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  1.  
  2. object Main extends App {
  3.   def xx(x:Double):Double = math.pow(x, x)
  4.  
  5.   def trapezoid(f:Double=>Double, a:Double, b:Double):Double = {
  6.     (b-a)*(f(a)+f(b))/2
  7.   }
  8.   def simpson(f:Double=>Double, a:Double, b:Double):Double = {
  9.     (b-a)*(f(a) + 4*f((a+b)/2) + f(b))/6
  10.   }
  11.   def simpson38(f:Double=>Double, a:Double, b:Double):Double = {
  12.     (b-a)*(f(a) + 3*f((2*a+b)/3) + 3*f((a+2*b)/3) + f(b))/8
  13.   }
  14.   def boole(f:Double => Double, a:Double, b:Double):Double = {
  15.     (b-a)*(7*f(a) + 32*f((3*a+b)/4) + 12*f((a+b)/2) + 32*f((a+3*b)/4) + 7*f(b))/90
  16.   }
  17.  
  18.  
  19.   def integrate(f:Double => Double,
  20.     algorithm:(Double=>Double, Double, Double)=>Double,
  21.     a:Double, b:Double, n:Long):Double = {
  22.     (0L until n).foldLeft(0.0)((r,i) => {
  23.       val x0 = a + (b-a)*i/n
  24.       val x1 = a + (b-a)*(i+1)/n
  25.       r + algorithm(f, x0, x1)
  26.     })
  27.   }
  28.  
  29.  
  30.   def diff(method:(Double=>Double, Double, Double)=>Double, n:Int):Double = {
  31.     17128.111274826415512 - integrate(xx, method, 1, 6, n)
  32.   }
  33.  
  34.   def solve(method:(Double=>Double, Double, Double)=>Double,
  35.     eps:Double, n:Int=1):Int = {
  36.     if (diff(method, n).abs>eps){
  37.       solve(method, eps, n+1)
  38.     } else {
  39.       n
  40.     }
  41.   }
  42.  
  43.   println("trapezoid: %d".format(solve(trapezoid, 0.1)))
  44.   println("simpson: %d".format(solve(simpson, 0.1)))
  45.   println("simpson38: %d".format(solve(simpson38, 0.1)))
  46.   println("boole: %d".format(solve(boole, 0.1)))
  47.  
  48. }
  49.  
Success #stdin #stdout 1.89s 382272KB
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Standard input is empty
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trapezoid: 1648
simpson: 40
simpson38: 32
boole: 10
https://ideone.com/hFFSEy
language:
Scala (scala 2.12.8)
created:
9 years ago
visibility:
public

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