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1
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2 (ns clojureDemo.project-euler
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3
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4 (:refer-clojure :exclude [+ - / *
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5 assoc conj dissoc empty get into seq
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6 = < > <= >= zero?
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7 ])
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8
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9 (:use [clojure.contrib.generic
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10 arithmetic
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11 collection
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12 comparison
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13 ])
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14
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15 (:use [clojure.contrib
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16 combinatorics
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17 repl-utils
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18 def
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19 duck-streams
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20 shell-out
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21 import-static
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22 lazy-seqs
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23 logging
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24 map-utils
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25 math
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26 mock
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27 monads
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28 ns-utils
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29 seq-utils
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30 function-utils
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31 profile
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32 str-utils
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33 ])
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34
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35 (:use [clojure.contrib.pprint :exclude [write]])
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36
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37 (:use [clojure.contrib.pprint.examples
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38 hexdump
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39 json
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40 multiply
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41 props
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42 show-doc
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43 xml
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44 ])
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45
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46 (:import java.io.File)
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47 (:import [java.util Calendar Date])
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48
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49 )
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50
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51
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52
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53
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54
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55 (defn range-sum
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56 "calculates the sum of a range. Takes the exact same arguments
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57 as clojure.core/range equilivent to (reduce + (range start end step)), but O(1)."
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58 ([end]
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59 (/ (* end (- end 1) ) 2))
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60
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61 ([start end]
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62 (- (range-sum end) (range-sum start)))
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63
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64 ([start end step]
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65 (letfn [(zero-sum [end step] (* step (range-sum 0 (ceil (/ end step)))))]
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66 (+ (zero-sum (- end start) step) (* start (int (/ (- end start) step)))))))
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67
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68
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69
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70 (defn range-sum-squares
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71 "equivalent to (reduce + (map #(expt % 2) (range start end step))),
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72 but runs in O(1) time."
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73 ([end]
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74 (let [n (- end 1)]
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75 (- (* (expt n 3) 1/3) ;continous volume
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76 (+ (* -1/6 n) (* -1/2 (expt n 2)))))) ;discrete correction
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77
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78 ([start end]
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79 (- (range-sum-squares end) (range-sum-squares start)))
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80
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81 ([start end step]
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82 ;; (letfn [(zero-sum-squares [end step]
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83 ;; (* step step (range-sum-squares 0 (ceil (/ end step)))))]
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84 ;; (+
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85 ;; (* 2 step (range-sum (ceil (/ (- end start) step))))
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86 ;; (zero-sum end step)
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87 ;; (* start start (int (/ (- end start) step)))))))
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88 ))
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89
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90
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91 (defn prime-factors
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92 "all the prime factors of the number n"
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93 [n]
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94 (filter #(= 0 (rem n %)) (for [p primes :while (<= p n)] p)))
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95
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96 (defn factor? [a b] (= 0 (rem a b)))
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97
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98 (defn factor-map [a b]
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99 (if (factor? a b)
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100 {b (quot a b)}
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101 nil))
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102
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103
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104 (defn divides? [numerator divisor] (= (rem numerator divisor) 0))
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105
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106
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107 (def != (comp not =))
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108
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109
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110 (defn decompose [number factor]
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111 (loop [n number counter 0]
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112 (if (!= (rem n factor) 0)
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113 counter
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114 (recur (/ n factor) (inc counter)))))
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115
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116
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117
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118
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119
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120
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121
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122 (defn single-factor [{num :current-num index :prime-index factors :prime-factors :as old-state}]
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123 (let [divisor (nth primes index)
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124 new-index (inc index)
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125 done? (= num 1)]
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126 (if (divides? num divisor)
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127 (let [new-num (/ num (expt divisor (decompose num divisor)))
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128 factors (assoc factors divisor (decompose num divisor))]
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129 [[factors done?] (assoc old-state
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130 :current-num new-num :prime-index new-index :prime-factors factors)])
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131
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132 [[factors done?] (assoc old-state
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133 :current-num num :prime-index new-index :prime-factors factors)])))
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134
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135
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136 (defn wtf "a is not used" [a] (domonad state-m [part single-factor] part))
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137
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138 (defn fuck-it []
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139 (domonad state-m
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140 [[factors done?]
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141 (state-m-until second wtf nil)]
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142
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143 factors))
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144
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145 (defn prime-factor-map [num]
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146
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147 (first ((fuck-it) {:prime-factors {}
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148 :prime-index 0
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149 :current-num num})))
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150
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151 (defn prime-factors-monad [num]
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152 (sort (keys (prime-factor-map num))))
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153
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154
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155
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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 ;; fun with state monad
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161 ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
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162
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163
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164 (defn ++ [{num :num :as world}]
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165 (let [num++ (inc num)]
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166 [num++ (assoc world :num num++)]))
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167
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168 (defn huh? []
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169 (with-monad state-m
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170 (domonad [x ++
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171 y ++]
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172 y)))
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173
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174
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175 (comment
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176
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177 huh?
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178 ->
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179 ((let [m-bind (fn m-bind-state [mv f]
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180 (fn [s]
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181 (let [[v ss] (mv s)]
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182 ((f v) ss))))]
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183 (m-bind
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184 ++ (fn [x] ++))) {:num 1})
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185
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186
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187 )
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188
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189
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190 (defn wordify [n] (cl-format nil "~R" n))
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191
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192 (defn british-letter-count-prof [n]
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193 (prof :total
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194 (let [and? (prof :rem-test (if (and (> n 99) (!= 0 (rem n 100))) 3 0))
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195 word (prof :wordify (wordify n))
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196 word-seq (prof :sequence (seq word))
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197 word-filter (prof :filter (filter #(Character/isLetter %) word-seq))
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198 word-count (prof :count (count word-filter))
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199 answer (prof :add (+ and? word-count))]
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200 answer)))
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201
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202 (defn british-letter-count-prof2
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203 "now this is faster, because it uses string manipulation. go profiling!"
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204 [n]
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205 (prof :total
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206 (let [and? (prof :rem-test (if (and (> n 99) (!= 0 (rem n 100))) 3 0))
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207 word (prof :wordify (wordify n))
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208 word-regex (prof :regex (re-gsub #"[\W-,]" "" word))
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209
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210 word-count (prof :count (.length word-regex))
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211 answer (prof :add (+ and? word-count))]
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212 answer)))
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213
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214
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215
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216
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217
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218
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219
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220
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221
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222
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223
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224
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225
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226
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227
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228
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229
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230
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231
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232 ;pseudo code for primes
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233
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234 ;fn prime-decomposition
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235 ; [n]
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236 ; map = {}
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237 ;
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238 ; for x in primes
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239 ; add to map (divide teh fick out n x)
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240 ; n = n / prime-factors
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241 ; if n == 1 BREAK;
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242 ;
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243 ;
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244
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245
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246
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247 (defn rng [seed]
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248 (let [m 259200
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249 value (/ (float seed) (float m))
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250 next (rem (+ 54773 (* 7141 seed)) m)]
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251 [value next]))
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252
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253
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254 (defn yeah! []
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255 (let [name sequence-m
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256 m-bind (:m-bind name)
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257 m-result (:m-result name)
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258 m-zero (:m-zero name)
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259 m-plus (:m-plus name)]
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260
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261
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262 (m-bind (range 5) (fn [a] (m-bind [2 3] (fn [b] (m-result (+ a b))))))))
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263
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264
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265 (defn ohhhh!! []
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266
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267 (let
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268 [name state-m
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269 m-bind (:m-bind name)
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270 m-result (:m-result name) ]
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271
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272 (m-bind rng (fn [x1] (m-bind rng (fn [x2] (m-result (+ x1 x2))))))))
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273
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274
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275
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276 (defmulti palindrome? class)
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277
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278 (defmethod palindrome? (class "string") [a]
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279 (= (seq a) (reverse a)))
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280
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281 (defmethod palindrome? (class 500) [a]
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282 (palindrome? (str a)))
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283
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284
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285
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286
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287
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288
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289
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290
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291 (defn circulars
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292 "returns a vector of all the circular permutations of a number"
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293 [n]
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294 (map #(Integer. (apply str %)) (rotations (seq (str n)))))
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295
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296
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297 (defn prime-factors
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298 [n]
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299 (for [a primes :while (<= a n) :when (= (rem n a) 0)] a))
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300
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301
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302 (defmethod = [nil java.lang.Integer] [ a b ]
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303 false)
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304
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305
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306
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307 (def mil 1000000)
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308 (def bil 1000000000)
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309
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310 (defn primes-under-million [] (apply hash-set (take 78498 primes)))
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311 (def primes-under-million (memoize primes-under-million))
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312
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313
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314 (defn primes-under-billion [] (apply hash-set (take 664579 primes)))
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315 (def primes-under-billion (memoize primes-under-billion))
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316
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317
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318
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319
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320
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321 (defn prime? [n] (not (nil? (get (primes-under-billion) n))))
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322
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323
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324 (defn circular-memoize
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325 "assumes that f is a predicate that takes in a number for which,
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326 if the predicate is true for the number, it is also true for all
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327 of the circular permutations of the number. Memoizes the result
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328 for all circular permutations so as to avoid subsequent computation."
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329 [f]
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330 (let [mem (atom {})]
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331 (fn [n]
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332 (if-let [e (find @mem n)]
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333 (val e)
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334 (let [ret (f n)]
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335 (dorun (for [circ (circulars n)]
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336 (swap! mem assoc n ret)))
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337 ret)))))
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338
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339 (defn circularly-prime?
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340 [n]
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341 (not (some (comp not prime?) (circulars n))))
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342
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343 (def circularly-prime? (memoize circularly-prime?))
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344
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345
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346 (defmethod = :default [& args]
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347 (apply clojure.core/= args))
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348
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349 (def logins
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350 (map str
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351 [319 680 180 690 129 620 762 689 762 318
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352 368 710 720 710 629 168 160 689 716 731
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353 736 729 316 729 729 710 769 290 719 680
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354 318 389 162 289 162 718 729 319 790 680
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355 890 362 319 760 316 729 380 319 728 716]))
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356
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357 (defn remove-multiples [n]
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358 (reduce (fn [a b] (if (= (last a) b) a (conj a b))) [] n))
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359
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360 (defn insert [item n vect]
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361 (let [split (split-at n vect)]
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362 (apply vector (flatten [(first split) item (last split)]))))
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363
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364 (defn expand-code [old-code [c b a]]
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365 (let [main-length (count old-code)]
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366 (for [x (range (inc main-length)) y (range (inc x)) z (range (inc y))]
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367 (insert c z (insert b y (insert a x old-code))))))
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368
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369 (defn domain-expand-contract [old-domain constraint]
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370 (let [new-domain
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371 (map remove-multiples
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372 (remove-multiples
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373 (sort
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374 (apply concat
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375 (map #(expand-code % constraint) old-domain)))))
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376 min-code-length (apply min (map count new-domain)) ]
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377 (map #(apply str %) (filter #(= (count %) min-code-length) new-domain))))
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378 (def domain-expand-contract (memoize domain-expand-contract))
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379
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380
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381
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382 (defn lazy-fibo
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383 ([] (concat [0 1] (lazy-fibo 0 1)))
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384 ([a b] (let [n (+ a b)] (lazy-seq (cons n (lazy-fibo b n))))))
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385
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386
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387 (defn collatz-seq [n]
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388 (lazy-seq
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389 (cond (= n 1) [1]
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390 (even? n) (lazy-seq (cons n (collatz-seq (/ n 2))))
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391 (odd? n) (lazy-seq (cons n (collatz-seq (+ 1 (* 3 n))))))))
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392 (def collatz-seq (memoize collatz-seq))
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393
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394
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395
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396 (defn pythagorean-triple? [a b c]
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397 (let [[a b c] (sort [a b c])]
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398 (= (+ (* a a) (* b b) ) (* c c))))
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399
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400
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401 (defn sum-squares [coll]
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402 (reduce + (map #(* % %) coll)))
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403
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404
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405 (defn british-letter-count [n]
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406
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407 (let [and? (if (and (> n 99) (!= 0 (rem n 100))) 3 0)]
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408
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409 (+ and? (count (filter #(Character/isLetter %) (seq (wordify n)))))))
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410
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411
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412
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413 (defmacro apply-macro
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414 "This is evil. Don't ever use it. It makes a macro behave like a
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415 function. Seriously, how messed up is that?
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416
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417 Evaluates all args, then uses them as arguments to the macro as with
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418 apply.
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419
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420 (def things [true true false])
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421 (apply-macro and things)
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422 ;; Expands to: (and true true false)"
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423 [macro & args]
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424 (cons macro (flatten (map eval args))))
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425
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426 (defn fun1 [] (Thread/sleep 5000) 5)
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427
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428 (defn fun2 [] (Thread/sleep 30000) 5)
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429
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430
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431 (def naturals (iterate inc 0))
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432
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433
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434
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435
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436 (defn race []
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437 (let [result (ref nil)
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438 threads [(Thread. (fn [] (try
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439 (let [answer (fun1)]
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440 (dosync (ref-set result answer)))
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441 (catch Exception _ nil))))
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442 (Thread. (fn [] (try
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443 (let [answer (fun2)]
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444 (dosync (ref-set result answer)))
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445 (catch Exception _ nil))))]]
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446
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447 (dorun (map #(.start %) threads))
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448 (loop []
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449 (if (!= (deref result) nil)
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450 (do (dorun (map #(.stop %) threads))
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451 (deref result))
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452 (recur)))))
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453
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454
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455
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456
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457
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458
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459
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460 (defn make-date [year month day] (do (let [date (Calendar/getInstance)] (.set date year month day 0 0) date)))
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461
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462 (def jan-1-1901 (make-date 1900 0 1))
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463
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464 (defn sunday? [#^java.util.Calendar date] (= 7 (.getDay (.getTime date))))
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465
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466
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467
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468
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469
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470
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471 (comment
|
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472
|
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473 ;; ----------------------------------------------------------------------
|
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474 ;; Answers
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rlm@1
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475 ;; ----------------------------------------------------------------------
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476
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rlm@1
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477 ; Problem 1
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478 (+ (range-sum 0 1001 3) (range-sum 0 1001 5) (* -1 (range-sum 0 1001 15)))
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479
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rlm@1
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480 ; Problem 2
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481 (reduce + (for [a (filter even? (fibs)) :while (<= a 4000000 )] a))
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482
|
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rlm@1
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483 ; Problem 3
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484 (apply max (prime-factors 600851475143))
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485
|
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rlm@1
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486 ; Problem 4
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487 (reduce max (for [a (range 100 1000) b (range 100 1000) :when (palindrome? (* a b))] (* a b)))
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488
|
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rlm@1
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489 ; Problem 5
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490 (reduce lcm (range 1 21))
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491
|
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rlm@1
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492 ; Problem 6
|
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rlm@1
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493 (- (expt (range-sum 101) 2) (range-sum-squares 101))
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494
|
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rlm@1
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495 ; Problem 7
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496 (nth primes 10000)
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497
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498
|
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rlm@1
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499 ; Problem 9
|
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500 (reduce * (first (for [a (range 1 1000) b (range 1 a) c [(sqrt (sum-squares [a b]))]
|
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501 :when (= (+ a b c) 1000)] [a b c])))
|
|
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502
|
|
rlm@1
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503 ; Problem 10
|
|
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504 (reduce + (for [a primes :while (< a 2000000)] a))
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505
|
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506
|
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507
|
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508
|
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509
|
|
rlm@1
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510 ; Problem 14
|
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511 (first (reduce (fn [a b] (if (> (count a) (count b)) a b)) [] (map collatz-seq (range 1 mil))))
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512
|
|
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513
|
|
rlm@1
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514 ; Problem 16
|
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515 (reduce + (map #(Character/getNumericValue %) (seq (str (expt 2 1000)))))
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516
|
|
rlm@1
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517 ; Problem 17
|
|
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518 (reduce + (map british-letter-count (range 1 1001)))
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519
|
|
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520
|
|
rlm@1
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521 ; Problem 24
|
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522 (nth (lex-permutations [ 0 1 2 3 4 5 6 7 8 9]) (- mil 1))
|
|
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523
|
|
rlm@1
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524 ; Problem 33
|
|
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525 (reduce * (for [num (range 1 10)
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|
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526 den (range 1 10)
|
|
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|
527 weird (range 1 10)
|
|
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|
528 top [(+ num (* 10 weird))]
|
|
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|
529 bottom [(+ weird (* 10 den))]
|
|
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|
530 :when (and (> (/ top bottom) 1) (= (/ top bottom) (/ num den)))]
|
|
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|
531 (/ bottom top)))
|
|
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|
532
|
|
rlm@1
|
533 ; Problem 35
|
|
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|
534 (count (filter circularly-prime? (primes-under-million)))
|
|
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|
535
|
|
rlm@1
|
536 ; Problem 40
|
|
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|
537 (let [fff (apply str (take 1030000 naturals))]
|
|
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|
538 (reduce * (map #(Character/getNumericValue (nth fff %))
|
|
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539 (map (fn [x] (expt 10 x)) (range 7)) )))
|
|
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|
540
|
|
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|
541
|
|
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|
542
|
|
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|
543
|
|
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|
544
|
|
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|
545
|
|
rlm@1
|
546 ; Problem 79
|
|
rlm@1
|
547 (reduce domain-expand-contract [""] logins)
|
|
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|
548
|
|
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|
549 )
|
|
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|
550
|
|
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551
|
|
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|
552
|
|
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553
|
|
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|
554
|
|
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|
555
|
|
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|
556
|
|
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|
557
|
|
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|
558
|
|
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|
559
|
