26 if (a > b) 0 else powerOfTwo(a) + sumPowersOfTwo(a + 1, b) |
26 if (a > b) 0 else powerOfTwo(a) + sumPowersOfTwo(a + 1, b) |
27 |
27 |
28 sumPowersOfTwo(2, 4) |
28 sumPowersOfTwo(2, 4) |
29 */ |
29 */ |
30 |
30 |
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31 /* |
31 def sum(f: Int => Int, a: Int, b: Int): Int = |
32 def sum(f: Int => Int, a: Int, b: Int): Int = |
32 if (a > b) 0 else f(a) + sum(f, a + 1, b) //> sum: (f: Int => Int, a: Int, b: Int)Int |
33 if (a > b) 0 else f(a) + sum(f, a + 1, b) |
33 |
34 |
34 //def sumInts(a: Int, b: Int): Int = sum(id, a, b) |
35 //def sumInts(a: Int, b: Int): Int = sum(id, a, b) |
35 //def sumInts(a: Int, b: Int): Int = sum((x: Int) => x, a, b) |
36 //def sumInts(a: Int, b: Int): Int = sum((x: Int) => x, a, b) |
36 def sumInts(a: Int, b: Int): Int = sum(x => x, a, b) |
37 def sumInts(a: Int, b: Int): Int = sum(x => x, a, b) |
37 //> sumInts: (a: Int, b: Int)Int |
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38 //def sumSquares(a: Int, b: Int): Int = sum(square, a, b) |
38 //def sumSquares(a: Int, b: Int): Int = sum(square, a, b) |
39 //def sumSquares(a: Int, b: Int): Int = sum((x: Int) => x * x, a, b) |
39 //def sumSquares(a: Int, b: Int): Int = sum((x: Int) => x * x, a, b) |
40 def sumSquares(a: Int, b: Int): Int = sum(x => x * x, a, b) |
40 def sumSquares(a: Int, b: Int): Int = sum(x => x * x, a, b) |
41 //> sumSquares: (a: Int, b: Int)Int |
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42 def sumPowersOfTwo(a: Int, b: Int): Int = sum(powerOfTwo, a, b) |
41 def sumPowersOfTwo(a: Int, b: Int): Int = sum(powerOfTwo, a, b) |
43 //> sumPowersOfTwo: (a: Int, b: Int)Int |
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44 |
42 |
45 def id(x: Int): Int = x //> id: (x: Int)Int |
43 def id(x: Int): Int = x |
46 def square(x: Int): Int = x * x //> square: (x: Int)Int |
44 def square(x: Int): Int = x * x |
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45 */ |
47 def powerOfTwo(x: Int): Int = if (x == 0) 1 else 2 * powerOfTwo(x - 1) |
46 def powerOfTwo(x: Int): Int = if (x == 0) 1 else 2 * powerOfTwo(x - 1) |
48 //> powerOfTwo: (x: Int)Int |
47 //> powerOfTwo: (x: Int)Int |
49 |
48 |
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49 |
50 // 5.2: Currying |
50 // 5.2: Currying |
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51 |
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52 def sum(f: Int => Int): (Int, Int) => Int = { |
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53 def sumF(a: Int, b: Int): Int = |
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54 if (a > b) 0 else f(a) + sumF(a + 1, b) |
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55 sumF |
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56 } //> sum: (f: Int => Int)(Int, Int) => Int |
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57 |
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58 def sumInts = sum(x => x) //> sumInts: => (Int, Int) => Int |
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59 def sumSquares = sum(x => x * x) //> sumSquares: => (Int, Int) => Int |
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60 def sumPowersOfTwo = sum(powerOfTwo) //> sumPowersOfTwo: => (Int, Int) => Int |
51 |
61 |
52 |
62 sumSquares(1,10) + sumPowersOfTwo(10,20) //> res0: Int = 2096513 |
53 |
63 sum(x => x * x)(2,4) //> res1: Int = 29 |
54 |
64 |
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65 // 5.3: Finding Fixed Points of Functions |
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66 |
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67 val tolerance = 0.001 //> tolerance : Double = 0.001 |
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68 def isCloseEnough(x: Double, y: Double) = Math.abs((x-y) / x) < tolerance |
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69 //> isCloseEnough: (x: Double, y: Double)Boolean |
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70 def fixedPoint(f: Double => Double)(firstGuess: Double) = { |
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71 def iterate(guess: Double): Double = { |
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72 val next = f(guess) |
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73 if (isCloseEnough(guess, next)) next |
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74 else iterate(next) |
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75 } |
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76 iterate(firstGuess) |
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77 } //> fixedPoint: (f: Double => Double)(firstGuess: Double)Double |
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55 } |
106 } |