user
Task

Generate 100 <x,y> coordinate pairs such that x and y are integers sampled from the uniform distribution with the condition that   

10
≤

x

2
+

y

2
≤
15
{\displaystyle {\displaystyle 10\leq {\sqrt {x^{2}+y^{2}}}\leq 15}}
.   
Then display/plot them. The outcome should be a "fuzzy" circle. The actual number of points plotted may be less than 100, given that some pairs may be generated more than once.

There are several possible approaches to accomplish this. Here are two possible algorithms.

1) Generate random pairs of integers and filter out those that don't satisfy this condition:

:   10
    ≤

    x

    2
    +

    y

    2
    ≤
    15
    {\displaystyle {\displaystyle 10\leq {\sqrt {x^{2}+y^{2}}}\leq 15}}
    .

2) Precalculate the set of all possible points (there are 404 of them) and select randomly from this set.
assistant
(formerly Perl 6)

**Works with**: rakudo version 2015.09

```
my @range = -15..16;

my @points = gather for @range X @range -> ($x, $y) {
    take [$x,$y] if 10 <= sqrt($x*$x+$y*$y) <= 15
}
my @samples = @points.roll(100); # or .pick(100) to get distinct points

# format and print
my %matrix;
for @range X @range -> ($x, $y) { %matrix{$y}{$x} = ' ' }
%matrix{.[1]}{.[0]} = '*' for @samples;
%matrix{$_}{@range}.join(' ').say for @range;

```

Output:

```
                                  *
                    *                 *
              *     *   *         *         *
            * *         *               *
                      *           *       *   *     *
              *   *
            *     *                                   *
      *     *                                 *       *
                                              *
            *                                   * *   *
      *   *                                         *
      * *                                         *     *
      *
  *     *
                                                      * * *
  * *   * *
      *                                             *   *
    *
    *     *
  *     *
            * *                                       *
      *                                           *   *
                                          *         *
          *                                   *       *
              *         *       *         * * *     *
          *   *     *                   *     * *
                              *     *   *   *
                  *                 *
                                *     * *
```

Turning that program completely inside-out and reducing to a single statement with a single non-parameter variable, we get another version that also works.

This uses, among other things, a 0-based matrix rather than a hash, a given on the first line that allows us to print the final value of the matrix straight from its initial declaration, a for statement feeding a for statement modifier, a lambda that unpacks a single x-y argument into two variables, the functional form of pick rather than the method form, a quasi-list comprehension in the middle loop that filters each given with a when, precalculated squared limits so we don't have to take the square root, use of X- and X\*\* to subtract and exponentiate both $x and $y in parallel.

After the given do has loaded up @matrix with our circle, the map on the first line substitutes a space for any undefined matrix element, and the extra space between elements is supplied by the stringification of the list value, performed by the prefix ~ operator, the unary equivalent of concatenation in Raku.

At this point you would be justified in concluding that we are completely mad. :-)

```
(say ~.map: { $_ // ' ' } for my @matrix) given do
    -> [$x, $y] { @matrix[$x][$y] = '*' } for pick 100, do
        for ^32 X ^32 -> ($x, $y) {
            [$x,$y] when 100..225 given [+] ($x,$y X- 15) X** 2;
        }

```

Output:

```
                       *   *     *
                        * *     *
                          *       * * *   *     *
                    *   * * *         *         *
        *     *             *         *     *     *
          *     *                             *
      *                                   * * *   *
          * *                                 *     *
      * *
                                                    *   *
                                                    *
  *                                               *     *

    *                                               *
* *                                                 * * *   *
      *   *

        *                                         * *   *
          *                                         * *
      * *   *                                         *
                                                  *   *
    *   *
        * *                                     *
      * *   *                           * *           *
              *               *         *         *
              * *       *   *           *     *
              * * *                         *
                  * *   *       * *
                    *       * *
```