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Title: tree data structure
Description: it is a complete reference of the tree data structure. It presents a comprehensive look at the ideas, analysis, and implementation details of data structures as a specialized topic in applied algorithms. This book examines efficient ways to realize query and update operations on sets of numbers, intervals, or strings by various data structures, including search trees, structures for sets of intervals or piecewise constant functions, orthogonal range search structures, heaps, union-find structures, dynamization and persistence of structures, structures for strings, and hash tables. Instead of relegating data structures to trivial material used to illustrate object-oriented programming methodology, this is the first volume to show data structures as a crucial algorithmic topic. Numerous code examples in C and more than 500 references
Description: it is a complete reference of the tree data structure. It presents a comprehensive look at the ideas, analysis, and implementation details of data structures as a specialized topic in applied algorithms. This book examines efficient ways to realize query and update operations on sets of numbers, intervals, or strings by various data structures, including search trees, structures for sets of intervals or piecewise constant functions, orthogonal range search structures, heaps, union-find structures, dynamization and persistence of structures, structures for strings, and hash tables. Instead of relegating data structures to trivial material used to illustrate object-oriented programming methodology, this is the first volume to show data structures as a crucial algorithmic topic. Numerous code examples in C and more than 500 references
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Tree Definitions
&
Types of Trees
© Gunnar Gotshalks
TreeFundamentals–1
On Pointers
© Gunnar Gotshalks
TreeFundamentals–2
On Pointers – 2
© Gunnar Gotshalks
TreeFundamentals–3
On Pointers – 3
© Gunnar Gotshalks
TreeFundamentals–4
Trees
© Gunnar Gotshalks
TreeFundamentals–5
Terminology
© Gunnar Gotshalks
TreeFundamentals–6
Terminology – 2
© Gunnar Gotshalks
TreeFundamentals–7
Terminology – 3
• Root – node with no parent
• Leaf – node with no children – also called external (all
other nodes are internal)
© Gunnar Gotshalks
TreeFundamentals–8
Tree Definition
© Gunnar Gotshalks
TreeFundamentals–9
Terminology – 4
© Gunnar Gotshalks
TreeFundamentals–10
Terminology – 5
• Node level & node depth – the path length from the root
> The root is level 0 and depth 0
> Other nodes depth is 1 + depth of parent
© Gunnar Gotshalks
TreeFundamentals–11
Terminology – 6
• Height of a tree – The longest path length from the root to
a leaf
...
»
Pointers are indices to the array (addresses relative to
the start of the array scaled by the size of a pointer)
»
Use arithmetic to compute where the children are
• Binary trees are a special case
»
Heaps are usully implemented using arrays to represent
a complete binary tree
© Gunnar Gotshalks
TreeFundamentals–24
Array Representation – 2
• Mapping between a complete binary tree and an array
© Gunnar Gotshalks
TreeFundamentals–25
Array Representation – 3
• In general for an N’ary tree the following set of
relationships holds – the root must have index 0
child_1 = N * parent + 1
child_2 = N * parent + 2
child_3 = N * parent + 3
•••
child_N = N * parent + N
Nodes are numbered
in breadth traversal
order
• The binary case is an exception where the root can be
index 1 because 2*1 = 2, the index adjacent to the root
»
This gives the pair 2 * parent & 2 * parent + 1, which is
less arithmetic than the above, and the inverse to find
the parent is easier to compute
...
© Gunnar Gotshalks
TreeFundamentals–27
An Example
© Gunnar Gotshalks
TreeFundamentals–28
Title: tree data structure
Description: it is a complete reference of the tree data structure. It presents a comprehensive look at the ideas, analysis, and implementation details of data structures as a specialized topic in applied algorithms. This book examines efficient ways to realize query and update operations on sets of numbers, intervals, or strings by various data structures, including search trees, structures for sets of intervals or piecewise constant functions, orthogonal range search structures, heaps, union-find structures, dynamization and persistence of structures, structures for strings, and hash tables. Instead of relegating data structures to trivial material used to illustrate object-oriented programming methodology, this is the first volume to show data structures as a crucial algorithmic topic. Numerous code examples in C and more than 500 references
Description: it is a complete reference of the tree data structure. It presents a comprehensive look at the ideas, analysis, and implementation details of data structures as a specialized topic in applied algorithms. This book examines efficient ways to realize query and update operations on sets of numbers, intervals, or strings by various data structures, including search trees, structures for sets of intervals or piecewise constant functions, orthogonal range search structures, heaps, union-find structures, dynamization and persistence of structures, structures for strings, and hash tables. Instead of relegating data structures to trivial material used to illustrate object-oriented programming methodology, this is the first volume to show data structures as a crucial algorithmic topic. Numerous code examples in C and more than 500 references