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K: 5 P: 9 K: 1 P: 2 P: 6 K: 8 K: 7 P: 4

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K: 5. P: 9. K:1. K: 8. P:2. P: 6. K: 7. P: 4. K: 5. P: 9. K:1. K: 8. P:2. P: 6. Is the treap a heap?. K: 7. P: 4. P: 9. P:2. P: 6. For every node v, the search key in v is greater than or equal to those in the children of v. P: 4. K: 5. P: 9. K:1. K: 8. P:2. P: 6. - PowerPoint PPT Presentation

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K: 5

P: 9

K:1P:2

P: 6

K: 8

K: 7

P: 4

K: 5

P: 9

K:1P:2

P: 6

K: 8

K: 7

P: 4

Is the treap a heap?

P: 9

P:2P: 6

P: 4

For every node v, the search key in v is greater than or equal to those in the children of v

K: 5

P: 9

K:1P:2

P: 6

K: 8

K: 7

P: 4

Not a complete tree! NO!

K: 5

P: 9

K:1P:2

P: 6

K: 8

K: 7

P: 4

Is the treap a Binary Search Tree?

K: 5

K:1 K: 8

K: 7BST? Yes!

K: 5

K:1 K: 8

K: 7

All keys smaller than the root are stored in the left subtree

All keys larger than the root are sorted in the right subtree

(K, P)(5,9)(7,4)(8,6)(1,2)

K: 5

P: 9K:1P:2 P: 6

K: 8K: 7

P: 4

(K, P)(5,9)(7,4)(8,6)(1,2)

K: 5

P: 9

K:1P:2

P: 6

K: 8

K: 7

P: 4

K: 5

P: 9

K:1P:2

P: 6

K: 8

K: 7

P: 4

K: 5

P: 9

K:1P:2

P: 6

K: 8

K: 7

P: 4

K: 5

P: 9

K:1P:2

P: 6

K: 8

K: 7

P: 4

Assume no duplicate key / priority, only one treap is possible

(2,5) (5,2) (3,1) (4,7) (9,4) (8,3)

K:2P:5

K:5P:2

K:3P:1

K:4P:7

K:9P:4

K:8P:3

K:2P:5

K:5P:2

K:3P:1

K:4P:7

K:9P:4

K:8P:3

Arrange from left to right,

Smallest key Biggest key

K:2P:5

K:5P:2

K:3P:1

K:4P:7

K:9P:4

K:8P:3

Without destroying left to right arrangement,Shift the “nodes” up and down

Biggest priority

Smallest priority

K:2P:5

K:5P:2K:3

P:1

K:4P:7

K:9P:4

K:8P:3

K:2P:5

K:5P:2

K:3P:1

K:4P:7

K:9P:4

K:8P:3

: > ? @ > G = K 5 H 5 A B 8 3 @ 0 = = K 5 A C 2 5 ; 8 G 5 = = K" href="https://vdocuments.us/-52645-2006-0-9-8-2-k-a-g-k-5-h-5-a-b-8-3-.html">! 52645-2006, 0 9 : 8 2 K A > : > ? @ > G = K 5 H 5 A B 8 3 ......! " 52645-2006, 0 9 : 8 2 K A > : > ? @ > G = K 5 H 5 A B 8 3 @ 0 = = K 5 A C 2 5 ; 8 G 5 = = K

4 k" href="https://vdocuments.us/-237521-92-0-b-k-5-g-0-b-k-5-5-b-4-k-8-a-k-b-237521-92.html">! 23752.1-92, ; 0 B K ? 5 G 0 B = K 5. 5 B > 4 K 8 A ? K B ...newtch.ru/wp-content/uploads/2016/09/33872_gost_23752.1-92.pdf · ! " 23752.1-92, ; 0 b k ? 5 g 0 b = k 5. 5 b > 4 k

3 > a 5 g 5 = 8 o > 1 i 5 3 > = 0 7" href="https://vdocuments.us/-617-2006-c-1-k-5-4-k-5-8-0-b-c-k-5-c-3-617-2006.html">! 617-2006, @ C 1 K < 5 4 = K 5 8 ; 0 B C = = K 5 : @ C 3 ...! " 617-2006, " @ c 1 k < 5 4 = k 5 8 ; 0 b c = = k 5 : @ c 3 ; > 3 > a 5 g 5 = 8 o > 1 i 5 3 > = 0 7

! 12767-94, ; 8 B K ? 5 @ 5 : @ K B 8 9 6 5 ; 5 7 > 1 5 B ...gostexpert.ru/data/files/12767-94/bab2793df3619c79dd7b6f96e8973… · ! " 12767-94, ; 8 b k ? 5 @ 5 : @ k b 8 9 6 5 ;

1 5 b > = = k 5 ? @ 5 4 2 0 @ 8 b 5 ; l = > = 0 ? @ o 6 5 = = k" href="https://vdocuments.us/-259120-91-8-b-k-6-5-5-7-1-5-b-k-5-5-4-259120-91.html">! 25912.0-91, ; 8 B K 6 5 ; 5 7 > 1 5 B > = = K 5 ? @ 5 4 ... · ! " 25912.0-91, ; 8 b k 6 5 ; 5 7 > 1 5 b > = = k 5 ? @ 5 4 2 0 @ 8 b 5 ; l = > = 0 ? @ o 6 5 = = k

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; L 3 0, ; 5 = B K, ; 8 A B K 8 ? ; 8 B K ; 0 B C = = K 5. " 5 E = 8 G 5 A : 8 5 C A ; > 2 8 O" href="https://vdocuments.us/-2208-2007-l-3-0-5-b-k-8-a-b-k-8-8-b-k-0-2208-2007.html">! 2208-2007, $ > ; L 3 0, ; 5 = B K, ; 8 A B K 8 ? ; 8 B K ; 0 ...! " 2208-2007, $ > ; L 3 0, ; 5 = B K, ; 8 A B K 8 ? ; 8 B K ; 0 B C = = K 5. " 5 E = 8 G 5 A : 8 5 C A ; > 2 8 O

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@ 8 G = K 5. 1 I 8 5 B 5 E = 8 G 5 A : 8" href="https://vdocuments.us/-2787-75-5-b-0-k-g-5-k-5-2-b-8-g-k-5-1-old-2787-75.html">! 2787-75, 5 B 0 ; ; K G 5 @ = K 5 2 B > @ 8 G = K 5. 1 …old.ruslom.com/_/704/gost_2787_75.pdf! " 2787-75, 5 B 0 ; ; K G 5 @ = K 5 2 B > @ 8 G = K 5. 1 I 8 5 B 5 E = 8 G 5 A : 8

SL-BARCAB-5-K - SL-BARCAB-5-ASH-K - INSTRUCTIVO

ESTADÍSTICAS - FECHA · 2 . 1 k 4 . 5 k 4 . 4 k 3 . 8 k 4 . 5 k 2 .5 k 3 .7 k 4 .4 k 2 . 8 k 4 . 9 k 5 . 7 k 4 . 7 k 5 .8 k 3 .4 k 3 .1 k 5 .2 k g p m x p m to p 5 a s s i s t s

1 5 B > = = K 5 1 5 7 = 0 ? > @ = K 5. " 5 E = 8 G 5 A : 8 5 C A ; > 2 8 O Reinforced" href="https://vdocuments.us/-6482-88-c-1-k-6-5-5-7-1-5-b-k-5-1-5-7-0-.html">! 6482-88, @ C 1 K 6 5 ; 5 7 > 1 5 B > = = K 5 1 5 7 = 0 ......! " 6482-88, " @ C 1 K 6 5 ; 5 7 > 1 5 B > = = K 5 1 5 7 = 0 ? > @ = K 5. " 5 E = 8 G 5 A : 8 5 C A ; > 2 8 O Reinforced

; c g 5 = 8 5 < > = b 0 6 = k e 8 ? > 4 ; 5 6 0 i 8 e < 5 b" href="https://vdocuments.us/-23664-79-0-b-k-5-g-0-b-k-5-c-g-5-8-5-23664-79-.html">! 23664-79, ; 0 B K ? 5 G 0 B = K 5. > ; C G 5 = 8 5 ... · ! " 23664-79, ; 0 b k ? 5 g 0 b = k 5. > ; c g 5 = 8 5 < > = b 0 6 = k e 8 ? > 4 ; 5 6 0 i 8 e < 5 b

volume 5 Kenstan - Locks · Volume 5 Catalog Keymatic Line of Locks Kenstan LOCK COMPANY K 3 K 2 K 5 K 10 K 9 K 8 K 7 K 12 K 13 K 14 K 1 K 11 K 6 Introduction Cam Locks Drawer/Door

4 = k 5 @ > ; 8 : > 2 k 5 8 2 b c ; > g = k 5. ! " 13568-97, & 5 ? 8 ? @ 8 2 > 4 =" href="https://vdocuments.us/-13568-97-5-8-8-2-4-k-5-8-2-k-5-8-.html">! 13568-97, & 5 ? 8 ? @ 8 2 > 4 = K 5 @ > ; 8 : > 2 K 5 8 ... · ! " 13568-97, & 5 ? 8 ? @ 8 2 > 4 = k 5 @ > ; 8 : > 2 k 5 8 2 b c ; > g = k 5. ! " 13568-97, & 5 ? 8 ? @ 8 2 > 4 =

web srp.19 · EUROVENT CERTIFIED PERFORMANCE K 7-5 K25 K 6-5 K 5-6 K 20 K K 5-5 . 8. 9.10 (m3/h) x 25 (rrðs) 30 40 50 100110 150 K 12 K 5-3 K 4-3 K 5-2 K 3-3 K 4—2 3. 20 15 K 3-2

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= B 0 6 = K 5 > : > = = K 5 A ? 0 @ > ? @ > = 8 F 0 5 < K" href="https://vdocuments.us/-52749-2007-2-k-b-0-6-k-5-k-5-a-0-.html">! 52749-2007, ( 2 K < > = B 0 6 = K 5 > : > = = K 5 A ? 0 ......! " 52749-2007, ( 2 K < > = B 0 6 = K 5 > : > = = K 5 A ? 0 @ > ? @ > = 8 F 0 5 < K

12°0'0W N 0 8 Bonthe District Map 1 5 . 9 k m This map is ... k m 1 3. 8 k m 3 2 . 2 k m 1 2 . 2 k m 2 9 . 5 k 6 . 5 k m 5. 7 k m 5. 2 k m 1 5 . 9 k m 16.7 k m 3. 1 k m 2. 5 k m 6

bioRxiv preprint doi: . … · 222 (3 6( & ' ( (0 ' " ?(,( ; " $ ! $ ' ( 222 (3 6( ) ' ( *# (0 ' " ?(,(; " $ ! '""% ekk***( ( k & k $ 5 ' 5 "5 % 5 ' 5 " 5 " & "

ArcView Print Job - conselldemallorca.cat · k. 6 4 k . 6 1 k . 6 5 50 1 0 0 1 0 0 5 0 1 5 0 200 2 5 0 k .5 7 k . 5 6 100 100 0 1 5 0 200 2 0 0 2 5 0 k . 5 9 k.58 k . 6 0 5 0 1 0

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