Javascript - 使用高階生成器進行過濾以生成素數

發表於2024-02-23
JavaScript
生成器大家都知道是怎麼一回事，但是高階生成器又是什麼東西呢？今天小編就帶著大家來一起了解一下吧……

先上程式碼：

function* numFrom(start: number) {
    while (true) yield start++
}

function* filter(nums: Generator<number>, prime: number) {
    for (const n of nums) if (n % prime !== 0) yield n
}

let cur = numFrom(2)

for (let i = 0; i < 10; i++) {
    const prime = cur.next()
    if (!prime.done) {
        console.log(i, ':', prime.value)
        cur = filter(cur, prime.value)
    }
}

結果：

0 : 2
1 : 3
2 : 5
3 : 7
4 : 11
5 : 13
6 : 17
7 : 19
8 : 23
9 : 29

其中函式 filter 傳入一個生成器，返回一個新的生成器，我們可以把它稱為高階生成器。

function* filter(nums: Generator<number>, prime: number) {
    for (const n of nums) if (n % prime !== 0) yield n
}

它的作用是過濾掉 nums: Generator<number> 生成的數中能被 prime 整除的數：

const gen = filter(numFrom(10), 3)
for (let i = 0; i < 10; i++) {
    const n = gen.next()
    if (!n.done) console.log(n.value)
}

結果：

10
11
13
14
16
17
19
20
22
23

可以看到，3 的倍數，12、15、18、21 已經被過濾掉了。

如果我們再把函式返回值作為引數傳給 filter，就能過濾掉多個值了：

let gen = filter(numFrom(10), 3) // 從 10 開始，不能被 3 整除的數
gen = filter(gen, 5) // 從 10 開始，不能被 3 和 5 整除的數
...

只要我們不斷把當前的生成器和產生的素數傳入，我們就能夠實現過濾，相當於使用篩法生成素數。

let cur = numFrom(2)

for (let i = 0; i < 10; i++) {
    const prime = cur.next()
    if (!prime.done) {
        console.log(i, ':', prime.value)
        cur = filter(cur, prime.value) // 產生新的生成器
    }
}
numFrom(2) -> filter(2) -> filter(3) -> filter(5) -> filter(7) ...

如果還不太清除，可以在控制檯列印詳細過程：

function* numFrom(start: number) {
    while (true) {
        console.log('\nnum yield', start)
        yield start++
    }
}

let filterDeep = 0
function* filter(nums: Generator<number>, prime: number) {
    const deep = filterDeep++
    for (const n of nums)
        if (n % prime !== 0) {
            console.log(`filter yield[${deep}] ${n}`)
            yield n
        } else console.log(`filtered[${deep}] ${n} by ${prime}`)
}

let cur = numFrom(2)

for (let i = 0; i < 10; i++) {
    const prime = cur.next()
    if (!prime.done) {
        console.log(i, ':', prime.value)
        cur = filter(cur, prime.value)
    }
}

結果：

num yield 2
0 : 2

num yield 3
filter yield[0] 3
1 : 3

num yield 4
filtered[0] 4 by 2

num yield 5
filter yield[0] 5
filter yield[1] 5
2 : 5

num yield 6
filtered[0] 6 by 2

num yield 7
filter yield[0] 7
filter yield[1] 7
filter yield[2] 7
3 : 7

num yield 8
filtered[0] 8 by 2

num yield 9
filter yield[0] 9
filtered[1] 9 by 3

num yield 10
filtered[0] 10 by 2

num yield 11
filter yield[0] 11
filter yield[1] 11
filter yield[2] 11
filter yield[3] 11
4 : 11

num yield 12
filtered[0] 12 by 2

num yield 13
filter yield[0] 13
filter yield[1] 13
filter yield[2] 13
filter yield[3] 13
filter yield[4] 13
5 : 13

num yield 14
filtered[0] 14 by 2

num yield 15
filter yield[0] 15
filtered[1] 15 by 3

num yield 16
filtered[0] 16 by 2

num yield 17
filter yield[0] 17
filter yield[1] 17
filter yield[2] 17
filter yield[3] 17
filter yield[4] 17
filter yield[5] 17
6 : 17

num yield 18
filtered[0] 18 by 2

num yield 19
filter yield[0] 19
filter yield[1] 19
filter yield[2] 19
filter yield[3] 19
filter yield[4] 19
filter yield[5] 19
filter yield[6] 19
7 : 19

num yield 20
filtered[0] 20 by 2

num yield 21
filter yield[0] 21
filtered[1] 21 by 3

num yield 22
filtered[0] 22 by 2

num yield 23
filter yield[0] 23
filter yield[1] 23
filter yield[2] 23
filter yield[3] 23
filter yield[4] 23
filter yield[5] 23
filter yield[6] 23
filter yield[7] 23
8 : 23

num yield 24
filtered[0] 24 by 2

num yield 25
filter yield[0] 25
filter yield[1] 25
filtered[2] 25 by 5

num yield 26
filtered[0] 26 by 2

num yield 27
filter yield[0] 27
filtered[1] 27 by 3

num yield 28
filtered[0] 28 by 2

num yield 29
filter yield[0] 29
filter yield[1] 29
filter yield[2] 29
filter yield[3] 29
filter yield[4] 29
filter yield[5] 29
filter yield[6] 29
filter yield[7] 29
filter yield[8] 29
9 : 29

參考：

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