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1 module Exercise_1 where |
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2 import Test.QuickCheck |
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3 |
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4 {---------------------------------------------------------------------} |
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5 {- G1.1 -} |
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6 threeDifferent :: Integer -> Integer -> Integer -> Bool |
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7 threeDifferent x y z = (x /= y) && (y /= z) && (z /= x) |
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8 |
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9 |
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10 fourEqual :: Integer -> Integer -> Integer -> Integer -> Bool |
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11 fourEqual w x y z = (w == x) && (x == y) && (y == z) |
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12 |
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13 |
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14 {- |
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15 threeDifferent (2+3) 5 (11 ` div ` 2) |
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16 ((2+3) /= 5) && (5 /= (11 ` div ` 2)) && ((11 ` div ` 2) /= (2+3)) |
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17 (5 /= 5) && ((5 /= (11 ` div ` 2)) && ((11 ` div ` 2) /= (2+3))) |
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18 False && ((5 /= (11 ` div ` 2)) && ((11 ` div ` 2) /= (2+3))) |
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19 False |
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20 |
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21 Schritte von oben nach unten: |
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22 threeDifferent ersetzen |
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23 Linke Seite des ersten && |
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24 5 /= 5 auswerten |
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25 False && x = False (&& ist rechtsassoizativ) |
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26 |
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27 |
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28 --- |
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29 |
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30 |
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31 fourEqual (2+3) 5 (11 ` div ` 2) (21 ` mod ` 11) |
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32 ((2+3) == 5) && (5 == (11 ` div ` 2)) && ((11 ` div ` 2) == (21 ` mod ` 11)) |
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33 (5 == 5) && (5 == (11 ` div ` 2)) && ((11 ` div ` 2) == (21 ` mod ` 11)) |
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34 True && (5 == (11 ` div ` 2)) && ((11 ` div ` 2) == (21 ` mod ` 11)) |
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35 (5 == (11 ` div ` 2)) && ((11 ` div ` 2) == (21 ` mod ` 11)) |
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36 (5 == 5) && ((11 ` div ` 2) == (21 ` mod ` 11)) |
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37 True && ((11 ` div ` 2) == (21 ` mod ` 11)) |
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38 ((11 ` div ` 2) == (21 ` mod ` 11)) |
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39 (5 == (21 ` mod ` 11)) |
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40 (5 == 10) |
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41 False |
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42 |
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43 Schritte von oben nach unten: |
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44 fourEqual ersetzen |
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45 Linke Seite des ersten && |
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46 5 == 5 auswerten |
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47 True && x = x |
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48 Linke Seite des zweiten && (div ist Ganzzahldivision) |
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49 5 == 5 auswerten |
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50 True && x = x |
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51 Links nach rechts |
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52 5 == 10 auswerten |
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53 -} |
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54 |
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55 |
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56 |
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57 {---------------------------------------------------------------------} |
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58 {- G1.2 -} |
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59 fac :: Integer -> Integer |
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60 fac 0 = 1 |
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61 fac n | n > 0 = n * fac (n-1) |
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62 |
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63 |
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64 sum_ten :: Integer -> Integer |
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65 sum_ten n = sum_ten' n 9 |
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66 where |
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67 sum_ten' :: Integer -> Integer -> Integer |
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68 sum_ten' n 0 = n |
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69 sum_ten' n x = n + x + sum_ten' n (x-1) |
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70 |
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71 |
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72 sum_ten_gauss :: Integer -> Integer |
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73 sum_ten_gauss n = 10 * n + 45 |
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74 |
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75 |
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76 |
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77 {---------------------------------------------------------------------} |
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78 {- G1.3 -} |
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79 {- |
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80 g ist leicht veraendert, um Mehrdeutigkeiten zu vermeiden. |
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81 Original: |
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82 g :: Integer -> Integer |
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83 g n = if n < 10 then n*n else n |
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84 -} |
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85 |
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86 g :: Integer -> Integer |
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87 g n = if n < 10 then n*n else 2*n |
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88 |
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89 |
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90 max_g :: Integer -> Integer |
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91 max_g n |
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92 | n <= 0 = 0 |
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93 | otherwise = |
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94 if (g x < g n) then n else x |
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95 where |
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96 x = max_g (n-1) |
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97 |
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98 |
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99 max_g' :: Integer -> Integer |
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100 max_g' n |
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101 | n < 0 = 0 |
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102 | n <= 9 = n |
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103 -- Siehe Aenderung von g |
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104 | n < 41 = 9 |
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105 | otherwise = n |
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106 |
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107 |
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108 prop_max_g :: Integer -> Bool |
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109 prop_max_g n = |
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110 max_g n == max_g' n |
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111 |
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112 |
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113 |
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114 {---------------------------------------------------------------------} |
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115 {- Aufgabe H1.1 -} |
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116 {-WETT-} {- Diese Zeile nicht entfernen -} |
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117 sum_max_sq :: Integer -> Integer -> Integer -> Integer |
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118 sum_max_sq x y z = max x y ^ 2 + min x y `max` z ^ 2 |
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119 {-TTEW-} {- Diese Zeile nicht enfernen! -} |
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120 |
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121 |
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122 |
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123 {---------------------------------------------------------------------} |
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124 {- Aufgabe H1.2 -} |
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125 {- Teil 1 -} |
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126 f :: Integer -> Integer |
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127 f n |
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128 | n > 100 = n - 10 |
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129 | otherwise = f (f (n + 11)) |
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130 |
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131 |
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132 {- Teil 2 -} |
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133 {- |
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134 - [(x, f x) | x <- [0,1,2,3,42,101,1001,-10]] |
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135 - |
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136 - ( x, f x) |
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137 - ----------- |
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138 - ( 0, 91) |
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139 - ( 1, 91) |
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140 - ( 2, 91) |
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141 - ( 3, 91) |
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142 - ( 42, 91) |
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143 - ( 101, 91) |
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144 - (1001, 991) |
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145 - ( -10, 91) |
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146 -} |
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147 |
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148 |
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149 {- Teil 3 -} |
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150 f' :: Integer -> Integer |
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151 f' n = if n > 101 then n - 10 else 91 |
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152 |
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153 |
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154 {- Quickcheck test -} |
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155 prop_f n = f n == f' n |
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156 |
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157 |
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158 |
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159 {---------------------------------------------------------------------} |
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160 {- Aufgabe H1.3 -} |
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161 {- Teil 1 -} |
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162 is_square' :: Integer -> Integer -> Bool |
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163 is_square' n 0 = n == 0 |
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164 is_square' n m |
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165 | m < 0 = False |
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166 | otherwise = m * m == n || is_square' n (m-1) |
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167 |
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168 |
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169 {- Teil 2 -} |
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170 is_square :: Integer -> Bool |
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171 is_square n |
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172 | n < 0 = False |
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173 | otherwise = is_square' n n |
