Hi, I’m Avnish

Let’s consider a problem where we have to buy oranges and apples but under the following conditions. The difference between 2X the number of oranges and the number of apples should be 3. The sum of 4X the number of oranges and the number of apples should be 9. The difference between 5X the number of oranges and 3X the number of apples should be 7. System of Linear Equations These conditions could be modeled using the following equations ...

A matrix is a rank 2 tensor i.e. an array expanding in a maximum of two independent dimensions. Multiple vectors could be arranged in rows or columns to create a matrix. $$\vec{a} = \begin{bmatrix} 5 \\ 6 \\ 7 \end{bmatrix}\ \ \vec{b} = \begin{bmatrix} 7 \\ 9 \\ 10 \end{bmatrix}$$ $$\textbf{A} = \begin{bmatrix} \vec{a} & \vec{b} \end{bmatrix} = \begin{bmatrix} 5 & 7 \\ 6 & 9 \\ 7 & 10 \end{bmatrix}$$ $$\textbf{B} = \begin{bmatrix} \vec{a} \\ \vec{b} \end{bmatrix} = \begin{bmatrix} 5 & 6 & 7 \\ 7 & 9 & 10 \end{bmatrix}$$ ...

A vector could represent the magnitude of a quantity broken down into its various components, for example, the velocity of an object moving on a 2D plane could be represented using the vector $\vec{v} = \begin{bmatrix} 8 & 9 \end{bmatrix}$. On a 2D plane $8$ and $9$ could be called the horizontal and vertical components of the vector $\vec{v}$ respectively. But the words horizontal and vertical on a 2D or 3D plane are relative to the viewer (try rotating the figure above anti-clockwise). ...

In linear algebra, a tensor is an array of data expanding in multiple (or zero) independent dimensions. It is used to represent quantities/equations/functions with multiple components, for example, the equation $3x+2y=0$ could be represented with the tensor $[3\ 2\ 0]$ where each value in the tensor represents the different components of the equation. The number of independent dimensions of a tensor is called its rank. Vectors and matrices could be generalized with the term tensor. The following Venn diagram visualizes the connection between them. ...

Inspired by Julia Evan’s blog Get your work recognized: write a brag document I created this tool to keep a record of my brags in Markdown Format and refer them later to create a formatted bragging document. A bragging or hype document is created to keep a record of achievements over time. This document/information extracted from this document could be shared with managers or used for self-reflection and improvement. I refer to it during my daily standups and weekly sync-up meetings. ...

Problem Statement We have to implement the reorderList function that takes the head node of a linked list as input and reorders its nodes in the format specified below. Given an input list like the following: $$Node_0 \rightarrow Node_1 \rightarrow Node_2 \rightarrow \dots \rightarrow Node_{(n-2)} \rightarrow Node_{(n-1)} \rightarrow Node_n$$ the reorderList function should reorder its nodes as: $$Node_0 \rightarrow Node_n \rightarrow Node_1 \rightarrow Node_{(n-1)} \rightarrow Node_2 \rightarrow Node_{(n-2)} \rightarrow \dots$$ ...

Problem Statement We have to implement the mergeTwoLists function that takes the head nodes of two sorted linked lists as input and returns the head node of the merged linked list as the output. Optimal Solution To merge both linked lists we can use the two-pointer approach by maintaining an iterator on both linked lists and comparing their values. The smaller value will be selected and inserted at the end of a new list. The result would be a merged sorted linked list. ...

Problem Statement We have to implement the reverseList function that takes the head node of a linked list as an input and returns the head node of the reversed linked list in the output. Brute Force Solution If we iterate over the input linked list and insert its value at the beginning of a new list the result would be a reversed linked list. ...

To solve problems like Two Sums, Product Except Self, or Contains Duplicate we have to access multiple values at the same time from a sequential data structure (for example, a Linked List or an Array). The initial instinct while solving these problems is to use nested loops where each layer of the loop will maintain a different iterator on the data structure. But this approach does not scale well with the size of input as a single order of nested loops has $O(n^2)$ worst-case time complexity. ...

Ollama provides an interface to self-host and interact with open-source LLMs (Large Language Models) using its binary or container image. Managing LLMs using Ollama is like managing container lifecycle using container engines like docker or podman. Ollama commands pull and run are used to download and execute LLMs respectively, just like the ones used to manage containers with podman or docker. Tags like 13b-python and 7b-code are used to manage different variations of an LLM. ...