Problem Statement: We assume that the standard input contains a sequence of non-zero integers between - 121 and 121, which ends with 0. This sequence will be given by the user. 1. Write an algorithm, called Decomposition_Powers_Three, which produces the decomposition of each integer using powers of 3, namely 1, 3, 9, 27, and 81, and the + and - operators. Each power of 3 should appear at most once in the decomposition. Examples: 1 = 1 2 = 3 - 1 3 = 3 4 = 3 + 1 7 = 9 - 3 + 1 14 = 27 - 9 - 3 - 1 43 = 81 - 27 - 9 - 3 + 1 121 = 81 + 27 + 9 + 3 + 1 2. Show that the algorithm Decomposition_Powers_Three is correct using an informal proof (i.e., discussion). 3. Give a program corresponding to Decomposition_Powers_Three, using any of your favorite programming languages. Observation: The intervals [-121,-41], [-40,-14], [-13,-5], [-4,-2], [-1,-1], [1,1], [2,4], [5,13], [14,40], and [41,121] play a particular role. Subject: C++ Programming
Problem Statement: We assume that the standard input contains a sequence of non-zero integers
between - 121 and 121, which ends with 0. This sequence will be given by the user.
1. Write an
decomposition of each integer using powers of 3, namely 1, 3, 9, 27, and 81, and the +
and - operators. Each power of 3 should appear at most once in the decomposition.
Examples: 1 = 1
2 = 3 - 1
3 = 3
4 = 3 + 1
7 = 9 - 3 + 1
14 = 27 - 9 - 3 - 1
43 = 81 - 27 - 9 - 3 + 1
121 = 81 + 27 + 9 + 3 + 1
2. Show that the algorithm Decomposition_Powers_Three is correct using an informal proof
(i.e., discussion).
3. Give a program corresponding to Decomposition_Powers_Three, using any of your
favorite
Observation: The intervals [-121,-41], [-40,-14], [-13,-5], [-4,-2], [-1,-1], [1,1], [2,4], [5,13],
[14,40], and [41,121] play a particular role.
Subject: C++ Programming
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