How can express this imperative function in a functional, array-based language like K (or Q)?

Question

In sloppy C++:

vector<int> x(10), y(10); // Assume these are initialized with some values.

// BTW, 4 is just a const -- it's part of the algorithm and is arbitrarily chosen.

vector<int> result1(x.size() - 4 + 1); // A place to hold a resulting array.
vector<int> result2(x.size() - 4 + 1); // A place to hold another resulting array.

// Here's the code I want to express functionally.
for (int i = 0; i <= x.size() - 4; i++) {
    int best = x[i + 0] - y[i + 0];
    int bad = best;
    int worst = best;
    for(int j = 0; j < 4; j++) {
        int tmp = x[i + j] - y[i + 0];
        bad = min(bad, tmp);
        if(tmp > best) {
            best = tmp;
            worst = bad;
        }
    }
    result1[i] = best
    result2[i] = worst
}

I would most like to see this in kdb and Q but other functional languages are welcome.

It is trying to calculate two things: First, at each point in x, we want the maximum over the next 4 elements (let's call this Nx = max(x), at location Px, where Px = 0..3. Second, at each point in x, we want the minimum over the next Px points. — Badmanchild, Jul 19 '11 at 19:59

score 5 · Answer 1 · answered Mar 23 '12 at 02:39

porting @silentbicycle's k directly to q yields

q)a:1+til 8
q)b:8#0
q){(max x;min x)}flip{4#y _ x}[a+b;]each til count a
4 5 6 7 8 8 8 8
1 2 3 4 5 6 7 8

another approach, slightly more vectorized (imao):

q){(max;min)@\:flip 4#'(til count x)_\:x+y}[a;b]
4 5 6 7 8 8 8 8
1 2 3 4 5 6 7 8

score 4 · Accepted Answer · answered Jul 23 '11 at 14:13

In Kona (an open-source K dialect):

First, set some example values (using same as the Clojure solution):

a:1+!8;b:8#0        / a is 1..8, b is eight 0s

Then:

{(|/x;&/x)}@+{4#y _ x}[a+b;]'!#a

Where a and b are your x and y variables above. (K makes a special case for the variables x, y, and z.)

To break that up a bit more:

maxmin:{(|/x;&/x)}  / (max;min) pairs of x
get4:{4#y _ x}      / next 4 from x, starting at y
                    / with <4 remaining, will repeat; doesn't matter for min or max
/ maxmin applied to flipped results of get4(a-b) at each index 0..(length a)-1
maxmin@+get4[a-b;]'!#a

/ result
(4 5 6 7 8 8 8 8
 1 2 3 4 5 6 7 8)

score 1 · Answer 3 · edited Oct 06 '11 at 15:29

1

In Clojure (a dialect of Lisp):

(defn minmax [x y](map #(vector (- (apply max %1) %2) (- (apply min %1) %2)))(partition-all 4 1 x) y)

(minmax [1 2 3 4 5 6 7 8] [0 0 0 0 0 0 0 0])

will give

[([4 1] [5 2] [6 3] [7 4] [8 5] [8 6] [8 7] [8 8])`(result 1, result 2) as output..

Then

(map #(first %1) result) is result1
(map #(last %1) result) is result2

edited Oct 06 '11 at 15:29

Peter Mortensen

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answered Jul 20 '11 at 01:52

KaKa

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How can express this imperative function in a functional, array-based language like K (or Q)?

3 Answers3