Bajardi: buronov umid qabul Qildi: Isroilov Sh Samarqand -2022 Heap tree tuzulmasi va ustida amallar bajarish algoritmlari

const array = [null, 100, 70, 80, 20, 30, 20, 50]
Min heap:
const array = [null, 10, 14, 17, 20, 30, 21, 44]
Agar biz array’dan i-nchi elementni ko’rsak:
1.uning parent’i – floor (i-1)/2 indeksda;
2.uning chap child’i – 2 * i indeksda;
3.uning o’ng child’i – 2 *i + 1 indeksda.
Binary heap ustida amallar
Priority queue’da bo’lgani singari, Binary heap ustida ham ikkita amal bor. Qo’shish (insert yoki enqueue) va eng katta (eng kichik) qiymatini o’chirish (delete yoki dequeue). Shuningdek qo’shilgan va o’chirilgan elementlardan so’ng, heap’ning tartibini to’g’rilash uchun ichki – cho’ktirish (sink) va ko’tarish (swim) amallari ham mavjud.
Insert. Heap’ga node (element) qo’shish uchun:
1)Elementni tree’ning eng pastiga qo’shamiz (array’ning ohiriga qo’shamiz).
2)Qo’shilgan elementning parent’iga qaraymiz. Agar parent’i o’zidan katta bo’lsa, ularning o’rnini almashtiramiz.
3)Solishtirish va almashtirishlarni element parent’idan katta bo’lguncha davom ettiramiz.
Delete. O’chirish’da biz eng katta (yoki eng kichik) qiymati root’da joylashganini bilganimiz uchun ishimiz osonroq, o’chiriladigan elementni topish O(1) vaqt oladi.
O’chirish uchun:
1.root elementni ohirgi element bilan o’rnini almashtiramiz: array[1] ni array[array.length – 1] bilan. Keyin ohirgi elementni o’chiramiz.
2.yangi root’ni uning child’lari bilan solishtiramiz. Agar u child’dan kichik bo’lsa (min heap uchun – child’dan katta bo’lsa), ularning o’rnini almashtiramiz. Ikki child’dan ham kichkina bo’lib qolganda kattaroq qiymatdagi child bilan o’rnini almashtiramiz.
3.shu tariqa solishtirish va almashtirish bilan elementni uning child’larida katta holda qolgunga qadar davom ettiramiz
Qo’shish va o’chirish amallarini qanday ishlashini bilib olgach, istalgan tartiblanmagan array’dan binary heap hosil qilishimiz mumkin.

Kod:
Priority queue kabi, Binary heap’da amallar bittadan ko’p bo’lgani uchun API yozamiz
class BinaryHeap {
constructor(arr = [], asc = true) {
this.arr = arr
this.asc = asc
}
enqueue(item) {
// Heap'ga yangi item qo'shamiz
this.arr[this.arr.length === 0 ? 1 : this.arr.length] = item
// Uning pozitsiyasini to'g'rilaymiz
this.swim(this.arr.length - 1)
}
dequeue() {
let max = this.arr[1]
// root va ohirgi element o'rnini almashtiramiz.
this.arr[1] = this.arr[this.arr.length - 1]
this.arr[this.arr.length - 1] = max
// Ohirgi elementni o'chiramiz
this.arr.pop()

// Birinchi elementning pozitsiyasini to'g'rilaymiz.

this.sink(1)
// O'chirilgan elementning qiymatini qaytaramiz
return max
}
swim(index) {
while (index > 1 &&
(
this.asc && this.arr[Math.floor(index / 2)] > this.arr[index] ||
!this.asc && this.arr[Math.floor(index / 2)] < this.arr[index]
)
) {
// Parent va child o'rnini almashtiramiz
this.swap(index, Math.floor(index / 2))
index = Math.floor(index / 2)
} }
sink(index, len = this.arr.length) {
while (Math.floor(index / 2) <= len) {
let j = 2 * index
if (j < len &&
(
this.asc && this.arr[j] > this.arr[j + 1] ||
!this.asc && this.arr[j] < this.arr[j + 1]
)
) {
j++
}
if (!(this.asc && this.arr[index] > this.arr[j] || !this.asc && this.arr[index] < this.arr[j])) {
break
}
this.swap(index, j)
index = j
} }
isEmpty() {
// heap bo'shligini tekshirish
return this.arr.length < 2
}
swap(a, b) {
[this.arr[a], this.arr[b]] = [this.arr[b], this.arr[a]]
}
show() {
return this.arr
}}
/**
* USAGE
*/

const array = [3, 4, 6, 2, 9, 1]

const binaryHeap = new BinaryHeap([], false)
array.map(item => binaryHeap.enqueue(item))
binaryHeap.dequeue()
console.log(binaryHeap.show())