[Problem 4] Consider a tree X in which each node has at most 4 descendants, called A node, B node,C node and D node. There are n nodes in such a tree. Each node in tree X holds an integer value k > 1,which we can access with node.value method. Let T(n) denote the time complexity of the followingalgorithm, which takes tree X as its input.H(X.root)if (X.root NIL) thenreturnelseH(X.root. A)H(X.root.B)c = c 3*X.root.valueH(X.root.C)H(X.root.D)// assume c is some global variable, initially set to 0.Determine the asymptotic bound of the time complexity T(n) for the algorithm H and formally prove itscorrectness to receive points.

Introduction Time complexity is a kind of complexity that basically demonstrates the time…

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Database System Concepts

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Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

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Question

[Problem 4] Consider a tree X in which each node has at most 4 descendants, called A node, B node,
C node and D node. There are n nodes in such a tree. Each node in tree X holds an integer value k > 1,
which we can access with node.value method. Let T(n) denote the time complexity of the following
algorithm, which takes tree X as its input.
H(X.root)
if (X.root NIL) then
return
else
H(X.root. A)
H(X.root.B)
c = c 3*X.root.value
H(X.root.C)
H(X.root.D)
// assume c is some global variable, initially set to 0.
Determine the asymptotic bound of the time complexity T(n) for the algorithm H and formally prove its
correctness to receive points.

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