2021-06-15 07:49:18 +00:00
---
id: 5900f3b31000cf542c50fec6
2021-09-03 08:11:45 +00:00
title: 'Problema 71: Frações ordenadas'
2021-06-15 07:49:18 +00:00
challengeType: 5
forumTopicId: 302184
dashedName: problem-71-ordered-fractions
---
# --description--
2021-09-03 08:11:45 +00:00
Considere a fração $\frac{n}{d}$, onde `n` e `d` são números inteiros e positivos. Se `n` < `d` e o maior divisor comum, ${{HCF}(n, d)} = 1$, ela é chamada de fração irredutível.
2021-06-15 07:49:18 +00:00
2021-09-03 08:11:45 +00:00
Se nós listarmos o conjunto de frações irredutíveis onde `d` = 8, em ordem ascendente, temos:
2021-06-15 07:49:18 +00:00
$$\frac{1}{8}, \frac{1}{7}, \frac{1}{6}, \frac{1}{5}, \frac{1}{4}, \frac{2}{7}, \frac{1}{3}, \frac{3}{8}, \frac{\textbf2}{\textbf5}, \frac{3}{7}, \frac{1}{2}, \frac{4}{7}, \frac{3}{5}, \frac{5}{8}, \frac{2}{3}, \frac{5}{7}, \frac{3}{4}, \frac{4}{5}, \frac{5}{6}, \frac{6}{7}, \frac{7}{8}$$
2021-09-03 08:11:45 +00:00
Podemos ver que $\frac{2}{5}$ está imediatamente à esquerda de $\frac{3}{7}$.
2021-06-15 07:49:18 +00:00
2021-09-03 08:11:45 +00:00
Ao listar o conjunto de frações irredutíveis em ordem ascendente, onde `d` ≤ `limit` , encontre o numerador da fração imediatamente à esquerda de $\frac{3}{7}$.
2021-06-15 07:49:18 +00:00
# --hints--
2021-09-03 08:11:45 +00:00
`orderedFractions(8)` deve retornar um número.
2021-06-15 07:49:18 +00:00
```js
assert(typeof orderedFractions(8) === 'number');
```
2021-09-03 08:11:45 +00:00
`orderedFractions(8)` deve retornar `2` .
2021-06-15 07:49:18 +00:00
```js
assert.strictEqual(orderedFractions(8), 2);
```
2021-09-03 08:11:45 +00:00
`orderedFractions(10)` deve retornar `2` .
2021-06-15 07:49:18 +00:00
```js
assert.strictEqual(orderedFractions(10), 2);
```
2021-09-03 08:11:45 +00:00
`orderedFractions(9994)` deve retornar `4283` .
2021-06-15 07:49:18 +00:00
```js
assert.strictEqual(orderedFractions(9994), 4283);
```
2021-09-03 08:11:45 +00:00
`orderedFractions(500000)` deve retornar `214283` .
2021-06-15 07:49:18 +00:00
```js
assert.strictEqual(orderedFractions(500000), 214283);
```
2021-09-03 08:11:45 +00:00
`orderedFractions(1000000)` deve retornar `428570` .
2021-06-15 07:49:18 +00:00
```js
assert.strictEqual(orderedFractions(1000000), 428570);
```
# --seed--
## --seed-contents--
```js
function orderedFractions(limit) {
return true;
}
orderedFractions(8);
```
# --solutions--
```js
function orderedFractions(limit) {
const fractions = [];
const fractionValues = {};
const highBoundary = 3 / 7;
let lowBoundary = 2 / 7;
for (let denominator = limit; denominator > 2; denominator--) {
let numerator = Math.floor((3 * denominator - 1) / 7);
let value = numerator / denominator;
if (value > highBoundary || value < lowBoundary ) {
continue;
}
fractionValues[value] = [numerator, denominator];
fractions.push(value);
lowBoundary = value;
}
fractions.sort();
return fractionValues[fractions[fractions.length - 1]][0];
}
```