Graphs: Shortest Paths and Minimum Spanning Trees
... • Inserting edge e into T will create a cycle • There must be an edge on this cycle which is not in K (why??). Call this edge e’ • e’ must be in T - S, so (by our lemma) w(e’) >= w(e) • We could form a new spanning tree T’ by swapping e for e’ in T (prove this is a spanning tree). • w(T’) is clearly ...
... • Inserting edge e into T will create a cycle • There must be an edge on this cycle which is not in K (why??). Call this edge e’ • e’ must be in T - S, so (by our lemma) w(e’) >= w(e) • We could form a new spanning tree T’ by swapping e for e’ in T (prove this is a spanning tree). • w(T’) is clearly ...
Powerpoint - MHS Comp Sci
... The left and right children of the i-th node, if they are present, have the numbers 2i and 2i+1 and its parent has the number i/2 (truncated to an integer) ...
... The left and right children of the i-th node, if they are present, have the numbers 2i and 2i+1 and its parent has the number i/2 (truncated to an integer) ...
advanced algorithms
... point. When the actual insertion is done, no further corrections are needed, so no need to traverse back up the tree. So, T-Down insertion can be done iteratively which is generally faster. Insertion is always done as a leaf (as in ordinary BST insertion). ...
... point. When the actual insertion is done, no further corrections are needed, so no need to traverse back up the tree. So, T-Down insertion can be done iteratively which is generally faster. Insertion is always done as a leaf (as in ordinary BST insertion). ...
Implementing algebraically specified abstract data types in an
... In this section we define the storage relations of an ADT. A storage relation describes the way in which primitive sorted terms, the "data", are removed and selected from a term of the derived sort, the "data structure". The relation incorporates some implementation decisions because, in general, th ...
... In this section we define the storage relations of an ADT. A storage relation describes the way in which primitive sorted terms, the "data", are removed and selected from a term of the derived sort, the "data structure". The relation incorporates some implementation decisions because, in general, th ...
Data Structures: Lists
... requires: list L is not empty. input: none results: the current element is removed from the list. If the resulting list is empty current is set to NULL. If successor of the deleted element exists it is made the new current element otherwise first element is made the new current element. output: none ...
... requires: list L is not empty. input: none results: the current element is removed from the list. If the resulting list is empty current is set to NULL. If successor of the deleted element exists it is made the new current element otherwise first element is made the new current element. output: none ...
R-Trees
... Use the transformation technique Z-ordering and quadtrees New methods: Spatial Access Methods SAMs ...
... Use the transformation technique Z-ordering and quadtrees New methods: Spatial Access Methods SAMs ...
Dynamic Ham-Sandwich Cuts in the Plane
... there is one convex point set (or equivalently, one convex polygon) of each color, so k = 2. Another case of interest is when P1 , P2 , . . . , Pk form nested convex point sets. In this case, we obtain the convex-hull peeling layers or onion peeling [Bar76, Edd82] of the points P1 ∪ P2 ∪ · · · Pk . ...
... there is one convex point set (or equivalently, one convex polygon) of each color, so k = 2. Another case of interest is when P1 , P2 , . . . , Pk form nested convex point sets. In this case, we obtain the convex-hull peeling layers or onion peeling [Bar76, Edd82] of the points P1 ∪ P2 ∪ · · · Pk . ...
Multidimensional Access Methods
... spatial access methods (SAMs). Point access methods have primarily been designed to perform spatial searches on point databases (i.e., databases that store only points). The points may be embedded in two or more dimensions, but they do not have a spatial extension. Spatial access methods, however, c ...
... spatial access methods (SAMs). Point access methods have primarily been designed to perform spatial searches on point databases (i.e., databases that store only points). The points may be embedded in two or more dimensions, but they do not have a spatial extension. Spatial access methods, however, c ...
Linked List
... Look at the else part of the second if statement. This is where the www.hndit.com function will perform its action since the list is not empty, and the first node does not contain the value 7.9. Just like insertNode, this function uses nodePtr and previousNode to traverse the list. The while loop t ...
... Look at the else part of the second if statement. This is where the www.hndit.com function will perform its action since the list is not empty, and the first node does not contain the value 7.9. Just like insertNode, this function uses nodePtr and previousNode to traverse the list. The while loop t ...
Quadtree
A quadtree is a tree data structure in which each internal node has exactly four children. Quadtrees are most often used to partition a two-dimensional space by recursively subdividing it into four quadrants or regions. The regions may be square or rectangular, or may have arbitrary shapes. This data structure was named a quadtree by Raphael Finkel and J.L. Bentley in 1974. A similar partitioning is also known as a Q-tree. All forms of quadtrees share some common features: They decompose space into adaptable cells Each cell (or bucket) has a maximum capacity. When maximum capacity is reached, the bucket splits The tree directory follows the spatial decomposition of the quadtree.