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# Write an algorithm, called Decomposition_Powers_Three, which produces the decomposition of

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.

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