freeCodeCamp/problem-433-steps-in-euclids-algorithm.english.md at 81a0c0c8e07a6c3a4f99228a8af10967fa0c53d9

Valeriy 79d9012432 fix(curriculum): quotes in tests (#18828 )

* fix(curriculum): tests quotes

* fix(curriculum): fill seed-teardown

* fix(curriculum): fix tests and remove unneeded seed-teardown

2018-10-20 23:32:47 +05:30

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id, challengeType, title

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

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, '<code>euler433()</code> should return 326624372659664.');

Challenge Seed

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

euler433();

Solution

// solution required

1.1 KiB Raw Blame History