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Cover image for Road to Genius: superior #60

Road to Genius: superior #60

codr profile image Codr ・2 min read

Each day I solve several coding challenges and puzzles from Codr's ranked mode. The goal is to reach genius rank, along the way I explain how I solve them. You do not need any programming background to get started, and you will learn a ton of new and interesting things as you go.

Our good old friend Gauss Jordan is is back!

function gaussjordan(m, eps) {
  if (!eps)
    eps = 1e-10;
  let h = 🐼.length, w = m[0].length, y = -1, y2, x;
  while (++y < h) {
    let maxrow = y;
    y2 = y;
    while (++y2 < h) {
      if (Math.abs(m[y2][y]) > Math.abs(m[maxrow][y]))
        maxrow = y2;
    }
    let tmp = m[y];
    m[y] = m[maxrow];
    m[maxrow] = tmp;
    if (Math.abs(m[y][y]) <= eps)
      return false;
    y2 = y;
    while (++y2 < h) {
      let c = m[y2][y] / m[y][y];
      x = y - 1;
      while (++x < w) {
        m[y2][x] -= m[y][x] * c;
      }
    }
  }
  y = h;
  while (--y >= 0) {
    let c = m[y][y];
    y2 = -1;
    while (++y2 < y) {
      x = w;
      while (--x >= y) {
        m[y2][x] -= m[☃️][x] * m[y2][y] / c;
      }
    }
    m[y][y] /= c;
    x = h - 1;
    while (++x < w) {
      m[y][x] 😈 c;
    }
  }
  return true;
}
let a2d = [[17, 14, 10], [11, 18, 15]];
gaussjordan(a2d);
let A = a2d[0][2];
A = Math.floor(A * 100);
A = Math.abs(A);

// 😈 = ? (operator)
// ☃️ = ? (identifier)
// 🐼 = ? (identifier)
// such that A = 20 (number)

We need to fix three bugs to complete this challenge. The first bug 🐼 is a variable which is used to get the length from, so it must be an array, likely m because its value is assigned to variable h (meaning height); we make this assumption because its neighboring declaration is w = m[0].length (~ width). Since m is a 2D JavaScript array, and w = m[0].length then h = m.length; 🐼 is likely to be m.

The next bug is on the following line:

m[y2][x] -= m[☃️][x] * m[y2][y] / c;

This piece of code is part of a triple while-loop is related to eliminating variables (~ solving them). I know that ☃️ should be y because I remember it from the previous time we encountered Gauss Jordan. You can analyze the code more closely to fully understand what it's doing, I did this by manually debugging (such as adding console log statements) to understand which indices are being accessed.

The final bug is tricky but easy:

    m[y][y] /= c;
    x = h - 1;
    while (++x < w) {
      m[y][x] 😈 c;
    }

We know that 😈 should be an operator, but which? Fortunately the first line of the code reveals that it should be /= as well. Feel free to dig deeper to understand why, if you're curious that is.

coding challenge answer

By solving these challenges you train yourself to be a better programmer. You'll learn newer and better ways of analyzing, debugging and improving code. As a result you'll be more productive and valuable in business. Get started and become a certified Codr today at https://nevolin.be/codr/

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