#12
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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2.3 Methematical Analysis of Nonrecursive Algorithms
1. Lighter or heavier? You have n>2 identical-looking coins and a two-pan
halance scale with no weights. One of the coins is a fake, but you do not know
whether it is lighter or heavier than the genuine coins, which all weigh the
same. Design a e(1) algorithm to determine whether the fake coin is lighter
or heavier than the others.
12 Door in a wall You are facing a wall that stretches infinitely in both direc-
nions There is a door in the wall, but you know neither how far away nor in
which direction. You can see the door only when you are right next to it. De-
sign an algorithm that enables you to reach the door by walking at most 0(n)
steps where n is the (unknown to you) number of steps between your initial
position and the door. [Par95]
2.3 Mathematical Analysis of Nonrecursive Algorithms
In this section, we systematically apply the general framework outlined in Section
21 to analyzing the time efficiency of nonrecursive algorithms. Let us start wit
a very simple example that demonstrates all the principal steps typically taken
analyzing such algorithms.
EXAMDLE](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F26fe8f9d-a829-4ffe-94fa-74d9058056a0%2Fb1420ed2-bc5c-4c6b-9246-5a383961d229%2F5tb02g4_processed.jpeg&w=3840&q=75)
Transcribed Image Text:61
2.3 Methematical Analysis of Nonrecursive Algorithms
1. Lighter or heavier? You have n>2 identical-looking coins and a two-pan
halance scale with no weights. One of the coins is a fake, but you do not know
whether it is lighter or heavier than the genuine coins, which all weigh the
same. Design a e(1) algorithm to determine whether the fake coin is lighter
or heavier than the others.
12 Door in a wall You are facing a wall that stretches infinitely in both direc-
nions There is a door in the wall, but you know neither how far away nor in
which direction. You can see the door only when you are right next to it. De-
sign an algorithm that enables you to reach the door by walking at most 0(n)
steps where n is the (unknown to you) number of steps between your initial
position and the door. [Par95]
2.3 Mathematical Analysis of Nonrecursive Algorithms
In this section, we systematically apply the general framework outlined in Section
21 to analyzing the time efficiency of nonrecursive algorithms. Let us start wit
a very simple example that demonstrates all the principal steps typically taken
analyzing such algorithms.
EXAMDLE
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