In the friends level of abstracting recursion, you can give your friend any legal instance that is smaller than yours according to some measure as long as you solve in your own any instance that is sufficiently small. For which of these algorithms has this been done? If so, what is your measure of the size of the instance? On input instance (n, m), either bound the depth to which the algorithm recurses as a function of n and m, or prove that there is at least one path down the recursion tree that is infinite. algorithm R, (n, m) (pre-cond): n & m ints. (post-cond): Say Hi begin if(n ≤ 0) else end if end algorithm Print("Hi") R₂(n-1,2m) algorithm R, (n, m) (pre-cond): n & m ints. (post-cond): Say Hi begin if(n ≤ 0) else Print("Hi") Rb(n-1, m) R₁(n, m - 1) end if end algorithm

Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
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In the friends level of abstracting recursion,
you can give your friend any legal instance that is smaller than yours according to some
measure as long as you solve in your own any instance that is sufficiently small. For
which of these algorithms has this been done? If so, what is your measure of the size of
the instance? On input instance (n, m), either bound the depth to which the algorithm
recurses as a function of n and m, or prove that there is at least one path down the
recursion tree that is infinite.
algorithm R, (n, m)
(pre-cond): n & mints.
(post-cond): Say Hi
begin
if(n ≤ 0)
else
Print("Hi")
R₂ (n - 1,2m)
end if
end algorithm
algorithm R, (n, m)
(pre-cond): n & m ints.
(post-cond): Say Hi
begin
if(n ≤ 0)
else
Print("Hi")
Rb(n-1, m)
R₂(n, m-1)
end if
end algorithm
Transcribed Image Text:In the friends level of abstracting recursion, you can give your friend any legal instance that is smaller than yours according to some measure as long as you solve in your own any instance that is sufficiently small. For which of these algorithms has this been done? If so, what is your measure of the size of the instance? On input instance (n, m), either bound the depth to which the algorithm recurses as a function of n and m, or prove that there is at least one path down the recursion tree that is infinite. algorithm R, (n, m) (pre-cond): n & mints. (post-cond): Say Hi begin if(n ≤ 0) else Print("Hi") R₂ (n - 1,2m) end if end algorithm algorithm R, (n, m) (pre-cond): n & m ints. (post-cond): Say Hi begin if(n ≤ 0) else Print("Hi") Rb(n-1, m) R₂(n, m-1) end if end algorithm
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