Working Through SICP Exercises

As I work through SICP exercises, I will post them there.

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SICP Exercise 3.56 merge streams

Exercise 3.56.   A famous problem, first raised by  R. Hamming, is to enumerate, in ascending order with no repetitions, all positive integers with no prime factors other than 2, 3, or 5. One obvious way to do this is to simply test each integer in turn to see whether it has any factors other than 2, 3, and 5. But this is very inefficient, since, as the integers get larger, fewer and fewer of them fit the requirement. As an alternative, let us call the required stream of numbers  S  and notice the following facts about it. S  begins with 1. The elements of  (scale-stream S 2)  are also elements of  S . The same is true for  (scale-stream S 3)  and  (scale-stream 5 S) . These are all the elements of  S . Now all we have to do is combine elements from these sources. For this we define a procedure  merge  that combines two ordered streams into one ordered result stream, eliminating repetitions: (define...
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SICP Exercise 4.9 do for while until

Exercise 4.9.    Many languages support a variety of iteration constructs, such as  do ,  for ,  while , and  until . In Scheme, iterative processes can be expressed in terms of ordinary procedure calls, so special iteration constructs provide no essential gain in computational power. On the other hand, such constructs are often convenient. Design some iteration constructs, give examples of their use, and show how to implement them as derived expressions. SOLUTION The code and tests are  here . I have implemented the following expressions: do-while do-until for while The 'do-while' construct can be as follows: (do   (<one or more statements>)   while (condition) ) Use the while block construct to convert it as follows: (begin   <statements>   (while (condition)   <statements>   ) ) The 'do-until' construct can be as follows: (do   (<one or more statements>) ...
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SICP Exercise 2.96 pseudoremainder

Exercise 2.96. a.    Implement the procedure  pseudoremainder-terms , which is just like  remainder-terms  except that it multiplies the dividend by the integerizing factor described above before calling  div-terms . Modify  gcd-terms to use  pseudoremainder-terms , and verify that  greatest-common-divisor  now produces an answer with integer coefficients on the example in exercise  2.95 . b.    The GCD now has integer coefficients, but they are larger than those of  P 1 . Modify  gcd-terms  so that it removes common factors from the coefficients of the answer by dividing all the coefficients by their (integer) greatest common divisor. SOLUTION The code is here: Exercise 2.96 pseudoremainder Both part a and b of the exercise are verified in the tests. The final result is equal to polynomial P1 from exercise 2.95.
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