Blog down the gradient

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 doe

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

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