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Catalog Placements Assignment - Online

Name: Ganta Venkata Kousik
Roll No: 21pa1a0549
College: Vishnu Institute of Technology

Overview

This project is a simplified implementation of Shamir's Secret Sharing algorithm. The task is to find the constant term of a polynomial given a set of encoded roots in JSON format. The polynomial is represented as:

[ f(x) = a_m x^m + a_{m-1} x^{m-1} + \ldots + a_1 x + c ]

Where:

  • ( f(x) ) is the polynomial function
  • ( m ) is the degree of the polynomial
  • ( a_m, a_{m-1}, \ldots, a_1, c ) are coefficients (real numbers)
  • ( a_m \neq 0 ) (ensuring the polynomial is of degree ( m ))

Features

  • Reads input from JSON files containing encoded polynomial roots.
  • Decodes the y-values from various bases.
  • Uses Gaussian elimination to solve for the polynomial coefficients.
  • Outputs the constant term ( c ) for each test case.

Requirements

  • C++ compiler (e.g., g++)
  • RapidJSON library for JSON parsing

Setup

  1. Clone the Repository:

    git clone https://github.com/GantaVenkataKousik/catelog-online-assessment

  2. Install RapidJSON: Ensure that the RapidJSON library is installed and accessible in your include path.

  3. Compile the Code:

    g++ -o main main.cpp -I/path/to/rapidjson/include

Usage

  1. Prepare JSON Files: Ensure that your JSON files (input1.json, input2.json, etc.) are in the same directory as the executable.

  2. Run the Program:

    ./main

  3. Output: The program will output the constant term ( c ) for each test case.

Example JSON Format

{
"keys": {
    "n": 10,
    "k": 7
  },
  "1": {
    "base": "6",
    "value": "13444211440455345511"
  },
  "2": {
    "base": "15",
    "value": "aed7015a346d63"
  },
  "3": {
    "base": "15",
    "value": "6aeeb69631c227c"
  },
  "4": {
    "base": "16",
    "value": "e1b5e05623d881f"
  },
  "5": {
    "base": "8",
    "value": "316034514573652620673"
  },
  "6": {
    "base": "3",
    "value": "2122212201122002221120200210011020220200"
  },
  "7": {
    "base": "3",
    "value": "20120221122211000100210021102001201112121"
  },
  "8": {
    "base": "6",
    "value": "20220554335330240002224253"
  },
  "9": {
    "base": "12",
    "value": "45153788322a1255483"
  },
  "10": {
    "base": "7",
    "value": "1101613130313526312514143"
  }
}

Notes

  • Ensure that the JSON files are correctly formatted and contain valid data.
  • The program assumes that the number of roots provided (n) is greater than or equal to the minimum number of roots required (k).

Contact

For any questions or issues, please contact Ganta Venkata Kousik at venkatakousikcse01@gmail.com or 21pa1a0549@vishnu.edu.in