freeCodeCamp/curriculum/challenges/english/08-coding-interview-prep/project-euler/problem-433-steps-in-euclids-algorithm.english.md

id, challengeType, title, forumTopicId

id	challengeType	title	forumTopicId
5900f51d1000cf542c51002f	5	Problem 433: Steps in Euclid's algorithm	302104

Description

Let E(x0, y0) be the number of steps it takes to determine the greatest common divisor of x0 and y0 with Euclid's algorithm. More formally:x1 = y0, y1 = x0 mod y0xn = yn-1, yn = xn-1 mod yn-1 E(x0, y0) is the smallest n such that yn = 0.

We have E(1,1) = 1, E(10,6) = 3 and E(6,10) = 4.

Define S(N) as the sum of E(x,y) for 1 ≤ x,y ≤ N. We have S(1) = 1, S(10) = 221 and S(100) = 39826.

Find S(5·106).

Instructions

Tests

tests:
  - text: <code>euler433()</code> should return 326624372659664.
    testString: assert.strictEqual(euler433(), 326624372659664);

Challenge Seed

function euler433() {
  // Good luck!
  return true;
}

euler433();

Solution

// solution required