Chapter 05 Daily 3
These exercises are intended to be more challenging, for people who have completed the more straightforward exercises.
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myisqrt :: Int -> Int) Given a nonnegative integer n, produce the largest integer k so that k*k <= n. That is the “integer square root”. Do not use Float, sqrt, or functions like floor. -
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sps :: Int -> [(Int,Int)]) Can a number be expressed as the sum of two perfect squares? For example: $17 = 1^2 + 4^2$. Produce a list of ordered pairs whose squares sum to the given number. -
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rsum : Int -> (Int, Int)). Given an integer $n>1$, find two distinct integers $a$ and $b$ so that $1/a + 1/b = 1/n$. Hint: do some algebra first; stay away from floating point numbers. -
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n10mult :: Int -> [Int] -> Float) Given a number k and then a list of numbers, find the probability that randomly choosing k numbers from the list (with repetition) gives a multiple of 10. Suggestion: compute the probability by checking all possibilities. -
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sameSum :: [Int] -> ([Int],[Int])) Given ten distinct two digit numbers (in the decimal system), produce two disjoint subsets that have the same sum.You should first write a function that works when you give it the ten numbers in a list.
Testing Notes
(sameSum) If you want to test it to see that it works for lots of
numbers, you need a method of producing 10 distinct two digit
numbers. There are about $5.7 \times 10^{12}$ possibilities. By itself
this is a challenge. You can find a random list generator online?