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---
id: 5900f3b61000cf542c50fec8
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title: 'Problema 73: Contando frações em um intervalo'
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challengeType: 5
forumTopicId: 302186
dashedName: problem-73-counting-fractions-in-a-range
---
# --description--
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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.
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Se nós listarmos o conjunto de frações irredutíveis onde `d` ≤ 8, em ordem ascendente, temos:
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$$\frac{1}{8}, \frac{1}{7}, \frac{1}{6}, \frac{1}{5}, \frac{1}{4}, \frac{2}{7}, \frac{1}{3}, \mathbf{\frac{3}{8}, \frac{2}{5}, \frac{3}{7}}, \frac{1}{2}, \frac{4}{7}, \frac{3}{5}, \frac{5}{8}, \frac{2}{3}, \frac{5}{7}, \frac{3}{4}, \frac{4}{5}, \frac{5}{6}, \frac{6}{7}, \frac{7}{8}$$
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Podemos notar que há `3` frações entre $\frac{1}{3}$ e $\frac{1}{2}$.
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Quantas frações estão entre $\frac{1}{3}$ e $\frac{1}{2}$ no conjunto de frações irredutíveis, onde `d` ≤ `limit` ?
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# --hints--
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`countingFractionsInARange(8)` deve retornar um número.
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```js
assert(typeof countingFractionsInARange(8) === 'number');
```
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`countingFractionsInARange(8)` deve retornar `3` .
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```js
assert.strictEqual(countingFractionsInARange(8), 3);
```
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`countingFractionsInARange(1000)` deve retornar `50695` .
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```js
assert.strictEqual(countingFractionsInARange(1000), 50695);
```
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`countingFractionsInARange(6000)` deve retornar `1823861` .
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```js
assert.strictEqual(countingFractionsInARange(6000), 1823861);
```
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`countingFractionsInARange(12000)` deve retornar `7295372` .
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```js
assert.strictEqual(countingFractionsInARange(12000), 7295372);
```
# --seed--
## --seed-contents--
```js
function countingFractionsInARange(limit) {
return true;
}
countingFractionsInARange(8);
```
# --solutions--
```js
function countingFractionsInARange(limit) {
let result = 0;
const stack = [[3, 2]];
while (stack.length > 0) {
const [startDenominator, endDenominator] = stack.pop();
const curDenominator = startDenominator + endDenominator;
if (curDenominator < = limit) {
result++;
stack.push([startDenominator, curDenominator]);
stack.push([curDenominator, endDenominator]);
}
}
return result;
}
```