I am trying to calculate the 500th Fibonacci number in Clojure:
(defn fib-pair [[a b]] [b (+ a b)])
(nth (map first (iterate fib-pair [1 1])) 500)
ArithmeticException integer overflow clojure.lang.Numbers.throwIntOverflow (Numbers.java:1388)
This program failed because the number is too big: integer overflow. How to solve this problem?
The default integer type in Clojure is long. If you want to specify that an integer literal should be considered a clojure.lang.BigInt just add an N right after the number.
(defn fib-pair [[a b]] [b (+ a b)])
(nth (map first (iterate fib-pair [1N 1N])) 500)
;= 225591516161936330872512695036072072046011324913758190588638866418474627738686883405015987052796968498626N
You can actually get away with just specifying only one of the two initial values as a BigInt since:
(+ 1N 1)
;= 2N
(type (+ 1N 1))
;= clojure.lang.BigInt
You can use clojure.core/+' instead of clojure.core/+ in fib-pair
This will auto promote longs when needed.
(defn fib-pair [[a b]] [b (+' a b)])
You could also use type hints.
(defn fib-pair ^BigInteger [[^BigInteger a ^BigInteger b]] [b (+' a b)])
(nth (map first (iterate fib-pair [1 1])) 500)
See for more info
http://dev.clojure.org/display/doc/Documentation+for+1.3+Numerics
Related
When doing
(map f [0 1 2] [:0 :1])
f will get called twice, with the arguments being
0 :0
1 :1
Is there a simple yet efficient way, i.e. without producing more intermediate sequences etc., to make f get called for every value of the first collection, with the following arguments?
0 :0
1 :1
2 nil
Edit Addressing question by #fl00r in the comments.
The actual use case that triggered this question needed map to always work exactly (count first-coll) times, regardless if the second (or third, or ...) collection was longer.
It's a bit late in the game now and somewhat unfair after having accepted an answer, but if a good answer gets added that only does what I specifically asked for - mapping (count first-coll) times - I would accept that.
You could do:
(map f [0 1 2] (concat [:0 :1] (repeat nil)))
Basically, pad the second coll with an infinite sequence of nils. map stops when it reaches the end of the first collection.
An (eager) loop/recur form that walks to end of longest:
(loop [c1 [0 1 2] c2 [:0 :1] o []]
(if (or (seq c1) (seq c2))
(recur (rest c1) (rest c2) (conj o (f (first c1) (first c2))))
o))
Or you could write a lazy version of map that did something similar.
A general lazy version, as suggested by Alex Miller's answer, is
(defn map-all [f & colls]
(lazy-seq
(when-not (not-any? seq colls)
(cons
(apply f (map first colls))
(apply map-all f (map rest colls))))))
For example,
(map-all vector [0 1 2] [:0 :1])
;([0 :0] [1 :1] [2 nil])
You would probably want to specialise map-all for one and two collections.
just for fun
this could easily be done with common lisp's do macro. We could implement it in clojure and do this (and much more fun things) with it:
(defmacro cl-do [clauses [end-check result] & body]
(let [clauses (map #(if (coll? %) % (list %)) clauses)
bindings (mapcat (juxt first second) clauses)
nexts (map #(nth % 2 (first %)) clauses)]
`(loop [~#bindings]
(if ~end-check
~result
(do
~#body
(recur ~#nexts))))))
and then just use it for mapping (notice it can operate on more than 2 colls):
(defn map-all [f & colls]
(cl-do ((colls colls (map next colls))
(res [] (conj res (apply f (map first colls)))))
((every? empty? colls) res)))
in repl:
user> (map-all vector [1 2 3] [:a :s] '[z x c v])
;;=> [[1 :a z] [2 :s x] [3 nil c] [nil nil v]]
I know I can destructure a vector "from the front" like this:
(fn [[a b & rest]] (+ a b))
Is there any (short) way to access the last two elements instead?
(fn [[rest & a b]] (+ a b)) ;;Not legal
My current alternative is to
(fn [my-vector] (let [[a b] (take-last 2 my-vector)] (+ a b)))
and it was trying to figure out if there is way to do that in a more convenient way directly in the function arguments.
You can peel off the last two elements and add them thus:
((fn [v] (let [[b a] (rseq v)] (+ a b))) [1 2 3 4])
; 7
rseq supplies a reverse sequence for a vector in quick time.
We just destructure its first two elements.
We needn't mention the rest of it, which we don't do anything with.
user=> (def v (vec (range 0 10000000)))
#'user/v
user=> (time ((fn [my-vector] (let [[a b] (take-last 2 my-vector)] (+ a b))) v))
"Elapsed time: 482.965121 msecs"
19999997
user=> (time ((fn [my-vector] (let [a (peek my-vector) b (peek (pop my-vector))] (+ a b))) v))
"Elapsed time: 0.175539 msecs"
19999997
My advice would be to throw convenience to the wind and use peek and pop to work with the end of a vector. When your input vector is very large, you'll see tremendous performance gains.
(Also, to answer the question in the title: no.)
I am doing this exercise. Pascal's Trapezoid
My solution is:
(fn pascal[initseq]
(let [gen-nextseq (fn [s]
(let [s1 (conj (vec s) 0)
s2 (cons 0 s)]
(map + s1 s2)))]
(cons
initseq
(lazy-seq
(pascal
(gen-nextseq initseq))))))
I passed first three test cases, but failed the last one.
It says "java.lang.ArithmeticException: integer overflow"
So, is there a big integer in Clojure, or is there a better way to solve the problem?
Change + to +'. That will automagically get you a clojure.lang.BigInt if the result doesn't fit into a long. You can also use the N suffix on literals to get a BigInt.
(class (+' 3 2)) ;=> java.lang.Long
(class (+' 300000000000000000000000000000 2)) ;=> clojure.lang.BigInt
(class 3N) ;=> clojure.lang.BigInt
You can use +' instead of + for arbitrary precision.
(fn pascal[initseq]
(let [gen-nextseq (fn [s]
(let [s1 (conj (vec s) 0)
s2 (cons 0 s)]
(map + s1 s2)))]
^^
...
So you can modify the above marked potion of the code as follow.
(map +' s1 s2)))]
I can't figure out why this definition of a lazy primes sequence would cause non-termination. The stack-trace I get isn't very helpful (my one complaint about clojure is obtuse stack-traces).
(declare naturals is-prime? primes)
(defn naturals
([] (naturals 1))
([n] (lazy-seq (cons n (naturals (inc n))))))
(defn is-prime? [n]
(not-any? #(zero? (rem n %))
(take-while #(> n (* % %)) (primes))))
(defn primes
([] (lazy-seq (cons 2 (primes 3))))
([n] (let [m (first (filter is-prime? (naturals n)))]
(lazy-seq (cons m (primes (+ 2 m)))))))
(take 10 (primes)) ; this results in a stack overflow error
Let's start executing primes, and we'll magically realise one seq just to be clear. I'll ignore naturals because it's correctly lazy:
> (magically-realise-seq (primes))
=> (magically-realise-seq (lazy-seq (cons 2 (primes 3))))
=> (cons 2 (primes 3))
=> (cons 2 (let [m (first (filter is-prime? (naturals 3)))]
(lazy-seq (cons m (primes (+ 2 3))))))
=> (cons 2 (let [m (first (filter
(fn [n]
(not-any? #(zero? (rem n %))
(take-while #(> n (* % %)) (primes)))))
(naturals 3)))]
(lazy-seq (cons m (primes (+ 2 3))))))
I've substituted is-prime? in as a fn at the end there—you can see that primes will get called again, and realised at least once as take-while pulls out elements. This will then cause the loop.
The issue is that to know to calculate the "primes" function you are using the "is-prime?" function, and then to calculate the "is-prime?" function you are using "(primes)", hence the stack over flow.
So to calculate the "(primes 3)", you are need calculate the "(first (filter is-prime? (naturals 3)))", which is going to call "(is-prime? 1)", which is calling "(primes)", which in turns calls "(primes 3)". In other words you are doing:
user=> (declare a b)
#'user/b
user=> (defn a [] (b))
#'user/a
user=> (defn b [] (a))
#'user/b
user=> (a)
StackOverflowError user/b (NO_SOURCE_FILE:1)
To see how to generate prime numbers: Fast Prime Number Generation in Clojure
I think the problem is, that you're trying to use (primes) before it's already constructed.
Changing is-prime? like that fixes the problem:
(defn is-prime? [n]
(not-any? #(zero? (rem n %))
(take-while #(>= n (* % %)) (next (naturals)))))
(Note, that I've changed > with >=, otherwise it gives that 4 is prime. It still says that 1 is prime, which isn't true and may cause problems if you use is-prime? elsewhere.
I have a sequence s and a list of indexes into this sequence indexes. How do I retain only the items given via the indexes?
Simple example:
(filter-by-index '(a b c d e f g) '(0 2 3 4)) ; => (a c d e)
My usecase:
(filter-by-index '(c c# d d# e f f# g g# a a# b) '(0 2 4 5 7 9 11)) ; => (c d e f g a b)
You can use keep-indexed:
(defn filter-by-index [coll idxs]
(keep-indexed #(when ((set idxs) %1) %2)
coll))
Another version using explicit recur and lazy-seq:
(defn filter-by-index [coll idxs]
(lazy-seq
(when-let [idx (first idxs)]
(if (zero? idx)
(cons (first coll)
(filter-by-index (rest coll) (rest (map dec idxs))))
(filter-by-index (drop idx coll)
(map #(- % idx) idxs))))))
make a list of vectors containing the items combined with the indexes,
(def with-indexes (map #(vector %1 %2 ) ['a 'b 'c 'd 'e 'f] (range)))
#'clojure.core/with-indexes
with-indexes
([a 0] [b 1] [c 2] [d 3] [e 4] [f 5])
filter this list
lojure.core=> (def filtered (filter #(#{1 3 5 7} (second % )) with-indexes))
#'clojure.core/filtered
clojure.core=> filtered
([b 1] [d 3] [f 5])
then remove the indexes.
clojure.core=> (map first filtered)
(b d f)
then we thread it together with the "thread last" macro
(defn filter-by-index [coll idxs]
(->> coll
(map #(vector %1 %2)(range))
(filter #(idxs (first %)))
(map second)))
clojure.core=> (filter-by-index ['a 'b 'c 'd 'e 'f 'g] #{2 3 1 6})
(b c d g)
The moral of the story is, break it into small independent parts, test them, then compose them into a working function.
The easiest solution is to use map:
(defn filter-by-index [coll idx]
(map (partial nth coll) idx))
I like Jonas's answer, but neither version will work well for an infinite sequence of indices: the first tries to create an infinite set, and the latter runs into a stack overflow by layering too many unrealized lazy sequences on top of each other. To avoid both problems you have to do slightly more manual work:
(defn filter-by-index [coll idxs]
((fn helper [coll idxs offset]
(lazy-seq
(when-let [idx (first idxs)]
(if (= idx offset)
(cons (first coll)
(helper (rest coll) (rest idxs) (inc offset)))
(helper (rest coll) idxs (inc offset))))))
coll idxs 0))
With this version, both coll and idxs can be infinite and you will still have no problems:
user> (nth (filter-by-index (range) (iterate #(+ 2 %) 0)) 1e6)
2000000
Edit: not trying to single out Jonas's answer: none of the other solutions work for infinite index sequences, which is why I felt a solution that does is needed.
I had a similar use case and came up with another easy solution. This one expects vectors.
I've changed the function name to match other similar clojure functions.
(defn select-indices [coll indices]
(reverse (vals (select-keys coll indices))))
(defn filter-by-index [seq idxs]
(let [idxs (into #{} idxs)]
(reduce (fn [h [char idx]]
(if (contains? idxs idx)
(conj h char) h))
[] (partition 2 (interleave seq (iterate inc 0))))))
(filter-by-index [\a \b \c \d \e \f \g] [0 2 3 4])
=>[\a \c \d \e]
=> (defn filter-by-index [src indexes]
(reduce (fn [a i] (conj a (nth src i))) [] indexes))
=> (filter-by-index '(a b c d e f g) '(0 2 3 4))
[a c d e]
I know this is not what was asked, but after reading these answers, I realized in my own personal use case, what I actually wanted was basically filtering by a mask.
So here was my take. Hopefully this will help someone else.
(defn filter-by-mask [coll mask]
(filter some? (map #(if %1 %2) mask coll)))
(defn make-errors-mask [coll]
(map #(nil? (:error %)) coll))
Usage
(let [v [{} {:error 3} {:ok 2} {:error 4 :yea 7}]
data ["one" "two" "three" "four"]
mask (make-errors-mask v)]
(filter-by-mask data mask))
; ==> ("one" "three")