lec35 - Priority Search Trees Keys are distinct ordered...

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Priority Search Trees Keys are distinct ordered pairs (x i , y i ) . Basic operations. get(x,y) … return element whose key is (x , y) . delete(x,y) … delete and return element whose key is (x,y) . insert(x,y,e) … insert element e , whose key is (x , y) . Rectangle operations.
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minXinRectangle(x L ,x R ,y T ) Return element with min x -coordinate in the rectangle defined by the lines, x= x L , x= x R , y = 0 , y = y T , x L <= x R , 0 <= y T . I.e., return element with min x such that x L <= x <= x R and 0 <= y <= y T . x L x R y T
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maxXinRectangle(x L ,x R ,y T ) Return element with max x -coordinate in the rectangle defined by the lines, x= x L , x= x R , y = 0 , y = y T , x L <= x R , 0 <= y T . I.e., return element with max x such that x L <= x <= x R and 0 <= y <= y T . x L x R y T
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minYinXrange(x L ,x R ) Return element with min y -coordinate in the rectangle defined by the lines, x= x L , x= x R , y = 0 , y = infinity , x L <= x R . I.e., return element with min y such that x L <= x <= x R . x L x R
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enumerateRectangle(x L ,x R ,y T ) Return all elements in the rectangle defined by the lines, x= x L , x= x R , y = 0 , y = y T , x L <= x R , 0 <= y T . I.e., return all elements such that x L <= x <= x R and 0 <= y <= y T . x L x R y T
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Complexity O(log n) for each operation except for enumerateRectangle, where n is the number of elements in the tree.
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