What would be a more idiomatic way to partition a seq based on a seq of integers instead of just one integer?
Here's my implementation:
(defn partition-by-seq
"Return a lazy sequence of lists with a variable number of items each
determined by the n in ncoll. Extra values in coll are dropped."
[ncoll coll]
(let [partition-coll (mapcat #(repeat % %) ncoll)]
(->> coll
(map vector partition-coll)
(partition-by first)
(map (partial map last)))))
Then (partition-by-seq [2 3 6] (range))
yields ((0 1) (2 3 4) (5 6 7 8 9 10))
.
In number theory and combinatorics, a partition of a positive integer n, also called an integer partition, is a way of writing n as a sum of positive integers. Two sums that differ only in the order of their summands are considered the same partition. (If order matters, the sum becomes a composition.)
A multiset of positive integers that add to n is called a partition of n. Thus the partitions of 3 are 1+1+1, 1+2 (which is the same as 2+1) and 3. The number of partitions of k is denoted by p(k); in computing the partitions of 3 we showed that p(3)=3.
How many partitions will be formed for the integer 3? Explanation: We need to find the combinations of positive integers which give 3 as their sum. These will be {3}, {2,1}, {1,1,1}. Thus the correct answer is 3.
Ramanujan's approximate formula, developed in 1918, helped him spot that numbers ending in 4 or 9 have a partition number divisible by 5, and he found similar rules for partition numbers divisible by 7 and 11. Without offering a proof, he wrote that these numbers had “simple properties” possessed by no others.
Your implementation looks fine, but there could be a more simple solution which uses simple recursion wrapped in lazy-seq
(and turns out to be more efficient) than using map and existing partition-by as in your case.
(defn partition-by-seq [ncoll coll]
(if (empty? ncoll)
'()
(let [n (first ncoll)]
(cons (take n coll)
(lazy-seq (partition-by-seq (rest ncoll) (drop n coll)))))))
A variation on Ankur's answer, with a minor addition of laziness and when-let
instead of an explicit test for empty?
.
(defn partition-by-seq [parts coll]
(lazy-seq
(when-let [s (seq parts)]
(cons
(take (first s) coll)
(partition-by-seq (rest s) (nthrest coll (first s)))))))
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