const fs = require("fs");

function convertToBase10(numberInBaseStr, baseStr) {
  const base = parseInt(baseStr, 10);

  if (isNaN(base) || base < 2 || base > 36) {
    throw new Error("Base must be a number between 2 and 36.");
  }
  const numberStr = numberInBaseStr.toUpperCase();

  const validChars = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ".slice(0, base);

  for (const char of numberStr) {
    if (!validChars.includes(char)) {
      throw new Error(`Invalid digit '${char}' for base ${base}.`);
    }
  }

  const result = parseInt(numberStr, base);
  if (isNaN(result)) {
    throw new Error(`Invalid number '${numberInBaseStr}' for base ${base}.`);
  }

  return result;
}

// Lagrange Interpolation
function computeConstantTerm(points) {
  let c0 = 0;
  const m = points.length - 1;

  for (let i = 0; i <= m; i++) {
    const xi = points[i].x;
    const yi = points[i].y;
    let Li0 = 1;

    for (let j = 0; j <= m; j++) {
      if (j !== i) {
        const xj = points[j].x;
        const numerator = -xj;
        const denominator = xi - xj;

        Li0 *= numerator / denominator;
      }
    }

    c0 += yi * Li0;
  }

  return c0;
}


// this reads json file input
const d = fs.readFileSync("points.json", "utf8");
data = JSON.parse(d);

const points = []
for (const [key, value] of Object.entries(data)) {
  console.log(`${key}: ${value["base"]}`);
  if(key == "keys") {
    continue;
  }
  const nw = {
    "x": parseInt(key),
    "y": convertToBase10(value["value"],value["base"])
  }
  points.push(nw);
}
answer = {
    "constant term": computeConstantTerm(points),
}
jsonString = JSON.stringify(answer)
fs.writeFile("answer.json", jsonString, (err) => {
  if (err) {
    console.error("Error writing JSON to file:", err);
  } else {
    console.log("JSON data has been written to data.json");
  }
});