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Order 3: |
Min |
Max |
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All
leaf nodes have null pointers! |
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Susan Cooper |
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Data |
1 |
2 |
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Pointers |
2 |
3 |
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| 1 |
Insert |
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46 |
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46 |
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| 2 |
Insert |
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55 |
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46 |
55 |
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| 3 |
Insert |
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88 |
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55 |
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46 |
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88 |
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| 4 |
Insert |
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99 |
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55 |
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46 |
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88 |
99 |
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| 5 |
Insert |
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200 |
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88 |
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| Successor
of 55 not full |
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| Rotate
left to insert 200 |
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46 |
55 |
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99 |
200 |
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| 6 |
Insert |
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120 |
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children are full |
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| Evaluate
and split median (120) |
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88 |
120 |
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46 |
55 |
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200 |
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| 7 |
Insert |
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300 |
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88 |
120 |
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46 |
55 |
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200 |
300 |
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| 8 |
Insert |
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400 |
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88 |
200 |
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| Successor
of 120 not full |
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| Rotate
left to insert 400 |
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46 |
55 |
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99 |
120 |
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300 |
400 |
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| 9 |
Insert |
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500 |
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levels are full |
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200 |
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| Evaluate
and split median (400) |
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| Split
and bring down 88 from 200 |
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88 |
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400 |
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46 |
55 |
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99 |
120 |
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300 |
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500 |
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| 10 |
Insert |
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12 |
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200 |
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| Both
children are full |
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| Evaluate
and split median (46) |
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46 |
88 |
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400 |
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12 |
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99 |
120 |
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300 |
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500 |
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| 11 |
Insert |
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59 |
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200 |
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46 |
88 |
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400 |
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12 |
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55 |
59 |
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99 |
120 |
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300 |
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500 |
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| 12 |
Insert |
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62 |
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200 |
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55 |
88 |
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400 |
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12 |
46 |
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59 |
62 |
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99 |
120 |
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300 |
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500 |
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| 13 |
Insert |
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98 |
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| Left
subtree is full |
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| Evaluate
and split median (99) |
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200 |
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55 |
88 |
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400 |
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12 |
46 |
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59 |
62 |
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99 |
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300 |
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500 |
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98 |
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120 |
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| Bring
99 up to 55|88 and there is room in 400 |
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| Count
on right of root (200) is one…room to rotate and combine 200 with 400 |
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| Bring
the greatest value of left side (99) up to root |
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| 98
attaches to right of 88 and 120 is a jumper to left of 200|400 |
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99 |
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55 |
88 |
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200 |
400 |
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12 |
46 |
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59 |
62 |
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98 |
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120 |
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500 |
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| 14 |
Insert |
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93 |
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. |
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99 |
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55 |
88 |
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200 |
400 |
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12 |
46 |
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59 |
62 |
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93 |
98 |
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120 |
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500 |
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| 15 |
Insert |
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47 |
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| Evaluate
and split median (46) |
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99 |
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55 |
88 |
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200 |
400 |
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46 |
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59 |
62 |
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93 |
98 |
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120 |
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500 |
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12 |
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47 |
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| Both
children of root (99) is full |
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| Evaluate
and split median of 46|55|88 up to root |
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55 |
99 |
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46 |
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200 |
400 |
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12 |
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47 |
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59 |
62 |
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93 |
98 |
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120 |
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500 |
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| Now delete all
values in the order they were inserted |
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Start with… |
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55 |
99 |
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46 |
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200 |
400 |
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12 |
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47 |
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59 |
62 |
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93 |
98 |
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120 |
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500 |
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| 1 |
Delete |
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46 |
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| Both
pred. and succ. are same count |
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| Swap
with pred. (12) and delete 46 |
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