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Course: CPS 100, Fall 2009
School: Duke
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Word Count: 397

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Binary Balanced Search Trees Balanced Binary Search Trees Pathological BST Keeping BSTrees Balanced Insert nodes from ordered list Search: O(___) ? Binary Tree is balanced if height of left and right subtree differ by no more than one, recursively for all nodes. (Height of empty tree is -1) The Balanced Tree Keeps find, insert, delete O(log(N)) worst case. Pay small extra amount at each...

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Binary Balanced Search Trees Balanced Binary Search Trees Pathological BST Keeping BSTrees Balanced Insert nodes from ordered list Search: O(___) ? Binary Tree is balanced if height of left and right subtree differ by no more than one, recursively for all nodes. (Height of empty tree is -1) The Balanced Tree Keeps find, insert, delete O(log(N)) worst case. Pay small extra amount at each insertion to keep it balanced AVL Trees Red-Black Trees ... Several Well-known Systems Exist for This Examples Will look at AVL Trees CompSci 100E 41.1 CompSci 100E 41.2 AVL Trees AVL Trees AVL Trees Single Rotation Adelson-Velskii and Landis Discovered ways to keep BSTrees Balanced Insert into BST in normal way If tree no longer balanced, perform rotation(s) Rotations leave the tree balanced again An insertion into the left subtree of the left child of tree Adapted from Weiss, pp 567-568 Insertions // Used if it has caused loss of balance) // (Also used as part of double rotation operations) Tnode rotateWithLeftChild(TNode k2) //post: returns root of adjusted tree { TNode k1 = k2.left; k2.left = k1.right; k1.right = k2; return k1; } CompSci 100E 41.3 CompSci 100E 41.4 AVL Trees AVL Trees Single Rotation before k2 k1 after Single Rotation k1 k2 C A B Also: mirror image CompSci 100E 41.5 CompSci 100E 41.6 A B C AVL Trees AVL Tree Single Rotation Mirror image case Double Rotation TNode rotateWithRightChild(TNode k2) //post: returns root of adjusted tree { TNode k1 = k2.right; k2.right = k1.left; k1.left = k2; return k1; } An insertion into the right subtree of the left child of tree Adapted from Weiss, p 57 // Used after insertion into right subtree, k2, // of left child, k1, of k3 (if it has caused // loss of balance) TNode doubleRotateWithLeftChild(TNode k3) //post: returns root of adjusted tree { k3.left = rotateWithRightChild(k3.left); return rotateWithLeftChild(k3); } 41.7 CompSci 100E 41.8 CompSci 100E AVL Tree AVL Trees Double Rotation before k3 k1 k2 k3 after Double Rotation ...

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6.63 15.04 14.26 15.56 16.83 16.98 14.88 14.37 14.23 15.15 15.74 26.15 26.52 25.84 25.69 26.08 25.32 25.95 26.95 25.57 29.57 36.99 38.77 39.59 37.07 37.7 37.22 37.45 37.89 38.99 38.79 49.35 48.21 48.63 410.33 48.51
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W X b i C2f6&quot;egvCvrdvh6iCvY2yvtrr2vCvyr0egvYCgEl2lv ie b u b u b u x w q i x x e b u b n q i ie e e e X X be u b s i u s u b b u v V Cgvvd&amp;v2!add6Y{ V|Xf CYElevCbhCvuYxfwvrCgr)vCy2v02)V|V 2egv26\$vEvd b b b
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( {~ m { zyG}~ 0 G ~ t 0y k m| { 0~ p~m { 0y k { Y ym d dy ~ k { ym d k 2X B T4 RXaa22 D h 0c`C0bbSSIpap4h D2 B q { T4 2 B4 h 2 8 T4 2 22 D 2R Ta H F h h H 2 B4 2 42 1 rW) }0y YbICwD#Q`CSSYSPpHpD`AICQ8 k 5@8 ( Y}pm Y0Y
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BigMac Bread BusFare EngSal EngTax Service TeachSal TeachTax VacDays WorkHrs 31 9 1.27 44.3 44.1 280 21.8 28.2 31.9 1714 33 9 0.27 19.4 23.7 170 9.4 14.8 23.5 1792 98 23 0.09 15.4 20.3 100 2.2 4.3 17.4 2152 131 27 0.09 4.7 37.6 70 1.1 11.7 30.6 2
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Exotic Sire Total Trt 9 1 9 1 5 1 8 2 5 1 8 3 6 1 8 4 3 2 9 1 0 2 9 2 5 2 9 3 5 2 8 4 5 3 8 1 5 3 8 2 6 3 9 3 5 3 6 4 7 4 7 1 7 4 8 2 3 4 6 3 4 4 8 4 8 5 9 1 4 5 8 2 4 5 7 3 6 5 9 4 5 6 9 1 5 6 9 2 4 6 9 3 2 6 7 4 8 7 9 1 4
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Height Length Type 75 502 0 80 522 0 68 425 0 64 344 0 83 407 0 80 451 0 70 551 0 76 530 0 74 547 0 100 519 1 75 225 1 52 300 1 62 418 1 68 409 1 86 425 1 57 370 1 82 506 1 82 506 1 88 295 1 55 273 1 67 415 1 45 182 1 103 530 1
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D F S W 7.2 0 0 10.404 8.2 0 0 18.161 10.3 0 0 25.778 10.1 0 0 20.511 10.7 0 0 21.87 13.3 0 0 47.186 5.1 1 0 4.447 7.2 1 0 8.682 10.2 1 0 19.511 11.3 1 0 37.682 12.6 1 0 25.775 17.1 1 0 67.363 5.1 0 1 4.02 6.5 0 1 7.504 8.4 0 1 13.391
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BodyWt Dose LiverWt y 176 0.88 6.5 0.42 176 0.88 9.5 0.25 190 1 9 0.56 176 0.88 8.9 0.23 200 1 7.2 0.23 167 0.83 8.9 0.32 188 0.94 8 0.37 195 0.98 10 0.41 176 0.88 8 0.33 165 0.84 7.9 0.38 158 0.8 6.9 0.27 148 0.74 7.3 0.36 149 0.75 5.2
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Age Score 15 95 26 71 10 83 9 91 15 102 20 87 18 93 11 100 8 104 20 94 7 113 9 96 10 83 11 84 11 102 10 100 12 105 42 57 17 121 11 86 10 100
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smoke disease sex 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
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Discrete Time Survival Modelsj = P (Ti = j | Ti j, xi) = h(j + xi), where j is the discrete hazard, = (1, . . . , k ) are parameters characterizing the baseline hazard xi are time-independent covariates are regression coecients1Proportional
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www.stat.duke.edu/courses/Fall02/sta240/quiz4/quiz4data.htmlQuiz 4: Lab Exercise, 11/11/02 I will follow the NSEES Honor Code.Name:_ Signature:_1.[3 points] Circle the terms that describe the meadowfoam study: (a) (b) (c) (d) (e) completely r