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| author | Marshall Lochbaum <mwlochbaum@gmail.com> | 2021-02-15 15:24:47 -0500 |
|---|---|---|
| committer | Marshall Lochbaum <mwlochbaum@gmail.com> | 2021-02-15 15:24:47 -0500 |
| commit | 28e8c10388a0f139717cf73f40a02d939cdd8103 (patch) | |
| tree | 3057c975c1d7daadb3ae666433a62b47a89ebf0b /docs/doc | |
| parent | d36b409c5f09bb9cabeb9f4da17af63cfbbbce1b (diff) | |
Add info on higher-rank 𝕨 and extra element to Group doc
Diffstat (limited to 'docs/doc')
| -rw-r--r-- | docs/doc/group.html | 55 |
1 files changed, 40 insertions, 15 deletions
diff --git a/docs/doc/group.html b/docs/doc/group.html index 491fca81..2b03e5fa 100644 --- a/docs/doc/group.html +++ b/docs/doc/group.html @@ -7,7 +7,7 @@ <h1 id="group">Group</h1> <p>BQN replaces the <a href="https://aplwiki.com/wiki/Key">Key</a> operator from J or Dyalog APL, and <a href="https://aplwiki.com/wiki/Partition_representations">many forms of partitioning</a>, with a single (ambivalent) Group function <code><span class='Function'>⊔</span></code>. This function is somewhat related to the K function <code><span class='Function'>=</span></code> of the same name, but results in an array rather than a dictionary.</p> <h2 id="definition">Definition</h2> -<p>Group operates on a list of atomic-number indices and an array, treated as a list of its major cells or "values", to produce a list of groups, each of which is a selection from those cells. The two arrays have the same length, and each value cell is paired with the index at the same position. That index indicates the result group the cell should go into, with an "index" of ¯1 indicating that it should be dropped and not appear in the result.</p> +<p>Group operates on a list of atomic-number <a href="indices.html">indices</a> <code><span class='Value'>𝕨</span></code> and an array <code><span class='Value'>𝕩</span></code>, treated as a list of its major cells, to produce a list of groups, each containing some of the cells from <code><span class='Value'>𝕩</span></code>. The two arguments have the same length, and each cell in <code><span class='Value'>𝕩</span></code> is paired with the index in <code><span class='Value'>𝕨</span></code> at the same position, which indicates which result group should include that cell.</p> <a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=MOKAvzHigL8y4oC/MOKAvzEg4omNICJhYmNkZSIgICMgQ29ycmVzcG9uZGluZyBpbmRpY2VzIGFuZCB2YWx1ZXMKMOKAvzHigL8y4oC/MOKAvzEg4oqUICJhYmNkZSIgICMgVmFsdWVzIGdyb3VwZWQgYnkgaW5kZXg=">↗️</a><pre> <span class='Number'>0</span><span class='Ligature'>‿</span><span class='Number'>1</span><span class='Ligature'>‿</span><span class='Number'>2</span><span class='Ligature'>‿</span><span class='Number'>0</span><span class='Ligature'>‿</span><span class='Number'>1</span> <span class='Function'>≍</span> <span class='String'>"abcde"</span> <span class='Comment'># Corresponding indices and values </span>┌─ ╵ 0 1 2 0 1 @@ -16,9 +16,25 @@ <span class='Number'>0</span><span class='Ligature'>‿</span><span class='Number'>1</span><span class='Ligature'>‿</span><span class='Number'>2</span><span class='Ligature'>‿</span><span class='Number'>0</span><span class='Ligature'>‿</span><span class='Number'>1</span> <span class='Function'>⊔</span> <span class='String'>"abcde"</span> <span class='Comment'># Values grouped by index </span>⟨ "ad" "be" "c" ⟩ </pre> -<p>For example, we might choose to group a list of words by length. Within each group, cells maintain the ordering they had in the list originally.</p> -<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=cGhyYXNlIOKGkCAiQlFOIuKAvyJ1c2VzIuKAvyJub3RhdGlvbiLigL8iYXMi4oC/ImEi4oC/InRvb2wi4oC/Im9mIuKAvyJ0aG91Z2h0IgripYrLmCDiiaDCqOKKuOKKlCBwaHJhc2U=">↗️</a><pre> <span class='Value'>phrase</span> <span class='Gets'>←</span> <span class='String'>"BQN"</span><span class='Ligature'>‿</span><span class='String'>"uses"</span><span class='Ligature'>‿</span><span class='String'>"notation"</span><span class='Ligature'>‿</span><span class='String'>"as"</span><span class='Ligature'>‿</span><span class='String'>"a"</span><span class='Ligature'>‿</span><span class='String'>"tool"</span><span class='Ligature'>‿</span><span class='String'>"of"</span><span class='Ligature'>‿</span><span class='String'>"thought"</span> - <span class='Function'>⥊</span><span class='Modifier'>˘</span> <span class='Function'>≠</span><span class='Modifier'>¨</span><span class='Modifier2'>⊸</span><span class='Function'>⊔</span> <span class='Value'>phrase</span> +<p>A few extra options can be useful in some circumstances. First, an "index" of <code><span class='Number'>¯1</span></code> in <code><span class='Value'>𝕨</span></code> indicates that the corresponding cell should be dropped and not appear in the result. Second, <code><span class='Value'>𝕨</span></code> is allowed to have an extra element after the end, which gives a minimum length for the result: otherwise, the result will be just long enough to accomodate the highest index in <code><span class='Value'>𝕨</span></code>.</p> +<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=MOKAv8KvMeKAvzLigL8y4oC/wq8xIOKKlCAiYWJjZGUiICAjIERyb3AgYyBhbmQgZQow4oC/MeKAvzLigL8y4oC/MeKAvzYg4oqUICJhYmNkZSIgICMgTGVuZ3RoLTYgcmVzdWx0">↗️</a><pre> <span class='Number'>0</span><span class='Ligature'>‿</span><span class='Number'>¯1</span><span class='Ligature'>‿</span><span class='Number'>2</span><span class='Ligature'>‿</span><span class='Number'>2</span><span class='Ligature'>‿</span><span class='Number'>¯1</span> <span class='Function'>⊔</span> <span class='String'>"abcde"</span> <span class='Comment'># Drop c and e +</span>⟨ "a" ⟨⟩ "cd" ⟩ + <span class='Number'>0</span><span class='Ligature'>‿</span><span class='Number'>1</span><span class='Ligature'>‿</span><span class='Number'>2</span><span class='Ligature'>‿</span><span class='Number'>2</span><span class='Ligature'>‿</span><span class='Number'>1</span><span class='Ligature'>‿</span><span class='Number'>6</span> <span class='Function'>⊔</span> <span class='String'>"abcde"</span> <span class='Comment'># Length-6 result +</span>⟨ "a" "be" "cd" ⟨⟩ ⟨⟩ ⟨⟩ ⟩ +</pre> +<p>A third extension is that <code><span class='Value'>𝕨</span></code> doesn't really have to be a list: if not, then it groups <code><span class='Function'>-=</span><span class='Value'>𝕨</span></code>-cells of <code><span class='Value'>𝕩</span></code> instead of just <code><span class='Number'>¯1</span></code>-cells. These cells are placed in index order. This extension isn't compatible with the second option from above, because it's usually not possible to add just one extra element to a non-list array. One usage is to group the diagonals of a table. See if you can figure out how the code below does this.</p> +<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=4oqiIGEg4oaQICdhJyvipYrin5wo4oaVw5fCtCkz4oC/NQooK+KMnMK0wrfihpXCqOKJoiniirjiipQgYQ==">↗️</a><pre> <span class='Function'>⊢</span> <span class='Value'>a</span> <span class='Gets'>←</span> <span class='String'>'a'</span><span class='Function'>+⥊</span><span class='Modifier2'>⟜</span><span class='Paren'>(</span><span class='Function'>↕×</span><span class='Modifier'>´</span><span class='Paren'>)</span><span class='Number'>3</span><span class='Ligature'>‿</span><span class='Number'>5</span> +┌─ +╵"abcde + fghij + klmno" + ┘ + <span class='Paren'>(</span><span class='Function'>+</span><span class='Modifier'>⌜´</span><span class='Nothing'>·</span><span class='Function'>↕</span><span class='Modifier'>¨</span><span class='Function'>≢</span><span class='Paren'>)</span><span class='Modifier2'>⊸</span><span class='Function'>⊔</span> <span class='Value'>a</span> +⟨ "a" "bf" "cgk" "dhl" "eim" "jn" "o" ⟩ +</pre> +<p>For a concrete example, we might choose to group a list of words by length. Within each group, cells maintain the ordering they had in the list originally.</p> +<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=cGhyYXNlIOKGkCAiQlFOIuKAvyJ1c2VzIuKAvyJub3RhdGlvbiLigL8iYXMi4oC/ImEi4oC/InRvb2wi4oC/Im9mIuKAvyJ0aG91Z2h0IgriiY3LmCDiiaDCqOKKuOKKlCBwaHJhc2U=">↗️</a><pre> <span class='Value'>phrase</span> <span class='Gets'>←</span> <span class='String'>"BQN"</span><span class='Ligature'>‿</span><span class='String'>"uses"</span><span class='Ligature'>‿</span><span class='String'>"notation"</span><span class='Ligature'>‿</span><span class='String'>"as"</span><span class='Ligature'>‿</span><span class='String'>"a"</span><span class='Ligature'>‿</span><span class='String'>"tool"</span><span class='Ligature'>‿</span><span class='String'>"of"</span><span class='Ligature'>‿</span><span class='String'>"thought"</span> + <span class='Function'>≍</span><span class='Modifier'>˘</span> <span class='Function'>≠</span><span class='Modifier'>¨</span><span class='Modifier2'>⊸</span><span class='Function'>⊔</span> <span class='Value'>phrase</span> ┌─ ╵ ⟨⟩ ⟨ "a" ⟩ @@ -33,19 +49,28 @@ </pre> <p>(Could we define <code><span class='Value'>phrase</span></code> more easily? See <a href="#partitioning">below</a>.)</p> <p>If we'd like to ignore words of 0 letters, or more than 5, we can set all word lengths greater than 5 to 0, then reduce the lengths by 1. Two words end up with left argument values of ¯1 and are omitted from the result.</p> -<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=MSAty5wg4omk4p+cNeKKuMOXIOKJoMKoIHBocmFzZQripYrLmCB7MS3LnOKJpOKfnDXiirjDl+KJoMKo8J2VqX3iirjiipQgcGhyYXNl">↗️</a><pre> <span class='Number'>1</span> <span class='Function'>-</span><span class='Modifier'>˜</span> <span class='Function'>≤</span><span class='Modifier2'>⟜</span><span class='Number'>5</span><span class='Modifier2'>⊸</span><span class='Function'>×</span> <span class='Function'>≠</span><span class='Modifier'>¨</span> <span class='Value'>phrase</span> +<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=MSAty5wg4omk4p+cNeKKuMOXIOKJoMKoIHBocmFzZQriiY3LmCB7MS3LnOKJpOKfnDXiirjDl+KJoMKo8J2VqX3iirjiipQgcGhyYXNl">↗️</a><pre> <span class='Number'>1</span> <span class='Function'>-</span><span class='Modifier'>˜</span> <span class='Function'>≤</span><span class='Modifier2'>⟜</span><span class='Number'>5</span><span class='Modifier2'>⊸</span><span class='Function'>×</span> <span class='Function'>≠</span><span class='Modifier'>¨</span> <span class='Value'>phrase</span> ⟨ 2 3 ¯1 1 0 3 1 ¯1 ⟩ - <span class='Function'>⥊</span><span class='Modifier'>˘</span> <span class='Brace'>{</span><span class='Number'>1</span><span class='Function'>-</span><span class='Modifier'>˜</span><span class='Function'>≤</span><span class='Modifier2'>⟜</span><span class='Number'>5</span><span class='Modifier2'>⊸</span><span class='Function'>×≠</span><span class='Modifier'>¨</span><span class='Value'>𝕩</span><span class='Brace'>}</span><span class='Modifier2'>⊸</span><span class='Function'>⊔</span> <span class='Value'>phrase</span> + <span class='Function'>≍</span><span class='Modifier'>˘</span> <span class='Brace'>{</span><span class='Number'>1</span><span class='Function'>-</span><span class='Modifier'>˜</span><span class='Function'>≤</span><span class='Modifier2'>⟜</span><span class='Number'>5</span><span class='Modifier2'>⊸</span><span class='Function'>×≠</span><span class='Modifier'>¨</span><span class='Value'>𝕩</span><span class='Brace'>}</span><span class='Modifier2'>⊸</span><span class='Function'>⊔</span> <span class='Value'>phrase</span> +┌─ +╵ ⟨ "a" ⟩ + ⟨ "as" "of" ⟩ + ⟨ "BQN" ⟩ + ⟨ "uses" "tool" ⟩ + ┘ +</pre> +<p>Note that the length of the result is determined by the largest index. So the result never includes trailing empty groups. A reader of the above code might expect 5 groups (lengths 1 through 5), but there are no words of length 5, so the last group isn't there. To ensure the result always has 5 groups, we can add a <code><span class='Number'>5</span></code> at the end of the left argument.</p> +<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=4omNy5ggezXiiL7LnDEty5ziiaTin5w14oq4w5fiiaDCqPCdlal94oq44oqUIHBocmFzZQ==">↗️</a><pre> <span class='Function'>≍</span><span class='Modifier'>˘</span> <span class='Brace'>{</span><span class='Number'>5</span><span class='Function'>∾</span><span class='Modifier'>˜</span><span class='Number'>1</span><span class='Function'>-</span><span class='Modifier'>˜</span><span class='Function'>≤</span><span class='Modifier2'>⟜</span><span class='Number'>5</span><span class='Modifier2'>⊸</span><span class='Function'>×≠</span><span class='Modifier'>¨</span><span class='Value'>𝕩</span><span class='Brace'>}</span><span class='Modifier2'>⊸</span><span class='Function'>⊔</span> <span class='Value'>phrase</span> ┌─ ╵ ⟨ "a" ⟩ ⟨ "as" "of" ⟩ ⟨ "BQN" ⟩ ⟨ "uses" "tool" ⟩ + ⟨⟩ ┘ </pre> -<p>Note that the length of the result is determined by the largest index. So the result never includes trailing empty groups. A reader of the above code might expect 5 groups (lengths 1 through 5), but there are no words of length 5, so the last group isn't there.</p> <p>When Group is called dyadically, the left argument is used for the indices and the right is used for values, as seen above. When it is called monadically, the right argument, which must be a list, gives the indices and the values grouped are the right argument's indices, that is, <code><span class='Function'>↕≠</span><span class='Value'>𝕩</span></code>.</p> -<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=4qWKy5gg4oqUIDLigL8z4oC/wq8x4oC/Mg==">↗️</a><pre> <span class='Function'>⥊</span><span class='Modifier'>˘</span> <span class='Function'>⊔</span> <span class='Number'>2</span><span class='Ligature'>‿</span><span class='Number'>3</span><span class='Ligature'>‿</span><span class='Number'>¯1</span><span class='Ligature'>‿</span><span class='Number'>2</span> +<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=4omNy5gg4oqUIDLigL8z4oC/wq8x4oC/Mg==">↗️</a><pre> <span class='Function'>≍</span><span class='Modifier'>˘</span> <span class='Function'>⊔</span> <span class='Number'>2</span><span class='Ligature'>‿</span><span class='Number'>3</span><span class='Ligature'>‿</span><span class='Number'>¯1</span><span class='Ligature'>‿</span><span class='Number'>2</span> ┌─ ╵ ⟨⟩ ⟨⟩ @@ -57,7 +82,7 @@ <h3 id="multidimensional-grouping">Multidimensional grouping</h3> <p>Dyadic Group allows the right argument to be grouped along multiple axes by using a nested left argument. In this case, the left argument must be a list of numeric lists, and the result has rank <code><span class='Function'>≠</span><span class='Value'>𝕨</span></code> while its elements—as always—have the same rank as <code><span class='Value'>𝕩</span></code>. The result shape is <code><span class='Number'>1</span><span class='Function'>+⌈</span><span class='Modifier'>´¨</span><span class='Value'>𝕨</span></code>, while the shape of element <code><span class='Value'>i</span><span class='Function'>⊑</span><span class='Value'>𝕨</span><span class='Function'>⊔</span><span class='Value'>𝕩</span></code> is <code><span class='Value'>i</span><span class='Function'>+</span><span class='Modifier'>´</span><span class='Modifier2'>∘</span><span class='Function'>=</span><span class='Modifier'>¨</span><span class='Value'>𝕨</span></code>. If every element of <code><span class='Value'>𝕨</span></code> is sorted ascending and contains only non-negative numbers, we have <code><span class='Value'>𝕩</span><span class='Function'>≡∾</span><span class='Value'>𝕨</span><span class='Function'>⊔</span><span class='Value'>𝕩</span></code>, that is, Join is the inverse of Partition.</p> <p>Here we split up a rank-2 array into a rank-2 array of rank-2 arrays. Along the first axis we simply separate the first pair and second pair of rows—a partition. Along the second axis we separate odd from even indices.</p> -<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=4p+oMOKAvzDigL8x4oC/MSww4oC/MeKAvzDigL8x4oC/MOKAvzHigL8w4p+p4oqUKDEww5fihpU0KSvijJzihpU3">↗️</a><pre> <span class='Bracket'>⟨</span><span class='Number'>0</span><span class='Ligature'>‿</span><span class='Number'>0</span><span class='Ligature'>‿</span><span class='Number'>1</span><span class='Ligature'>‿</span><span class='Number'>1</span><span class='Separator'>,</span><span class='Number'>0</span><span class='Ligature'>‿</span><span class='Number'>1</span><span class='Ligature'>‿</span><span class='Number'>0</span><span class='Ligature'>‿</span><span class='Number'>1</span><span class='Ligature'>‿</span><span class='Number'>0</span><span class='Ligature'>‿</span><span class='Number'>1</span><span class='Ligature'>‿</span><span class='Number'>0</span><span class='Bracket'>⟩</span><span class='Function'>⊔</span><span class='Paren'>(</span><span class='Number'>10</span><span class='Function'>×↕</span><span class='Number'>4</span><span class='Paren'>)</span><span class='Function'>+</span><span class='Modifier'>⌜</span><span class='Function'>↕</span><span class='Number'>7</span> +<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=4p+oMOKAvzDigL8x4oC/MSww4oC/MeKAvzDigL8x4oC/MOKAvzHigL8w4p+pIOKKlCAoMTDDl+KGlTQpK+KMnOKGlTc=">↗️</a><pre> <span class='Bracket'>⟨</span><span class='Number'>0</span><span class='Ligature'>‿</span><span class='Number'>0</span><span class='Ligature'>‿</span><span class='Number'>1</span><span class='Ligature'>‿</span><span class='Number'>1</span><span class='Separator'>,</span><span class='Number'>0</span><span class='Ligature'>‿</span><span class='Number'>1</span><span class='Ligature'>‿</span><span class='Number'>0</span><span class='Ligature'>‿</span><span class='Number'>1</span><span class='Ligature'>‿</span><span class='Number'>0</span><span class='Ligature'>‿</span><span class='Number'>1</span><span class='Ligature'>‿</span><span class='Number'>0</span><span class='Bracket'>⟩</span> <span class='Function'>⊔</span> <span class='Paren'>(</span><span class='Number'>10</span><span class='Function'>×↕</span><span class='Number'>4</span><span class='Paren'>)</span><span class='Function'>+</span><span class='Modifier'>⌜</span><span class='Function'>↕</span><span class='Number'>7</span> ┌─ ╵ ┌─ ┌─ ╵ 0 2 4 6 ╵ 1 3 5 @@ -91,9 +116,9 @@ <p>Group can even be implemented with the same techniques as a bucket sort, which can be branchless and fast.</p> <h2 id="applications">Applications</h2> <p>The obvious application of Group is to group some values according to a known or computed property. If this property isn't an integer, it can be turned into one using Classify (monadic <code><span class='Function'>⊐</span></code>, identical to <code><span class='Function'>⍷</span><span class='Modifier2'>⊸</span><span class='Function'>⊐</span></code>). Classify numbers the unique values in its argument by first occurrence.</p> -<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=bG4g4oaQICJQaGVscHMi4oC/IkxhdHluaW5hIuKAvyJCasO4cmdlbiLigL8iQW5kcmlhbm92IuKAvyJCasO4cm5kYWxlbiIKY28g4oaQICJVUyIgICAg4oC/IlNVIiAgICAgIOKAvyJOTyIgICAgIOKAvyJTVSIgICAgICAg4oC/Ik5PIgripYrLmCBjbyDiipDiirjiipQgbG4=">↗️</a><pre> <span class='Value'>ln</span> <span class='Gets'>←</span> <span class='String'>"Phelps"</span><span class='Ligature'>‿</span><span class='String'>"Latynina"</span><span class='Ligature'>‿</span><span class='String'>"Bjørgen"</span><span class='Ligature'>‿</span><span class='String'>"Andrianov"</span><span class='Ligature'>‿</span><span class='String'>"Bjørndalen"</span> +<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=bG4g4oaQICJQaGVscHMi4oC/IkxhdHluaW5hIuKAvyJCasO4cmdlbiLigL8iQW5kcmlhbm92IuKAvyJCasO4cm5kYWxlbiIKY28g4oaQICJVUyIgICAg4oC/IlNVIiAgICAgIOKAvyJOTyIgICAgIOKAvyJTVSIgICAgICAg4oC/Ik5PIgriiY3LmCBjbyDiipDiirjiipQgbG4=">↗️</a><pre> <span class='Value'>ln</span> <span class='Gets'>←</span> <span class='String'>"Phelps"</span><span class='Ligature'>‿</span><span class='String'>"Latynina"</span><span class='Ligature'>‿</span><span class='String'>"Bjørgen"</span><span class='Ligature'>‿</span><span class='String'>"Andrianov"</span><span class='Ligature'>‿</span><span class='String'>"Bjørndalen"</span> <span class='Value'>co</span> <span class='Gets'>←</span> <span class='String'>"US"</span> <span class='Ligature'>‿</span><span class='String'>"SU"</span> <span class='Ligature'>‿</span><span class='String'>"NO"</span> <span class='Ligature'>‿</span><span class='String'>"SU"</span> <span class='Ligature'>‿</span><span class='String'>"NO"</span> - <span class='Function'>⥊</span><span class='Modifier'>˘</span> <span class='Value'>co</span> <span class='Function'>⊐</span><span class='Modifier2'>⊸</span><span class='Function'>⊔</span> <span class='Value'>ln</span> + <span class='Function'>≍</span><span class='Modifier'>˘</span> <span class='Value'>co</span> <span class='Function'>⊐</span><span class='Modifier2'>⊸</span><span class='Function'>⊔</span> <span class='Value'>ln</span> ┌─ ╵ ⟨ "Phelps" ⟩ ⟨ "Latynina" "Andrianov" ⟩ @@ -111,9 +136,9 @@ "US" ⟨ "Phelps" ⟩ ┘ </pre> -<p>However, this solution will fail if there are trailing keys with no values. To force the result to have a particular length you can append that length as a dummy index to each argument, then remove the last group after grouping.</p> -<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=Y291bnRyaWVzIOKGqSAiSVQi4oC/IkpQIuKAvyJOTyLigL8iU1Ui4oC/IlVTIuKAvyJaVyIKY291bnRyaWVzIOKJjcuYIGNvIGNvdW50cmllc3vwnZWX4oq44oqQ4oq4KMKvMeKGk+KKlOKXiyjiiL7in5wo4omg8J2VlykpKX0gbG4=">↗️</a><pre> <span class='Value'>countries</span> <span class='Gets'>↩</span> <span class='String'>"IT"</span><span class='Ligature'>‿</span><span class='String'>"JP"</span><span class='Ligature'>‿</span><span class='String'>"NO"</span><span class='Ligature'>‿</span><span class='String'>"SU"</span><span class='Ligature'>‿</span><span class='String'>"US"</span><span class='Ligature'>‿</span><span class='String'>"ZW"</span> - <span class='Value'>countries</span> <span class='Function'>≍</span><span class='Modifier'>˘</span> <span class='Value'>co</span> <span class='Value'>countries</span><span class='Brace'>{</span><span class='Value'>𝕗</span><span class='Modifier2'>⊸</span><span class='Function'>⊐</span><span class='Modifier2'>⊸</span><span class='Paren'>(</span><span class='Number'>¯1</span><span class='Function'>↓⊔</span><span class='Modifier2'>○</span><span class='Paren'>(</span><span class='Function'>∾</span><span class='Modifier2'>⟜</span><span class='Paren'>(</span><span class='Function'>≠</span><span class='Value'>𝕗</span><span class='Paren'>)))</span><span class='Brace'>}</span> <span class='Value'>ln</span> +<p>However, this solution will fail if there are trailing keys with no values. To force the result to have a particular length you can append that length to the left argument.</p> +<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=Y291bnRyaWVzIOKGqSAiSVQi4oC/IkpQIuKAvyJOTyLigL8iU1Ui4oC/IlVTIuKAvyJaVyIKY291bnRyaWVzIOKJjcuYIGNvIGNvdW50cmllc+KKuCjiipDiiL7iiaDiiJjiiqMp4oq44oqUIGxu">↗️</a><pre> <span class='Value'>countries</span> <span class='Gets'>↩</span> <span class='String'>"IT"</span><span class='Ligature'>‿</span><span class='String'>"JP"</span><span class='Ligature'>‿</span><span class='String'>"NO"</span><span class='Ligature'>‿</span><span class='String'>"SU"</span><span class='Ligature'>‿</span><span class='String'>"US"</span><span class='Ligature'>‿</span><span class='String'>"ZW"</span> + <span class='Value'>countries</span> <span class='Function'>≍</span><span class='Modifier'>˘</span> <span class='Value'>co</span> <span class='Value'>countries</span><span class='Modifier2'>⊸</span><span class='Paren'>(</span><span class='Function'>⊐∾≠</span><span class='Modifier2'>∘</span><span class='Function'>⊣</span><span class='Paren'>)</span><span class='Modifier2'>⊸</span><span class='Function'>⊔</span> <span class='Value'>ln</span> ┌─ ╵ "IT" ⟨⟩ "JP" ⟨⟩ @@ -137,7 +162,7 @@ <a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=JyAnKCjiiqIty5zCrMOXK2Ap4oiYPeKKlOKKoikiICBzdHJpbmcgd2l0aCAgc3BhY2VzICAgIg==">↗️</a><pre> <span class='String'>' '</span><span class='Paren'>((</span><span class='Function'>⊢-</span><span class='Modifier'>˜</span><span class='Function'>¬×+</span><span class='Modifier'>`</span><span class='Paren'>)</span><span class='Modifier2'>∘</span><span class='Function'>=⊔⊢</span><span class='Paren'>)</span><span class='String'>" string with spaces "</span> ⟨ ⟨⟩ ⟨⟩ "string" "with" ⟨⟩ "spaces" ⟩ </pre> -<p>However, trailing spaces are ignored because Group never produces trailing empty groups (to get them back we would use a dummy final character in the string). To avoid empty words, we should increase the word index only once per group of spaces. We can do this by taking the prefix sum of a list that is 1 only for a space with no space before it. To make such a list, we can use the <a href="shift.html">Shift Before</a> function, giving a list of previous elements. To treat the first element as if it's before a space (so that leading spaces have no effect rather than creating an initial empty group), we shift in a 1.</p> +<p>Trailing spaces are ignored because Group with equal-length arguments never produces trailing empty groups—to intentionally include them you'd replace <code><span class='Function'>=</span></code> with <code><span class='Paren'>(</span><span class='Function'>=∾</span><span class='Number'>0</span><span class='Modifier'>˙</span><span class='Paren'>)</span></code>. But in string processing we probably want to avoid empty words anywhere. To make this happen, we should increase the word index only once per group of spaces. We can do this by taking the prefix sum of a list that is 1 only for a space with no space before it. To make such a list, we can use the <a href="shift.html">Shift Before</a> function, giving a list of previous elements. To treat the first element as if it's before a space (so that leading spaces have no effect rather than creating an initial empty group), we shift in a 1.</p> <a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=KOKKouKJjTHiirjCuzziiqIpICcgJz0iICBzdHJpbmcgd2l0aCAgc3BhY2VzICAgIiAgIyBBbGwsIHRoZW4gZmlsdGVyZWQsIHNwYWNlcwriiY3in5wo4oqiLcucwqzDl8K3K2Ax4oq4wrs84oqiKScgJz0iICBzdHJpbmcgd2l0aCAgc3BhY2VzICAgIiAgIyBNb3JlIHByb2Nlc3NpbmcKJyAnKCjiiqIty5zCrMOXwrcrYDHiirjCuzziiqIp4oiYPeKKlOKKoikiICBzdHJpbmcgd2l0aCAgc3BhY2VzICAgIiAgIyBGaW5hbCByZXN1bHQKCicgJygowqwty5ziiqLDl8K3K2DCu+KKuD4p4oiY4omg4oqU4oqiKSIgIHN0cmluZyB3aXRoICBzcGFjZXMgICAiICAjIFNsaWdodGx5IHNob3J0ZXI=">↗️</a><pre> <span class='Paren'>(</span><span class='Function'>⊢≍</span><span class='Number'>1</span><span class='Modifier2'>⊸</span><span class='Function'>»<⊢</span><span class='Paren'>)</span> <span class='String'>' '</span><span class='Function'>=</span><span class='String'>" string with spaces "</span> <span class='Comment'># All, then filtered, spaces </span>┌─ ╵ 1 1 0 0 0 0 0 0 1 0 0 0 0 1 1 0 0 0 0 0 0 1 1 1 |