# Remove “lines” from a 2D vec

I have some code here that I am very unhappy with. The task I am trying to accomplish is this.

Given a 2d vec like this:

[[0 2 0] [1 3 5] [3 3 0]]


which can contain positive ints including zero I want to remove all lines that are greater zero.

Where the definition of line is the following:

A line is represented by the position n in every vec inside the 2d vec.

So my example above has three lines:

[0 1 3], [2 3 3] and [0 5 0].


The line that I want to remove from it according to my algortihm is [2 3 3] because every element is greater than zero.

So my 2d vec would now look like this:

[[0 0] [1 5] [3 0]]


And finally I want to pad the vecs to their original size filling them with zero for every removed line, so that it looks finally like this:

[[0 0 0] [0 1 5] [0 3 0]]


This is what I came up with:

(defn in?
"true if seq contains elm"
[seq elm]
(some #(= elm %) seq))

(defn not-in?
"true if seq does not contain elm"
[seq elm]
(not (in? seq elm)))

(defn all-greater-zero-at
"Given a 2-d vec [[0 1] [0 2]] return true if all elements at 'at' are
greater than zero"
[v at]
(not-in? (map #(if (> (nth % at) 0) true false) v) false))

(defn to-be-removed
"Returns a seq of positions to be removed (0 3 4)"
[v width]
(reduce (fn [a b] (if (all-greater-zero-at v b) (conj a b) a)) [] (range width)))

(defn remove-at
"Removes an element from a 1d vec"
[v at]
(into [] (concat (subvec v 0 at) (subvec v (+ at 1) (count v)))))

(defn insert-at
"inserts an element into a 1d vec"
[v elm at]
(into [] (concat (subvec v 0 at) elm (subvec v at (count v)))))

(defn remove-and-replace-all-at
[v at]
(map #(insert-at (remove-at % at)  at) v))

(defn replace-full-by-zero [v width]
(reduce (fn [a b] (remove-and-replace-all-at a b)) v (to-be-removed v width)))

(defn remove-zeros [v at]
(reduce (fn [a b] (conj a (remove-at b at))) [] v))

(defn fill-with-zeros
"Takes a 2d vec and pads ith with zeros up to width"
[v width]
(map #(into [] (concat (take (- width (count (first v))) (repeat 0)) %)) v))

(defn clean-grid
"removes all full lines"
[fbz tbr]
(loop [acc fbz tbr tbr i 0]
(if (empty? tbr)
acc
(recur (remove-zeros acc (- (first tbr) i)) (rest tbr) (inc i)))))

(defn remove-full-lines [v width]
(let [fbz (replace-full-by-zero v width)
tbr (to-be-removed v width)
cleaned-grid (clean-grid fbz tbr)]
(into [] (fill-with-zeros cleaned-grid width))))


This seems like a lot of code for such a "simple" algorithm and I assume there are a lot of better ways to do that, but just did not come up with a better one, so, please, go ahead and fix it, if you want to.

• Those look like 3D vecs, not 2D. – 200_success May 16 '15 at 16:17

A transpose function would be useful here. This is the code I came up with:

(defn transpose [m]
"Transposes a matrix, returning a new matrix. For 2D matrices, rows and columns are swapped."
(vec (apply map vector m)))

(defn any-zero? [r]
((complement not-any?) #(= 0 %) r))

(defn empty-matrix [x y]
(vec (repeat y (vec (repeat x 0)))))

(defn filter-matrix [m]
(let [row-size (-> m first count)
fm (filterv any-zero? m)
padding-size (- (count m) (count fm))]

(defn transform-matrix [m]
(-> m
transpose
filter-matrix
transpose))


Let's try it out:

=> (transform-matrix [[0 2 0] [1 3 5] [3 3 0]])
[[0 0 0] [0 1 5] [0 3 0]]


If you want to do more advanced operations on matrices I recommend looking into the core.matrix library.

Hope this helps!

• Thanks, this works. I just wonder why you call transpose three times in de-transpose? Shouldn't a single transpose be enough for the transformation back? – sveri May 16 '15 at 6:38
• @sveri Ah yes, you are right. I'll update my answer. – Dirk Geurs May 16 '15 at 9:38