fix(learn): rework Project Euler - Problem 58 (#41188)

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gikf
2021-02-20 07:36:32 +01:00
committed by GitHub
parent f5a905b7c2
commit 219339b2ce

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@ -22,20 +22,32 @@ Starting with 1 and spiralling anticlockwise in the following way, a square spir
It is interesting to note that the odd squares lie along the bottom right diagonal, but what is more interesting is that 8 out of the 13 numbers lying along both diagonals are prime; that is, a ratio of 8/13 ≈ 62%.
If one complete new layer is wrapped around the spiral above, a square spiral with side length 9 will be formed. If this process is continued, what is the side length of the square spiral for which the ratio of primes along both diagonals first falls below 10%?
If one complete new layer is wrapped around the spiral above, a square spiral with side length 9 will be formed. If this process is continued, what is the side length of the square spiral for which the percent of primes along both diagonals first falls below `percent`?
# --hints--
`spiralPrimes()` should return a number.
`spiralPrimes(50)` should return a number.
```js
assert(typeof spiralPrimes() === 'number');
assert(typeof spiralPrimes(50) === 'number');
```
`spiralPrimes()` should return 26241.
`spiralPrimes(50)` should return `11`.
```js
assert.strictEqual(spiralPrimes(), 26241);
assert.strictEqual(spiralPrimes(50), 11);
```
`spiralPrimes(15)` should return `981`.
```js
assert.strictEqual(spiralPrimes(15), 981);
```
`spiralPrimes(10)` should return `26241`.
```js
assert.strictEqual(spiralPrimes(10), 26241);
```
# --seed--
@ -43,16 +55,51 @@ assert.strictEqual(spiralPrimes(), 26241);
## --seed-contents--
```js
function spiralPrimes() {
function spiralPrimes(percent) {
return true;
}
spiralPrimes();
spiralPrimes(50);
```
# --solutions--
```js
// solution required
function spiralPrimes(percent) {
function isPrime(n) {
if (n <= 3) {
return n > 1;
} else if (n % 2 === 0 || n % 3 === 0) {
return false;
}
for (let i = 5; i * i <= n; i += 6) {
if (n % i === 0 || n % (i + 2) === 0) {
return false;
}
}
return true;
}
let totalCount = 1;
let primesCount = 0;
let curNumber = 1;
let curSideLength = 1;
let ratio = 1;
const wantedRatio = percent / 100;
while (ratio >= wantedRatio) {
curSideLength += 2;
for (let i = 0; i < 4; i++) {
curNumber += curSideLength - 1;
totalCount++;
if (i !== 3 && isPrime(curNumber)) {
primesCount++;
}
}
ratio = primesCount / totalCount;
}
return curSideLength;
}
```