euler / clojure / 55.clj

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48``` ```; If we take 47, reverse and add, 47 + 74 = 121, which is palindromic. ; ; Not all numbers produce palindromes so quickly. For example, ; ; 349 + 943 = 1292, ; 1292 + 2921 = 4213 ; 4213 + 3124 = 7337 ; ; That is, 349 took three iterations to arrive at a palindrome. ; ; Although no one has proved it yet, it is thought that some numbers, like 196, ; never produce a palindrome. A number that never forms a palindrome through ; the reverse and add process is called a Lychrel number. Due to the ; theoretical nature of these numbers, and for the purpose of this problem, we ; shall assume that a number is Lychrel until proven otherwise. In addition you ; are given that for every number below ten-thousand, it will either (i) become ; a palindrome in less than fifty iterations, or, (ii) no one, with all the ; computing power that exists, has managed so far to map it to a palindrome. In ; fact, 10677 is the first number to be shown to require over fifty iterations ; before producing a palindrome: 4668731596684224866951378664 (53 iterations, ; 28-digits). ; ; Surprisingly, there are palindromic numbers that are themselves Lychrel ; numbers; the first example is 4994. ; ; How many Lychrel numbers are there below ten-thousand? ; ; Answer: 249 (defn palindrom? [s] (let [size (count s) middle (int (/ size 2)) pre (.substring s 0 middle) i (if (even? size) middle (inc middle))] (= (list* pre) (reverse (.substring s i size))))) (defn strrev [s] (apply str (reverse s))) (defn step [s] (str (+ (bigint s) (bigint (strrev s))))) (defn lychrel? [n] (let [n (step (str n)) ; Don't count the number itself lseq (take-while #(not (palindrom? %)) (iterate step n))] (> (count (take 51 lseq)) 50))) (prn (count (filter lychrel? (range 1 10000)))) ```