Blog down the gradient

New Beginning for Google Play Music

noreply@blogger.com (Maharaj) — Thu, 13 Aug 2020 20:03:00 +0000

Google Play Music an ocean of music streaming will be having a new home at YouTube Music on December 2020. Google Play Music users have to transfer their music libraries, preference and playlists to YouTube Music.

Transfer from Google Play Music to YouTube Music can be done in following simple steps:

Download the YouTube Music app for respective store (Android/iOS).
Click on the transfer button in YouTube Music and all the data will be immediately be move.
The updated recommendations will appear immediately on YouTube Music home screen, and you will be notified via email or with in-app notification.

Watch the official video on transfer details by YouTube Music Here.

Havel-Hakimi Illustrated

noreply@blogger.com (Maharaj) — Thu, 29 Aug 2019 07:20:00 +0000

Havel-Hakimi algorithm is an algorithm which can verify whether there exists a simple graph for given degree sequence. Before we dive into the actual algorithm lets revisit some of the key terms: simple graph and degree sequences.

1. What is Simple Graph?

A simple graph is an undirected, unweighted graph with no self loops and no multi-edges.

2. Degree Sequences

A degree of a vertex i, is number of edges incident on i with self loops counted twice. Degree sequences is the arrangement of degree in non-ascending or non-descending order.


Figure 1:- Degree Sequences: Graph with degree sequence (4, 3, 2, 2,1)

3. Havel-Hakimi Algorithm

Put degree sequence in non-ascending order
Remove highest degree, k
Subtract 1 from next k entries in degree sequence
Repeat step 1, 2, 3 & stop until

If we get all zero entries -> simple graph exist
If we get at least one negative entry -> simple graph does not exist
If no enough entries -> simple graph does not exist

For example: Let us consider the degree sequence (4, 3, 2, 2, 1)
(4, 3, 2, 2, 1)
Highest degree, k = 4
Subtract 1 from the next k entries degree sequence excluding 4.
(2, 1, 1, 0)
Highest degree, k = 2
Subtract 1 from the next 2 entries
(0, 0, 0) -> All zeros
Therefore, simple graph exist for the degree sequence (4, 3, 2, 2, 1).

Caesar Says hello world!

noreply@blogger.com (Maharaj) — Tue, 25 Jun 2019 09:31:00 +0000

Few months back there was a problem set on Caesar cipher and it struck to me to write this one for the readers who are interested to learn about Caesar cipher.

Let's get started, in Caesar cipher we have predefined mapping of the 26 English alphabets with numbers from 0-25. Letter A corresponds to 0, letter B corresponds to 1, C corresponds to 2 and so on till Z corresponds to 25.

Mathematically,

Cipher text, C = (P+K) % 26. Where P is the plain text and K is key between 1 to 25. We cannot use K=0 as it will give back the same letters as plain text.

Plain text, P = (C-K) % 26. Where C is the cipher text obtained after encryption.

That was the vanilla Caesar cipher, now what about writing "hello world!" in Caesar Cipher. The task seems simple however note that the vanilla Caesar cipher does not have mapping for space and exclamation mark (!) symbols. Let us design our own mapping similar to that of vanilla mapping with these two symbols. We add ! and space characters at the end of the mapping, with ! = 26 and space = 27.

So, finally Cipher text becomes C = (P+K) % 28 and Plain text, P = (C-K) % 28. If you execute below c code will be find output as "mjqqte twqid".

#include<stdio.h>
#include<string.h>
void encrypt();
int main()
{
 encrypt();
 return 0;
}

void encrypt()
{
 int key=5; //set key here.
 char c[28]="abcdefghijklmnopqrstuvwxyz! ";
 char str[]="hello world!";
 printf("%s\n", str);
 int i=0;
 int j=0;
 for(j=0;j<strlen(str);j++)
 {
  int p;
  for(i=0;i<28;i++)
  {
   if(str[j]==c[i])
   {
    p=i;
   }
  }
  int x = (p+key);
  int val = x%28;
  printf("%c", c[val]);
 }
 printf("\n");
}

Hello world

noreply@blogger.com (Maharaj) — Sun, 19 Aug 2018 08:16:00 +0000

This is typical. Hello world!

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