Download - Struktur data 10 (min max heap)
![Page 1: Struktur data 10 (min max heap)](https://reader033.vdocuments.pub/reader033/viewer/2022052214/559488dd1a28ab027d8b462b/html5/thumbnails/1.jpg)
min-MAX HeapBy Sunarya D. Marwah
Copyright@Sunarya D. Marwah
![Page 2: Struktur data 10 (min max heap)](https://reader033.vdocuments.pub/reader033/viewer/2022052214/559488dd1a28ab027d8b462b/html5/thumbnails/2.jpg)
Min-Max Heap adalah struktur binary tree, dimanasuatu node x berada di level min maka semua node dibawahnya, nilainya harus lebih besar dari nilainode x tersebut, dan bila node x berada di level max, maka seluruh node dibawahnya harus lebih kecil darinilai node x tersebut.
Copyright@Sunarya D. Marwah
Min-MAX Heap
![Page 3: Struktur data 10 (min max heap)](https://reader033.vdocuments.pub/reader033/viewer/2022052214/559488dd1a28ab027d8b462b/html5/thumbnails/3.jpg)
Contoh Min-Max Heap
Copyright@Sunarya D. Marwah
Min-MAX Heap
15
65 80
20 30
35 50 55 60 45 70 75
25 40
Min
Min
Max
Max
![Page 4: Struktur data 10 (min max heap)](https://reader033.vdocuments.pub/reader033/viewer/2022052214/559488dd1a28ab027d8b462b/html5/thumbnails/4.jpg)
Hasse Diagram
Copyright@Sunarya D. Marwah
Min-MAX Heap
15
65 80
20 30
35 50 55 60 45 70 75
25 40
Min
Max
![Page 5: Struktur data 10 (min max heap)](https://reader033.vdocuments.pub/reader033/viewer/2022052214/559488dd1a28ab027d8b462b/html5/thumbnails/5.jpg)
Insert ke Min-Max Heap
Copyright@Sunarya D. Marwah
Min-MAX Heap
15
65 80
20 30
35 50 55 60 45 70 75
25 40
Min
Min
Max
Maxx
![Page 6: Struktur data 10 (min max heap)](https://reader033.vdocuments.pub/reader033/viewer/2022052214/559488dd1a28ab027d8b462b/html5/thumbnails/6.jpg)
x = 10; Insert(x)
Copyright@Sunarya D. Marwah
Min-MAX Heap
15
65 80
20 30
35 50 55 60 45 70 75
25 40
Min
Min
Max
Max10
= Tukar
x< 40
![Page 7: Struktur data 10 (min max heap)](https://reader033.vdocuments.pub/reader033/viewer/2022052214/559488dd1a28ab027d8b462b/html5/thumbnails/7.jpg)
Insert(10)
Copyright@Sunarya D. Marwah
Min-MAX Heap
15
65 80
20 30
35 50 55 60 45 70 75
25 10
Min
Min
Max
Max40
x< 15
![Page 8: Struktur data 10 (min max heap)](https://reader033.vdocuments.pub/reader033/viewer/2022052214/559488dd1a28ab027d8b462b/html5/thumbnails/8.jpg)
Insert(10)
Copyright@Sunarya D. Marwah
Min-MAX Heap
10
65 80
20 30
35 50 55 60 45 70 75
25 15
Min
Min
Max
Max40
![Page 9: Struktur data 10 (min max heap)](https://reader033.vdocuments.pub/reader033/viewer/2022052214/559488dd1a28ab027d8b462b/html5/thumbnails/9.jpg)
x = 85; Insert(85)
Copyright@Sunarya D. Marwah
Min-MAX Heap
15
65 80
20 30
35 50 55 60 45 70 75
25 40
Min
Min
Max
Max85
x > 40
![Page 10: Struktur data 10 (min max heap)](https://reader033.vdocuments.pub/reader033/viewer/2022052214/559488dd1a28ab027d8b462b/html5/thumbnails/10.jpg)
x = 85; Insert(85)
Copyright@Sunarya D. Marwah
Min-MAX Heap
15
65 80
20 30
35 50 55 60 45 70 75
25 40
Min
Min
Max
Max85
x > 80
![Page 11: Struktur data 10 (min max heap)](https://reader033.vdocuments.pub/reader033/viewer/2022052214/559488dd1a28ab027d8b462b/html5/thumbnails/11.jpg)
x = 85; Insert(85)
Copyright@Sunarya D. Marwah
Min-MAX Heap
15
65 85
20 30
35 50 55 60 45 70 75
25 40
Min
Min
Max
Max80
![Page 12: Struktur data 10 (min max heap)](https://reader033.vdocuments.pub/reader033/viewer/2022052214/559488dd1a28ab027d8b462b/html5/thumbnails/12.jpg)
Insert: +10 +20 +30 +40 +50 +60 +70
Copyright@Sunarya D. Marwah
Min-MAX Heap
10 Min
![Page 13: Struktur data 10 (min max heap)](https://reader033.vdocuments.pub/reader033/viewer/2022052214/559488dd1a28ab027d8b462b/html5/thumbnails/13.jpg)
Insert: +10 +20 +30 +40 +50 +60 +70
Copyright@Sunarya D. Marwah
Min-MAX Heap
10
20
Min
Max
![Page 14: Struktur data 10 (min max heap)](https://reader033.vdocuments.pub/reader033/viewer/2022052214/559488dd1a28ab027d8b462b/html5/thumbnails/14.jpg)
Insert: +10 +20 +30 +40 +50 +60 +70
Copyright@Sunarya D. Marwah
Min-MAX Heap
10
20 30
Min
Max
![Page 15: Struktur data 10 (min max heap)](https://reader033.vdocuments.pub/reader033/viewer/2022052214/559488dd1a28ab027d8b462b/html5/thumbnails/15.jpg)
Insert: +10 +20 +30 +40 +50 +60 +70
Copyright@Sunarya D. Marwah
Min-MAX Heap
10
20 30
40
Min
Min
Max
![Page 16: Struktur data 10 (min max heap)](https://reader033.vdocuments.pub/reader033/viewer/2022052214/559488dd1a28ab027d8b462b/html5/thumbnails/16.jpg)
Insert: +10 +20 +30 +40 +50 +60 +70
Copyright@Sunarya D. Marwah
Min-MAX Heap
10
40 30
20
Min
Min
Max
![Page 17: Struktur data 10 (min max heap)](https://reader033.vdocuments.pub/reader033/viewer/2022052214/559488dd1a28ab027d8b462b/html5/thumbnails/17.jpg)
Insert: +10 +20 +30 +40 +50 +60 +70
Copyright@Sunarya D. Marwah
Min-MAX Heap
10
40 30
20 50
Min
Min
Max
![Page 18: Struktur data 10 (min max heap)](https://reader033.vdocuments.pub/reader033/viewer/2022052214/559488dd1a28ab027d8b462b/html5/thumbnails/18.jpg)
Insert: +10 +20 +30 +40 +50 +60 +70
Copyright@Sunarya D. Marwah
Min-MAX Heap
10
50 30
20 40
Min
Min
Max
![Page 19: Struktur data 10 (min max heap)](https://reader033.vdocuments.pub/reader033/viewer/2022052214/559488dd1a28ab027d8b462b/html5/thumbnails/19.jpg)
Insert: +10 +20 +30 +40 +50 +60 +70
Copyright@Sunarya D. Marwah
Min-MAX Heap
10
50 30
20 40 60
Min
Min
Max
![Page 20: Struktur data 10 (min max heap)](https://reader033.vdocuments.pub/reader033/viewer/2022052214/559488dd1a28ab027d8b462b/html5/thumbnails/20.jpg)
Insert: +10 +20 +30 +40 +50 +60 +70
Copyright@Sunarya D. Marwah
Min-MAX Heap
10
50 60
20 40 30
Min
Min
Max
![Page 21: Struktur data 10 (min max heap)](https://reader033.vdocuments.pub/reader033/viewer/2022052214/559488dd1a28ab027d8b462b/html5/thumbnails/21.jpg)
Insert: +10 +20 +30 +40 +50 +60 +70
Copyright@Sunarya D. Marwah
Min-MAX Heap
10
50 60
20 40 30
Min
Min
Max
70
![Page 22: Struktur data 10 (min max heap)](https://reader033.vdocuments.pub/reader033/viewer/2022052214/559488dd1a28ab027d8b462b/html5/thumbnails/22.jpg)
Insert: +10 +20 +30 +40 +50 +60 +70
Copyright@Sunarya D. Marwah
Min-MAX Heap
10
50 70
20 40 30
Min
Min
Max
60
![Page 23: Struktur data 10 (min max heap)](https://reader033.vdocuments.pub/reader033/viewer/2022052214/559488dd1a28ab027d8b462b/html5/thumbnails/23.jpg)
DeleteDelete dari Min-Max Heap terdiri dari:
1. DeleteMin
2. DeleteMax
DeleteMin langsung mengambil elemen paling puncak yaitu level Min teratas , sedangkanDeleteMax harus memilih elemen terbesar di level Max teratas, baru melakukan DeleteMax.
Copyright@Sunarya D. Marwah
Min-MAX Heap
![Page 24: Struktur data 10 (min max heap)](https://reader033.vdocuments.pub/reader033/viewer/2022052214/559488dd1a28ab027d8b462b/html5/thumbnails/24.jpg)
DeleteBaik DeleteMin maupun DeleteMax, penggantinode yang dihapus diambil dari node denganelemen terkecil dari anak-anak dan cucu-cucunya, kemudian elemen yang kosong diisidari elemen terakhir, kemudian lakukan reheap.
Contoh delete akan menggunakan konstruksiheap yang ada di slide nomor 10.
Copyright@Sunarya D. Marwah
Min-MAX Heap
![Page 25: Struktur data 10 (min max heap)](https://reader033.vdocuments.pub/reader033/viewer/2022052214/559488dd1a28ab027d8b462b/html5/thumbnails/25.jpg)
DeleteMin
Copyright@Sunarya D. Marwah
Min-MAX Heap
15
65 85
20 30
35 50 55 60 45 70 75
25 40
Min
Min
Max
Max80
![Page 26: Struktur data 10 (min max heap)](https://reader033.vdocuments.pub/reader033/viewer/2022052214/559488dd1a28ab027d8b462b/html5/thumbnails/26.jpg)
DeleteMin
Copyright@Sunarya D. Marwah
Min-MAX Heap
65 85
20 30
35 50 55 60 45 70 75
25 40
Min
Min
Max
Max80
![Page 27: Struktur data 10 (min max heap)](https://reader033.vdocuments.pub/reader033/viewer/2022052214/559488dd1a28ab027d8b462b/html5/thumbnails/27.jpg)
Mencari elemen dengan nilai terkecil Heap[k] dari anak-anakdan cucu-cucunya, kemudian mengisi elemen puncak yang telah kosong.
Copyright@Sunarya D. Marwah
Min-MAX Heap
65 85
20 30
35 50 55 60 45 70 75
25 40
Min
Min
Max
Max80
![Page 28: Struktur data 10 (min max heap)](https://reader033.vdocuments.pub/reader033/viewer/2022052214/559488dd1a28ab027d8b462b/html5/thumbnails/28.jpg)
Copyright@Sunarya D. Marwah
Min-MAX Heap
20
65 85
30
35 50 55 60 45 70 75
25 40
Min
Min
Max
Max80
![Page 29: Struktur data 10 (min max heap)](https://reader033.vdocuments.pub/reader033/viewer/2022052214/559488dd1a28ab027d8b462b/html5/thumbnails/29.jpg)
Copyright@Sunarya D. Marwah
Min-MAX Heap
20
65 85
80 30
35 50 55 60 45 70 75
25 40
Min
Min
Max
Max
![Page 30: Struktur data 10 (min max heap)](https://reader033.vdocuments.pub/reader033/viewer/2022052214/559488dd1a28ab027d8b462b/html5/thumbnails/30.jpg)
Copyright@Sunarya D. Marwah
Min-MAX Heap
20
80 85
65 30
35 50 55 60 45 70 75
25 40
Min
Min
Max
Max
![Page 31: Struktur data 10 (min max heap)](https://reader033.vdocuments.pub/reader033/viewer/2022052214/559488dd1a28ab027d8b462b/html5/thumbnails/31.jpg)
Copyright@Sunarya D. Marwah
Min-MAX Heap
20
80 85
35 30
65 50 55 60 45 70 75
25 40
Min
Min
Max
Max
![Page 32: Struktur data 10 (min max heap)](https://reader033.vdocuments.pub/reader033/viewer/2022052214/559488dd1a28ab027d8b462b/html5/thumbnails/32.jpg)
DeleteMax
Pilih elemen terbesar di level max teratas, max = 85
Copyright@Sunarya D. Marwah
Min-MAX Heap
20
80 85
35 30
65 50 55 60 45 70 75
25 40
Min
Min
Max
Max
![Page 33: Struktur data 10 (min max heap)](https://reader033.vdocuments.pub/reader033/viewer/2022052214/559488dd1a28ab027d8b462b/html5/thumbnails/33.jpg)
DeleteMax
Pilih elemen terbesar dari anak-anak dan cucu-cucunya.
Copyright@Sunarya D. Marwah
Min-MAX Heap
20
80
35 30
65 50 55 60 45 70 75
25 40
Min
Min
Max
Max
![Page 34: Struktur data 10 (min max heap)](https://reader033.vdocuments.pub/reader033/viewer/2022052214/559488dd1a28ab027d8b462b/html5/thumbnails/34.jpg)
Copyright@Sunarya D. Marwah
Min-MAX Heap
20
80 75
35 30
65 50 55 60 45 70
25 40
Min
Min
Max
Max
![Page 35: Struktur data 10 (min max heap)](https://reader033.vdocuments.pub/reader033/viewer/2022052214/559488dd1a28ab027d8b462b/html5/thumbnails/35.jpg)
Kelebihan dari struktur Min-Max Heap dibandingdengan Heap biasa, adalah DeleteMin dan DeleteMaxbisa dilakukan dalam satu struktur.
Copyright@Sunarya D. Marwah
Min-MAX Heap