Even a pure functional language like Haskell supports iterative solutions in the form of list comprehension. The code shown here is based on an account by Thomas Hallgren (see ), extended to include factorial. 2. There are quite a few cases where a recursive solution is worse than an iterative one. Iterative solution. These two hand crafted functions are both much slower than the built-in factorial because Base uses some lookup table magics. GCD was defined two ways. factorial 0 acc = acc factorial n acc = factorial (n-1) $! For example, here are three different definitions of the factorial function in the language Haskell: The same kinds of techniques can also be used to encode behaviors more often associated with dependent types and polytypic programming, and are thus a topic of much recent interest in the Haskell community. Base = 0.477305071 Recursive = 517.544341882 Iterative = 491.569636915 So, the recursive factorial function is slightly slower than the iterative function. Haskell can use tail call optimisation to turn a recursion into a loop under the hood. We discussed pattern matching, the Maybe Monad, filter, map and head. Ok great! fix and fixed points []. For the two aforementioned examples that converge, this is readily seen: 3. Write a function which takes in an array and returns the result of adding up every item in the array: In JavaScript: Factorial in Haskell factorial :: Integer -> Integer factorial 0 = 1 ... Iterative computation • An iterative computation is one whose execution stack is bounded by a constant, independent of the length of the computation • Iterative computation starts with an initial state S 0 All solutions were written in Haskell but the algorithms easily translate to other languages. Even if we don’t know what a factorial is, we can understand it by reading this simple code. One way took an iterative approach while the second way, Euclid’s Algorithm, used a simple recursive method. A fixed point of a function f is a value a such that f a == a.For example, 0 is a fixed point of the function (* 3) since 0 * 3 == 0.This is where the name of fix comes from: it finds the least-defined fixed point of a function. An implementation of the factorial function can be either iterative or recursive, but the function itself isn't inherently either. (We'll come to what "least defined" means in a minute.) The last call returns 6, then fac(2, 3) returns 6, and finally the original call returns 6. We discussed the Fibonacci sequence, LCM and GCD. factorial n = fac n 1 Where fac n acc = if n < 2 then acc else fac (n-1) (acc*n) Write a factorial function with declarative style (Haskell): factorial n = product [1..n] factorial 5 -- 120. Haskell uses a lazy evaluation system which allows you define as many terms as you like, safe in the knowledge that the compiler will only allocate the ones you use in an expression. Factorial in iterative and functional style public long factorial(int n) { return LongStream .rangeClosed(1, n) .reduce((a, b) -> a * b) .getAsLong(); } factorial(5) // Output: 120 It’s worth repeating that by abstracting the how part we can write more maintainable and scalable software. Tail Calls Consider the factorial function below: When we make the call fac(3), two recursive calls are made: fac(2, 3) and fac(1, 6). Note that an implementation isn't necessarily either iterative or recursive. ( acc * n ) Note that we have used accumulator with strict evaluation in order to suppress the default laziness of Haskell computations - this code really computes new n and acc on every recursion step. A minute. are both much slower than the iterative function ’ s Algorithm used... n ] factorial 5 -- 120 but the algorithms easily translate other! In Haskell but the algorithms easily translate to other languages can use tail optimisation! 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