``**int** i = 0; i < N; i++) {

**for** (``**int** j = 0; j < M; j++) {

mat[i][j] += aux[i][j];

}

}

}

// Function that prints matrix mat[]

**void** printMatrix(``**int** mat[][M])

{

// Traverse each row

**for** (``**int** i = 0; i < N; i++) {

// Traverse each columns

**for** (``**int** j = 0; j < M; j++) {

cout << mat[i][j] << " "``;

}

cout << "\n"``;

}

}

// Function that performs each query in

// the given matrix and print the updated

// matrix after each operation performed

**void** matrixQuery(``**int** mat[][M], **int** Q,

query q[])

{

// Initialize all elements to 0

**int** aux[N][M] = {};

// Update auxiliary matrix

// by traversing each query

**for** (``**int** i = 0; i < Q; i++) {

// Update Query

updateQuery(q[i].x1, q[i].x2,

q[i].y1, q[i].y2,

q[i].K, aux);

}

updateMatrix(mat, aux);

// Print the updated matrix

printMatrix(mat);

}

// Driver Code

**int** main()

{

// Given Matrix

**int** mat[N][M] = { { 1, 0, 1, 2 },

{ 0, 2, 4, 1 },

{ 1, 2, 1, 0 } };

**int** Q = 1;

// Given Queries

query q[] = { { 0, 0, 1, 1, 2 } };

// Function Call

matrixQuery(mat, Q, q);

**return** 0;

}

Output:

3 2 1 2
2 4 4 1
1 2 1 0

Time Complexity:_ O(Q + N*M)_

Auxiliary Space:_ O(N*M)_

Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.

#dynamic programming #greedy #mathematical #matrix #array-range-queries #prefix-sum #submatrix

1598738400

## Final Matrix after incrementing submatrices by K in range given by Q queries

Given a 2D matrix mat[][] of size N*M and Q queries of the form {x1, y1, x2, y2, K}. For each query, the task is to add the value K to submatrix from cell (x1, y1) to (x2, y2). Print the matrix after all the queries performed.

Examples:

Input:_ N = 3, M = 4, mat[][] = {{1, 0, 1, 2}, {0, 2, 4, 1}, {1, 2, 1, 0}}, Q = 1, Queries[][] = {{0, 0, 1, 1, 2}}_

Output:

3 2 1 2

2 4 4 1

1 2 1 0

Explanation:

There is only one query i.e., updating the submatrix from cell mat[0][0] to mat[1][1] by increment of 2, the matrix becomes:

3 2 1 2

2 4 4 1

1 2 1 0

Input:_ N = 2, M = 3, mat[][] = {{3, 2, 1}, {2, 4, 4}}, Q = 1, Queries[][] = { {0, 1, 1, 2, -1}, {0, 0, 1, 1, 5}}_

Output:

8 6 0

7 8 3

Explanation:

For query 1, i.e., updating the submatrix from cell mat[0][1] to mat[1][2] by increment of (-1), the matrix becomes:

3 1 0

2 3 3

For query 2, i.e., updating the submatrix from cell mat[0][0] to mat[2][2] by increment of 5, the matrix becomes:

8 6 0

7 8 3

### Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Naive Approach: The simplest approach is to iterate over the submatrix and add K to all elements from mat[x1][y1] to mat[x2][y2] for each query. Print the matrix after the above operations.

Time Complexity:_ O(NMQ)_

Auxiliary Space:_ O(1)_

Efficient Approach: The idea is to use an auxiliary matrix to perform the update operations on the corners of the submatrix cells and then find the prefix sum of the matrix to get the resultant matrix. Below are the steps:

1. Initialize all elements of the auxiliary matrix say aux[][] to 0.
2. For each query {x1, y1, x2, y2, K} update the auxiliary matrix as:
• aux[x1][y1] += K
• if(x2 + 1 < N) then aux[x2 + 1][y1] -= K
• if(x2 + 1 < N && y2 + 1 < N) then aux[x2 + 1][y2 + 1] += K
• if(y2 + 1 < N) then aux[x1][y2 + 1] -= K
1. Find the prefix sum of each row of the auxiliary matrix.
2. Find the prefix sum of each column of the auxiliary matrix.
3. Now, update the auxiliary matrix as sum of elements at each respective cell of the auxiliary and the given matrix.
4. Print the auxiliary matrix after all the above operations.

Below is the illustration for how auxiliary matrix is created and updated for query[][] = {{0, 0, 1, 1, 2}, {0, 1, 2, 3, -1}}:

Below is the implementation of the above approach:

### C++

// C++ program for the above approach

#include <bits/stdc++.h>

**using** **namespace** std;

#define N 3

#define M 4

// Query data type

**struct** query {

**int** x1, x2, y1, y2, K;

};

// Function to update the given query

**void** updateQuery(``**int** from_x, **int** from_y,

**int** to_x, **int** to_y,

**int** k, **int** aux[][M])

{

// Update top cell

aux[from_x][from_y] += k;

// Update bottom left cell

**if** (to_x + 1 < N)

aux[to_x + 1][from_y] -= k;

// Update bottom right cell

**if** (to_x + 1 < N && to_y + 1 < M)

aux[to_x + 1][to_y + 1] += k;

// Update top right cell

**if** (to_y + 1 < M)

aux[from_x][to_y + 1] -= k;

}

// Function that updates the matrix

// mat[][] by adding elements of aux[][]

**void** updateMatrix(``**int** mat[][M], **int** aux[][M])

{

// Compute the prefix sum of all columns

**for** (``**int** i = 0; i < N; i++) {

**for** (``**int** j = 1; j < M; j++) {

aux[i][j] += aux[i][j - 1];

}

}

// Compute the prefix sum of all rows

**for** (``**int** i = 0; i < M; i++) {

**for** (``**int** j = 1; j < N; j++) {

aux[j][i] += aux[j - 1][i];

}

}

// Get the final matrix by adding

// mat and aux matrix at each cell

**for** (``**int** i = 0; i < N; i++) {

**for** (``**int** j = 0; j < M; j++) {

mat[i][j] += aux[i][j];

}

}

}

// Function that prints matrix mat[]

**void** printMatrix(``**int** mat[][M])

{

// Traverse each row

**for** (``**int** i = 0; i < N; i++) {

// Traverse each columns

**for** (``**int** j = 0; j < M; j++) {

cout << mat[i][j] << " "``;

}

cout << "\n"``;

}

}

// Function that performs each query in

// the given matrix and print the updated

// matrix after each operation performed

**void** matrixQuery(``**int** mat[][M], **int** Q,

query q[])

{

// Initialize all elements to 0

**int** aux[N][M] = {};

// Update auxiliary matrix

// by traversing each query

**for** (``**int** i = 0; i < Q; i++) {

// Update Query

updateQuery(q[i].x1, q[i].x2,

q[i].y1, q[i].y2,

q[i].K, aux);

}

updateMatrix(mat, aux);

// Print the updated matrix

printMatrix(mat);

}

// Driver Code

**int** main()

{

// Given Matrix

**int** mat[N][M] = { { 1, 0, 1, 2 },

{ 0, 2, 4, 1 },

{ 1, 2, 1, 0 } };

**int** Q = 1;

// Given Queries

query q[] = { { 0, 0, 1, 1, 2 } };

// Function Call

matrixQuery(mat, Q, q);

**return** 0;

}

Output:

3 2 1 2
2 4 4 1
1 2 1 0

Time Complexity:_ O(Q + N*M)_

Auxiliary Space:_ O(N*M)_

Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.

#dynamic programming #greedy #mathematical #matrix #array-range-queries #prefix-sum #submatrix

1657400640

## Introduction

Matrix is an ambitious new ecosystem for open federated Instant Messaging and VoIP. The basics you need to know to get up and running are:

• Everything in Matrix happens in a room. Rooms are distributed and do not exist on any single server. Rooms can be located using convenience aliases like #matrix:matrix.org or #test:localhost:8448.
• Matrix user IDs look like @matthew:matrix.org (although in the future you will normally refer to yourself and others using a third party identifier (3PID): email address, phone number, etc rather than manipulating Matrix user IDs)

The overall architecture is:

client <----> homeserver <=====================> homeserver <----> client
https://somewhere.org/_matrix      https://elsewhere.net/_matrix

#matrix:matrix.org is the official support room for Matrix, and can be accessed by any client from https://matrix.org/docs/projects/try-matrix-now.html or via IRC bridge at irc://irc.libera.chat/matrix.

Synapse is currently in rapid development, but as of version 0.5 we believe it is sufficiently stable to be run as an internet-facing service for real usage!

Matrix specifies a set of pragmatic RESTful HTTP JSON APIs as an open standard, which handle:

• Creating and managing fully distributed chat rooms with no single points of control or failure
• Eventually-consistent cryptographically secure synchronisation of room state across a global open network of federated servers and services
• Sending and receiving extensible messages in a room with (optional) end-to-end encryption
• Inviting, joining, leaving, kicking, banning room members
• Managing user accounts (registration, login, logout)
• Using 3rd Party IDs (3PIDs) such as email addresses, phone numbers, Facebook accounts to authenticate, identify and discover users on Matrix.
• Placing 1:1 VoIP and Video calls

These APIs are intended to be implemented on a wide range of servers, services and clients, letting developers build messaging and VoIP functionality on top of the entirely open Matrix ecosystem rather than using closed or proprietary solutions. The hope is for Matrix to act as the building blocks for a new generation of fully open and interoperable messaging and VoIP apps for the internet.

Synapse is a Matrix "homeserver" implementation developed by the matrix.org core team, written in Python 3/Twisted.

In Matrix, every user runs one or more Matrix clients, which connect through to a Matrix homeserver. The homeserver stores all their personal chat history and user account information - much as a mail client connects through to an IMAP/SMTP server. Just like email, you can either run your own Matrix homeserver and control and own your own communications and history or use one hosted by someone else (e.g. matrix.org) - there is no single point of control or mandatory service provider in Matrix, unlike WhatsApp, Facebook, Hangouts, etc.

We'd like to invite you to join #matrix:matrix.org (via https://matrix.org/docs/projects/try-matrix-now.html), run a homeserver, take a look at the Matrix spec, and experiment with the APIs and Client SDKs.

Thanks for using Matrix!

## Support

For support installing or managing Synapse, please join #synapse:matrix.org (from a matrix.org account if necessary) and ask questions there. We do not use GitHub issues for support requests, only for bug reports and feature requests.

Synapse's documentation is nicely rendered on GitHub Pages, with its source available in docs.

## Connecting to Synapse from a client

The easiest way to try out your new Synapse installation is by connecting to it from a web client.

Unless you are running a test instance of Synapse on your local machine, in general, you will need to enable TLS support before you can successfully connect from a client: see TLS certificates.

An easy way to get started is to login or register via Element at https://app.element.io/#/login or https://app.element.io/#/register respectively. You will need to change the server you are logging into from matrix.org and instead specify a Homeserver URL of https://<server_name>:8448 (or just https://<server_name> if you are using a reverse proxy). If you prefer to use another client, refer to our client breakdown.

If all goes well you should at least be able to log in, create a room, and start sending messages.

### Registering a new user from a client

By default, registration of new users via Matrix clients is disabled. To enable it, specify enable_registration: true in homeserver.yaml. (It is then recommended to also set up CAPTCHA - see docs/CAPTCHA_SETUP.md.)

Once enable_registration is set to true, it is possible to register a user via a Matrix client.

Your new user name will be formed partly from the server_name, and partly from a localpart you specify when you create the account. Your name will take the form of:

@localpart:my.domain.name

(pronounced "at localpart on my dot domain dot name").

As when logging in, you will need to specify a "Custom server". Specify your desired localpart in the 'User name' box.

## Security note

Matrix serves raw, user-supplied data in some APIs -- specifically the content repository endpoints.

Whilst we make a reasonable effort to mitigate against XSS attacks (for instance, by using CSP), a Matrix homeserver should not be hosted on a domain hosting other web applications. This especially applies to sharing the domain with Matrix web clients and other sensitive applications like webmail. See https://developer.github.com/changes/2014-04-25-user-content-security for more information.

Ideally, the homeserver should not simply be on a different subdomain, but on a completely different registered domain (also known as top-level site or eTLD+1). This is because some attacks are still possible as long as the two applications share the same registered domain.

To illustrate this with an example, if your Element Web or other sensitive web application is hosted on A.example1.com, you should ideally host Synapse on example2.com. Some amount of protection is offered by hosting on B.example1.com instead, so this is also acceptable in some scenarios. However, you should not host your Synapse on A.example1.com.

Note that all of the above refers exclusively to the domain used in Synapse's public_baseurl setting. In particular, it has no bearing on the domain mentioned in MXIDs hosted on that server.

Following this advice ensures that even if an XSS is found in Synapse, the impact to other applications will be minimal.

The instructions for upgrading synapse are in the upgrade notes. Please check these instructions as upgrading may require extra steps for some versions of synapse.

## Using a reverse proxy with Synapse

It is recommended to put a reverse proxy such as nginx, Apache, Caddy, HAProxy or relayd in front of Synapse. One advantage of doing so is that it means that you can expose the default https port (443) to Matrix clients without needing to run Synapse with root privileges.

For information on configuring one, see docs/reverse_proxy.md.

## Identity Servers

Identity servers have the job of mapping email addresses and other 3rd Party IDs (3PIDs) to Matrix user IDs, as well as verifying the ownership of 3PIDs before creating that mapping.

They are not where accounts or credentials are stored - these live on home servers. Identity Servers are just for mapping 3rd party IDs to matrix IDs.

This process is very security-sensitive, as there is obvious risk of spam if it is too easy to sign up for Matrix accounts or harvest 3PID data. In the longer term, we hope to create a decentralised system to manage it (matrix-doc #712), but in the meantime, the role of managing trusted identity in the Matrix ecosystem is farmed out to a cluster of known trusted ecosystem partners, who run 'Matrix Identity Servers' such as Sydent, whose role is purely to authenticate and track 3PID logins and publish end-user public keys.

You can host your own copy of Sydent, but this will prevent you reaching other users in the Matrix ecosystem via their email address, and prevent them finding you. We therefore recommend that you use one of the centralised identity servers at https://matrix.org or https://vector.im for now.

To reiterate: the Identity server will only be used if you choose to associate an email address with your account, or send an invite to another user via their email address.

Users can reset their password through their client. Alternatively, a server admin can reset a users password using the admin API or by directly editing the database as shown below.

First calculate the hash of the new password:

\$2a\$12\$xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

Then update the users table in the database:

WHERE name='@test:test.com';

## Synapse Development

The best place to get started is our guide for contributors. This is part of our larger documentation, which includes information for synapse developers as well as synapse administrators.

Developers might be particularly interested in:

Alongside all that, join our developer community on Matrix: #synapse-dev:matrix.org, featuring real humans!

### Quick start

Before setting up a development environment for synapse, make sure you have the system dependencies (such as the python header files) installed - see Platform-specific prerequisites.

To check out a synapse for development, clone the git repo into a working directory of your choice:

git clone https://github.com/matrix-org/synapse.git
cd synapse

Synapse has a number of external dependencies. We maintain a fixed development environment using Poetry. First, install poetry. We recommend:

pip install --user pipx
pipx install poetry

as described here. (See poetry's installation docs for other installation methods.) Then ask poetry to create a virtual environment from the project and install Synapse's dependencies:

poetry install --extras "all test"

This will run a process of downloading and installing all the needed dependencies into a virtual env.

We recommend using the demo which starts 3 federated instances running on ports 8080 - 8082:

poetry run ./demo/start.sh

(to stop, you can use poetry run ./demo/stop.sh)

If you just want to start a single instance of the app and run it directly:

# Create the homeserver.yaml config once
poetry run synapse_homeserver \
--server-name my.domain.name \
--config-path homeserver.yaml \
--generate-config \
--report-stats=[yes|no]

# Start the app
poetry run synapse_homeserver --config-path homeserver.yaml

### Running the unit tests

After getting up and running, you may wish to run Synapse's unit tests to check that everything is installed correctly:

poetry run trial tests

This should end with a 'PASSED' result (note that exact numbers will differ):

Ran 1337 tests in 716.064s

PASSED (skips=15, successes=1322)

For more tips on running the unit tests, like running a specific test or to see the logging output, see the CONTRIBUTING doc.

### Running the Integration Tests

Synapse is accompanied by SyTest, a Matrix homeserver integration testing suite, which uses HTTP requests to access the API as a Matrix client would. It is able to run Synapse directly from the source tree, so installation of the server is not required.

Testing with SyTest is recommended for verifying that changes related to the Client-Server API are functioning correctly. See the SyTest installation instructions for details.

## Platform dependencies

Synapse uses a number of platform dependencies such as Python and PostgreSQL, and aims to follow supported upstream versions. See the docs/deprecation_policy.md document for more details.

## Troubleshooting

### Running out of File Handles

If synapse runs out of file handles, it typically fails badly - live-locking at 100% CPU, and/or failing to accept new TCP connections (blocking the connecting client). Matrix currently can legitimately use a lot of file handles, thanks to busy rooms like #matrix:matrix.org containing hundreds of participating servers. The first time a server talks in a room it will try to connect simultaneously to all participating servers, which could exhaust the available file descriptors between DNS queries & HTTPS sockets, especially if DNS is slow to respond. (We need to improve the routing algorithm used to be better than full mesh, but as of March 2019 this hasn't happened yet).

If you hit this failure mode, we recommend increasing the maximum number of open file handles to be at least 4096 (assuming a default of 1024 or 256). This is typically done by editing /etc/security/limits.conf

Separately, Synapse may leak file handles if inbound HTTP requests get stuck during processing - e.g. blocked behind a lock or talking to a remote server etc. This is best diagnosed by matching up the 'Received request' and 'Processed request' log lines and looking for any 'Processed request' lines which take more than a few seconds to execute. Please let us know at #synapse:matrix.org if you see this failure mode so we can help debug it, however.

### Help!! Synapse is slow and eats all my RAM/CPU!

First, ensure you are running the latest version of Synapse, using Python 3 with a PostgreSQL database.

Synapse's architecture is quite RAM hungry currently - we deliberately cache a lot of recent room data and metadata in RAM in order to speed up common requests. We'll improve this in the future, but for now the easiest way to either reduce the RAM usage (at the risk of slowing things down) is to set the almost-undocumented SYNAPSE_CACHE_FACTOR environment variable. The default is 0.5, which can be decreased to reduce RAM usage in memory constrained enviroments, or increased if performance starts to degrade.

However, degraded performance due to a low cache factor, common on machines with slow disks, often leads to explosions in memory use due backlogged requests. In this case, reducing the cache factor will make things worse. Instead, try increasing it drastically. 2.0 is a good starting value.

Using libjemalloc can also yield a significant improvement in overall memory use, and especially in terms of giving back RAM to the OS. To use it, the library must simply be put in the LD_PRELOAD environment variable when launching Synapse. On Debian, this can be done by installing the libjemalloc1 package and adding this line to /etc/default/matrix-synapse:

This can make a significant difference on Python 2.7 - it's unclear how much of an improvement it provides on Python 3.x.

If you're encountering high CPU use by the Synapse process itself, you may be affected by a bug with presence tracking that leads to a massive excess of outgoing federation requests (see discussion). If metrics indicate that your server is also issuing far more outgoing federation requests than can be accounted for by your users' activity, this is a likely cause. The misbehavior can be worked around by setting the following in the Synapse config file:

presence:
enabled: false

### People can't accept room invitations from me

The typical failure mode here is that you send an invitation to someone to join a room or direct chat, but when they go to accept it, they get an error (typically along the lines of "Invalid signature"). They might see something like the following in their logs:

2019-09-11 19:32:04,271 - synapse.federation.transport.server - 288 - WARNING - GET-11752 - authenticate_request failed: 401: Invalid signature for server <server> with key ed25519:a_EqML: Unable to verify signature for <server>

This is normally caused by a misconfiguration in your reverse-proxy. See docs/reverse_proxy.md and double-check that your settings are correct.

Author: matrix-org
Source Code: https://github.com/matrix-org/synapse

#python

1620185280

## How model queries work in Django

**Read More : **How to make Chatbot in Python.

let’s just get into this diagram that I made so in here:

Describe each parameter in Django querset

we’re making a simple query for the myModel table so we want to pull out all the information in the database so we have this variable which is gonna hold a return value and we have our myModel models so this is simply the myModel model name so whatever you named your model just make sure you specify that and we’re gonna access the objects attribute once we get that object’s attribute we can simply use the all method and this will return all the information in the database so we’re gonna start with all and then we will go into getting single items filtering that data and go to our command prompt.

Here and we’ll actually start making our queries from here to do this let’s just go ahead and run** Python manage.py shell** and I am in my project file so make sure you’re in there when you start and what this does is it gives us an interactive shell to actually start working with our data so this is a lot like the Python shell but because we did manage.py it allows us to do things a Django way and actually query our database now open up the command prompt and let’s go ahead and start making our first queries.

#django #django model queries #django orm #django queries #django query #model django query #model query #query with django

1598731200

## Binary Matrix after flipping submatrices in given range for Q queries

Given a binary matrix arr[][] of dimensions M x N and Q queries of the form (x1, y1, x2, y2), where (x1, y1) and (x2, y2) denotes the top-left and bottom-right indices of the submatrix required to be flipped(convert 0s to 1s and vice versa) respectively. The task is to print the final matrix obtained after performing given Q queries

Examples:

Input:_ arr[][] = {{0, 1, 0}, {1, 1, 0}}, queries[][] = {{1, 1, 2, 3}}_

Output:_ [[1, 0, 1], [0, 0, 1]]_

Explanation:

_The submatrix to be flipped is equal to {{0, 1, 0}, {1, 1, 0}} _

The flipped matrix is {{1, 0, 1}, {0, 0, 1}}.

Input:_ arr[][] = {{0, 1, 0}, {1, 1, 0}}, queries[][] = {{1, 1, 2, 3}, {1, 1, 1, 1], {1, 2, 2, 3}}_

Output:_ [[0, 1, 0], [0, 1, 0]]_

Explanation:

Query 1:

_Submatrix to be flipped = [[0, 1, 0], [1, 1, 0]] _

_Flipped submatrix is [[1, 0, 1], [0, 0, 1]]. _

Therefore, the modified matrix is [[1, 0, 1], [0, 0, 1]].

_Query 2: _

_Submatrix to be flipped = [[1]] _

_Flipped submatrix is [[0]] _

Therefore, matrix is [[0, 0, 1], [0, 0, 1]].

Query 3:

_Submatrix to be flipped = [[0, 1], [0, 1]] _

_Flipped submatrix is [[1, 0], [1, 0]] _

Therefore, modified matrix is [[0, 1, 0], [0, 1, 0]].

### Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Naive Approach: The simplest approach to solve the problem for each query is to iterate over the given submatrices and for every element, check if it is 0 or 1, and flip accordingly. After completing these operations for all the queries, print the final matrix obtained.

Below is the implementation of the above approach :

• Python

## Python Program to implement

## the above approach

## Function to flip a submatrices

**def** manipulation(matrix, q):

## Boundaries of the submatrix

x1, y1, x2, y2 **=** q

## Iterate over the submatrix

**for** i **in** range``(x1``**-**``1``, x2):

**for** j **in** range``(y1``**-**``1``, y2):

## Check for 1 or 0

## and flip accordingly

**if** matrix[i][j]:

matrix[i][j] **=** 0

**else**``:

matrix[i][j] **=** 1

## Function to perform the queries

**def** queries_fxn(matrix, queries):

**for** q **in** queries:

manipulation(matrix, q)

## Driver Code

matrix **=** [[``0``, 1``, 0``], [``1``, 1``, 0``]]

queries **=** [[``1``, 1``, 2``, 3``], \

[``1``, 1``, 1``, 1``], \

[``1``, 2``, 2``, 3``]]

## Function call

queries_fxn(matrix, queries)

print``(matrix)

Output:

[[0, 1, 0], [0, 1, 0]]

Time complexity:_ O( N * M * Q)_

Auxiliary Space:_ O(1)_

Efficient Approach: The above approach can be optimized using Dynamic programming and Prefix Sum technique. Mark the boundaries of the submatrices involved in each query and then calculate prefix sum of the operations involved in the matrix and update the matrix accordingly. Follow the steps below to solve the problem:

• Initialize a 2D state space table dp[][] to store the count of flips at respective indices of the matrix
• For each query {x1, y1, x2, y2, K}, update the dp[][] matrix by the following operations:
• dp[x1][y1] += 1
• dp[x2 + 1][y1] -= 1
• dp[x2 + 1][y2 + 1] += 1
• dp[x1][y2 + 1] -= 1

Now, traverse over the dp[][] matrix and update dp[i][j] by calculating prefix sum of the rows and colums and diagonals by the following relation:

dp[i][j] = dp[i][j] + dp[i-1][j] + dp[i][j – 1] – dp[i – 1][j – 1]

If dp[i][j] is found to be odd, reduce mat[i – 1][j – 1] by 1.

Finally print the updated matrix mat[][] as the result.

Below is the implementation of the above approach :

• Python

## Python program to implement

## the above approach

## Function to modify dp[][] array by

## generating prefix sum

**def** modifyDP(matrix, dp):

**for** j **in** range``(``1``, len``(matrix)``**+**``1``):

**for** k **in** range``(``1``, len``(matrix[``0``])``**+**``1``):

## Update the tabular data

dp[j][k] **=** dp[j][k] **+** dp[j``**-**``1``][k] \

**+** dp[j][k``**-**``1``]``**-**``dp[j``**-**``1``][k``**-**``1``]

## If the count of flips is even

**if** dp[j][k] **%** 2 !``**=** 0``:

matrix[j``**-**``1``][k``**-**``1``] **=** int``(matrix[j``**-**``1``][k``**-**``1``]) ^ 1

## Function to update dp[][] matrix

## for each query

**def** queries_fxn(matrix, queries, dp):

**for** q **in** queries:

x1, y1, x2, y2 **=** q

## Update the table

dp[x1][y1] **+=** 1

dp[x2 **+** 1``][y2 **+** 1``] **+=** 1

dp[x1][y2 **+** 1``] **-=** 1

dp[x2 **+** 1``][y1] **-=** 1

modifyDP(matrix, dp)

## Driver Code

matrix **=** [[``0``, 1``, 0``], [``1``, 1``, 0``]]

queries **=** [[``1``, 1``, 2``, 3``], \

[``1``, 1``, 1``, 1``], \

[``1``, 2``, 2``, 3``]]

## Initialize dp table

dp **=** [[``0 **for** i **in** range``(``len``(matrix[``0``])``**+**``2``)] \

**for** j **in** range``(``len``(matrix)``**+**``2``)]

queries_fxn(matrix, queries, dp)

print``(matrix)

Output:

[[0, 1, 0], [0, 1, 0]]

Time Complexity:_ O(N * M )_

Auxiliary Space:_ O(N * M)_

Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.

#bit magic #dynamic programming #hash #mathematical #matrix #array-rearrange #binary-representation #prefix-sum #submatrix

1596631020

## Sum of prime numbers in range [L, R] from given Array for Q queries

Given an array arr[] of the size of N followed by an array of Q queries, of the following two types:

• Query Type 1: Given two integers L and R, find the sum of prime elements from index L to R where 0 <= L <= R <= N-1.
• Query Type 2: Given two integers i and X, change arr[i] = X where 0 <= i <= n-1.

Note:_ Every first index of the subquery determines the type of query to be answered._

**Example: **

_Input: _arr[] = {1, 3, 5, 7, 9, 11}, Q = { { 1, 1, 3}, {2, 1, 10}, {1, 1, 3 } }

_Output: _

15

12

_Explanation: _

First query is of type 1, so answer is (3 + 5 + 7), = 15

Second query is of type 2, so arr[1] = 10

Third query is of type 1, where arr[1] = 10, which is not prime hence answer is (5 + 7) = 12

Input:_ arr[] = {1, 2, 35, 7, 14, 11}, Q = { {2, 4, 3}, {1, 4, 5 } }_

Output:_ 14_

Explanation:

First query is of type 2, So update arr[4] = 3

Second query is of type 1, since arr[4] = 3, which is prime. So answer is (3 + 11) = 14

**Naive Approach: **The idea is to iterate for each query between L to R and perform the required operation on the given array.

_Time Complexity: _O(Q * N * (O(sqrt(max(arr[i]))

**Approach: ** To optimize the problem use Segment tree and Sieve Of Eratosthenes.

• First, create a boolean array that will mark the prime numbers.
• Now while making the segment tree only add those array elements as leaf nodes which are prime.
• C++
• Python3

// C++ program for the above approach

#include <bits/stdc++.h>

**using** **namespace** std;

**int** **const** MAX = 1000001;

**bool** prime[MAX];

// Function to find the prime numbers

**void** SieveOfEratosthenes()

{

// Create a boolean array prime[]

// and initialize all entries it as true

// A value in prime[i] will

// finally be false if i is Not a prime

**memset**``(prime, **true**``, **sizeof**``(prime));

**for** (``**int** p = 2; p * p <= MAX; p++) {

// Check if prime[p] is not

// changed, then it is a prime

**if** (prime[p] == **true**``) {

// Update all multiples of p

// greater than or equal to

// the square of it numbers

// which are multiple of p

// and are less than p^2 are

**for** (``**int** i = p * p; i <= MAX; i += p)

prime[i] = **false**``;

}

}

}

// Function to get the middle

// index from corner indexes

**int** getMid(``**int** s, **int** e)

{

**return** s + (e - s) / 2;

}

// Function to get the sum of

// values in the given range

// of the array

**int** getSumUtil(``**int**``* st, **int** ss,

**int** se, **int** qs,

**int** qe, **int** si)

{

// If segment of this node is a

// part of given range, then

// return the sum of the segment

**if** (qs <= ss && qe >= se)

**return** st[si];

// If segment of this node is

// outside the given range

**if** (se < qs || ss > qe)

**return** 0;

// If a part of this segment

// overlaps with the given range

**int** mid = getMid(ss, se);

**return** getSumUtil(st, ss, mid,

qs, qe,

2 * si + 1)

+ getSumUtil(st, mid + 1,

se, qs, qe,

2 * si + 2);

}

// Function to update the nodes which

// have the given index in their range

**void** updateValueUtil(``**int**``* st, **int** ss,

**int** se, **int** i,

**int** diff, **int** si)

{

// If the input index lies

// outside the range of

// this segment

**if** (i < ss || i > se)

**return**``;

// If the input index is in

// range of this node, then update

// the value of the node and its children

st[si] = st[si] + diff;

**if** (se != ss) {

**int** mid = getMid(ss, se);

updateValueUtil(st, ss, mid, i,

diff, 2 * si + 1);

updateValueUtil(st, mid + 1,

se, i, diff,

2 * si + 2);

}

}

// Function to update a value in

// input array and segment tree

**void** updateValue(``**int** arr[], **int**``* st,

**int** n, **int** i,

**int** new_val)

{

// Check for erroneous input index

**if** (i < 0 || i > n - 1) {

cout << "-1"``;

**return**``;

}

// Get the difference between

// new value and old value

**int** diff = new_val - arr[i];

**int** prev_val = arr[i];

// Update the value in array

arr[i] = new_val;

// Update the values of

// nodes in segment tree

// only if either previous

// value or new value

// or both are prime

**if** (prime[new_val]

|| prime[prev_val]) {

// If only new value is prime

**if** (!prime[prev_val])

updateValueUtil(st, 0, n - 1,

i, new_val, 0);

// If only new value is prime

**else** **if** (!prime[new_val])

updateValueUtil(st, 0, n - 1,

i, -prev_val, 0);

// If both are prime

**else**

updateValueUtil(st, 0, n - 1,

i, diff, 0);

}

}

// Return sum of elements in range

// from index qs (quey start) to qe

// (query end). It mainly uses getSumUtil()

**int** getSum(``**int**``* st, **int** n, **int** qs, **int** qe)

{

// Check for erroneous input values

**if** (qs < 0 || qe > n - 1 || qs > qe) {

cout << "-1"``;

**return** -1;

}

**return** getSumUtil(st, 0, n - 1,

qs, qe, 0);

}

// Function that constructs Segment Tree

**int** constructSTUtil(``**int** arr[], **int** ss,

**int** se, **int**``* st,

**int** si)

{

// If there is one element in

// array, store it in current node of

// segment tree and return

**if** (ss == se) {

// Only add those elements in segment

// tree which are prime

**if** (prime[arr[ss]])

st[si] = arr[ss];

**else**

st[si] = 0;

**return** st[si];

}

// If there are more than one

// elements, then recur for left and

// right subtrees and store the

// sum of values in this node

**int** mid = getMid(ss, se);

st[si]

= constructSTUtil(arr, ss, mid,

st, si * 2 + 1)

+ constructSTUtil(arr, mid + 1,

se, st,

si * 2 + 2);

**return** st[si];

}

// Function to construct segment

// tree from given array

**int**``* constructST(``**int** arr[], **int** n)

{

// Allocate memory for the segment tree

// Height of segment tree

**int** x = (``**int**``)(``**ceil**``(log2(n)));

// Maximum size of segment tree

**int** max_size = 2 * (``**int**``)``**pow**``(2, x) - 1;

// Allocate memory

**int**``* st = **new** **int**``[max_size];

// Fill the allocated memory st

constructSTUtil(arr, 0, n - 1, st, 0);

// Return the constructed segment tree

**return** st;

}

// Driver code

**int** main()

{

**int** arr[] = { 1, 3, 5, 7, 9, 11 };

**int** n = **sizeof**``(arr) / **sizeof**``(arr[0]);

**int** Q[3][3]

= { { 1, 1, 3 },

{ 2, 1, 10 },

{ 1, 1, 3 } };

// Function call

SieveOfEratosthenes();

// Build segment tree from given array

**int**``* st = constructST(arr, n);

// Print sum of values in

// array from index 1 to 3

cout << getSum(st, n, 1, 3) << endl;

// Update: set arr[1] = 10

// and update corresponding

// segment tree nodes

updateValue(arr, st, n, 1, 10);

// Find sum after the value is updated

cout << getSum(st, n, 1, 3) << endl;

**return** 0;

}

Output:

15
12

Time Complexity:_ O(Q * log N) _

Auxiliary Space:_ O(N)_

Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.

#advanced data structure #arrays #dynamic programming #hash #mathematical #tree #array-range-queries #prime number #segment-tree #sieve