4. (15 points) Give an algorithm that takes as input a positive integer n and a number x, and computes xn (i. e., x raised to the power n) by performing O(lgn) multiplications. Your algorithm CANNOT use the exponentiation operation, and may use only the basic arithmetic operations (addition, subtraction, multiplication, division, modulo). Moreover, the total number of basic arithmetic operations used should be O(lgn).

there is no universally accepted definition of art. although commonly used to describe something of beauty, or a skill which produces an aesthetic result, there is no clear line in principle between (say) a unique piece of handmade sculpture, and a mass-produced but visually attractive item. we might say that art requires thought - some kind of creative impulse - but this raises more questions: for example, how much thought is required? if someone flings paint at a canvas, hoping by this action to create a work of art, does the result automatically constitute art?

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