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 </pre><pre class="rust"><code><span class="kw">use </span>std::collections::{BTreeSet, BinaryHeap};
 <span class="kw">use </span>std::iter;
 <span class="kw">use </span>std::ops::RangeInclusive;

 <span class="kw">use </span>itertools::Itertools;

 <span class="kw">use </span><span class="kw">super</span>::blank_range::BlankRange;
 <span class="kw">use super</span>::{CompactSpace, RangeMapping};

 <span class="doccomment">/// Put the blanks for the sorted values into a binary heap
 </span><span class="kw">fn </span>get_blanks(values_sorted: <span class="kw-2">&amp;</span>BTreeSet&lt;u128&gt;) -&gt; BinaryHeap&lt;BlankRange&gt; {
     <span class="kw">let </span><span class="kw-2">mut </span>blanks: BinaryHeap&lt;BlankRange&gt; = BinaryHeap::new();
     <span class="kw">for </span>(first, second) <span class="kw">in </span>values_sorted.iter().tuple_windows() {
         <span class="comment">// Correctness Overflow: the values are deduped and sorted (BTreeSet property), that means
         // there&#39;s always space between two values.
         </span><span class="kw">let </span>blank_range = first + <span class="number">1</span>..=second - <span class="number">1</span>;
         <span class="kw">let </span>blank_range: <span class="prelude-ty">Result</span>&lt;BlankRange, <span class="kw">_</span>&gt; = blank_range.try_into();
         <span class="kw">if let </span><span class="prelude-val">Ok</span>(blank_range) = blank_range {
             blanks.push(blank_range);
         }
     }

     blanks
 }

 <span class="kw">struct </span>BlankCollector {
     blanks: Vec&lt;BlankRange&gt;,
     staged_blanks_sum: u128,
 }
 <span class="kw">impl </span>BlankCollector {
     <span class="kw">fn </span>new() -&gt; <span class="self">Self </span>{
         <span class="self">Self </span>{
             blanks: <span class="macro">vec!</span>[],
             staged_blanks_sum: <span class="number">0</span>,
         }
     }
     <span class="kw">fn </span>stage_blank(<span class="kw-2">&amp;mut </span><span class="self">self</span>, blank: BlankRange) {
         <span class="self">self</span>.staged_blanks_sum += blank.blank_size();
         <span class="self">self</span>.blanks.push(blank);
     }
     <span class="kw">fn </span>drain(<span class="kw-2">&amp;mut </span><span class="self">self</span>) -&gt; <span class="kw">impl </span>Iterator&lt;Item = BlankRange&gt; + <span class="lifetime">&#39;_ </span>{
         <span class="self">self</span>.staged_blanks_sum = <span class="number">0</span>;
         <span class="self">self</span>.blanks.drain(..)
     }
     <span class="kw">fn </span>staged_blanks_sum(<span class="kw-2">&amp;</span><span class="self">self</span>) -&gt; u128 {
         <span class="self">self</span>.staged_blanks_sum
     }
     <span class="kw">fn </span>num_staged_blanks(<span class="kw-2">&amp;</span><span class="self">self</span>) -&gt; usize {
         <span class="self">self</span>.blanks.len()
     }
 }
 <span class="kw">fn </span>num_bits(val: u128) -&gt; u8 {
     (<span class="number">128u32 </span>- val.leading_zeros()) <span class="kw">as </span>u8
 }

 <span class="doccomment">/// Will collect blanks and add them to compact space if more bits are saved than cost from
 /// metadata.
 </span><span class="kw">pub fn </span>get_compact_space(
     values_deduped_sorted: <span class="kw-2">&amp;</span>BTreeSet&lt;u128&gt;,
     total_num_values: u32,
     cost_per_blank: usize,
 ) -&gt; CompactSpace {
     <span class="kw">let </span><span class="kw-2">mut </span>compact_space_builder = CompactSpaceBuilder::new();
     <span class="kw">if </span>values_deduped_sorted.is_empty() {
         <span class="kw">return </span>compact_space_builder.finish();
     }

     <span class="kw">let </span><span class="kw-2">mut </span>blanks: BinaryHeap&lt;BlankRange&gt; = get_blanks(values_deduped_sorted);
     <span class="comment">// Replace after stabilization of https://github.com/rust-lang/rust/issues/62924

     // We start by space that&#39;s limited to min_value..=max_value
     </span><span class="kw">let </span>min_value = <span class="kw-2">*</span>values_deduped_sorted.iter().next().unwrap_or(<span class="kw-2">&amp;</span><span class="number">0</span>);
     <span class="kw">let </span>max_value = <span class="kw-2">*</span>values_deduped_sorted.iter().last().unwrap_or(<span class="kw-2">&amp;</span><span class="number">0</span>);

     <span class="comment">// +1 for null, in case min and max covers the whole space, we are off by one.
     </span><span class="kw">let </span><span class="kw-2">mut </span>amplitude_compact_space = (max_value - min_value).saturating_add(<span class="number">1</span>);
     <span class="kw">if </span>min_value != <span class="number">0 </span>{
         compact_space_builder.add_blanks(iter::once(<span class="number">0</span>..=min_value - <span class="number">1</span>));
     }
     <span class="kw">if </span>max_value != u128::MAX {
         compact_space_builder.add_blanks(iter::once(max_value + <span class="number">1</span>..=u128::MAX));
     }

     <span class="kw">let </span><span class="kw-2">mut </span>amplitude_bits: u8 = num_bits(amplitude_compact_space);

     <span class="kw">let </span><span class="kw-2">mut </span>blank_collector = BlankCollector::new();
     <span class="comment">// We will stage blanks until they reduce the compact space by at least 1 bit and then flush
     // them if the metadata cost is lower than the total number of saved bits.
     // Binary heap to process the gaps by their size
     </span><span class="kw">while let </span><span class="prelude-val">Some</span>(blank_range) = blanks.pop() {
         blank_collector.stage_blank(blank_range);

         <span class="kw">let </span>staged_spaces_sum: u128 = blank_collector.staged_blanks_sum();
         <span class="kw">let </span>amplitude_new_compact_space = amplitude_compact_space - staged_spaces_sum;
         <span class="kw">let </span>amplitude_new_bits = num_bits(amplitude_new_compact_space);
         <span class="kw">if </span>amplitude_bits == amplitude_new_bits {
             <span class="kw">continue</span>;
         }
         <span class="kw">let </span>saved_bits = (amplitude_bits - amplitude_new_bits) <span class="kw">as </span>usize * total_num_values <span class="kw">as </span>usize;
         <span class="comment">// TODO: Maybe calculate exact cost of blanks and run this more expensive computation only,
         // when amplitude_new_bits changes
         </span><span class="kw">let </span>cost = blank_collector.num_staged_blanks() * cost_per_blank;
         <span class="kw">if </span>cost &gt;= saved_bits {
             <span class="comment">// Continue here, since although we walk over the blanks by size,
             // we can potentially save a lot at the last bits, which are smaller blanks
             //
             // E.g. if the first range reduces the compact space by 1000 from 2000 to 1000, which
             // saves 11-10=1 bit and the next range reduces the compact space by 950 to
             // 50, which saves 10-6=4 bit
             </span><span class="kw">continue</span>;
         }

         amplitude_compact_space = amplitude_new_compact_space;
         amplitude_bits = amplitude_new_bits;
         compact_space_builder.add_blanks(blank_collector.drain().map(|blank| blank.blank_range()));
     }

     <span class="comment">// special case, when we don&#39;t collected any blanks because:
     // * the data is empty (early exit)
     // * the algorithm did decide it&#39;s not worth the cost, which can be the case for single values
     //
     // We drain one collected blank unconditionally, so the empty case is reserved for empty
     // data, and therefore empty compact_space means the data is empty and no data is covered
     // (conversely to all data) and we can assign null to it.
     </span><span class="kw">if </span>compact_space_builder.is_empty() {
         compact_space_builder.add_blanks(
             blank_collector
                 .drain()
                 .map(|blank| blank.blank_range())
                 .take(<span class="number">1</span>),
         );
     }

     <span class="kw">let </span>compact_space = compact_space_builder.finish();
     <span class="kw">if </span>max_value - min_value != u128::MAX {
         <span class="macro">debug_assert_eq!</span>(
             compact_space.amplitude_compact_space(),
             amplitude_compact_space
         );
     }
     compact_space
 }

 <span class="attribute">#[derive(Debug, Clone, Eq, PartialEq)]
 </span><span class="kw">struct </span>CompactSpaceBuilder {
     blanks: Vec&lt;RangeInclusive&lt;u128&gt;&gt;,
 }

 <span class="kw">impl </span>CompactSpaceBuilder {
     <span class="doccomment">/// Creates a new compact space builder which will initially cover the whole space.
     </span><span class="kw">fn </span>new() -&gt; <span class="self">Self </span>{
         <span class="self">Self </span>{ blanks: Vec::new() }
     }

     <span class="doccomment">/// Assumes that repeated add_blank calls don&#39;t overlap and are not adjacent,
     /// e.g. [3..=5, 5..=10] is not allowed
     ///
     /// Both of those assumptions are true when blanks are produced from sorted values.
     </span><span class="kw">fn </span>add_blanks(<span class="kw-2">&amp;mut </span><span class="self">self</span>, blank: <span class="kw">impl </span>Iterator&lt;Item = RangeInclusive&lt;u128&gt;&gt;) {
         <span class="self">self</span>.blanks.extend(blank);
     }

     <span class="kw">fn </span>is_empty(<span class="kw-2">&amp;</span><span class="self">self</span>) -&gt; bool {
         <span class="self">self</span>.blanks.is_empty()
     }

     <span class="doccomment">/// Convert blanks to covered space and assign null value
     </span><span class="kw">fn </span>finish(<span class="kw-2">mut </span><span class="self">self</span>) -&gt; CompactSpace {
         <span class="comment">// sort by start. ranges are not allowed to overlap
         </span><span class="self">self</span>.blanks.sort_unstable_by_key(|blank| <span class="kw-2">*</span>blank.start());

         <span class="kw">let </span><span class="kw-2">mut </span>covered_space = Vec::with_capacity(<span class="self">self</span>.blanks.len());

         <span class="comment">// begining of the blanks
         </span><span class="kw">if let </span><span class="prelude-val">Some</span>(first_blank_start) = <span class="self">self</span>.blanks.first().map(RangeInclusive::start) {
             <span class="kw">if </span><span class="kw-2">*</span>first_blank_start != <span class="number">0 </span>{
                 covered_space.push(<span class="number">0</span>..=first_blank_start - <span class="number">1</span>);
             }
         }

         <span class="comment">// Between the blanks
         </span><span class="kw">let </span>between_blanks = <span class="self">self</span>.blanks.iter().tuple_windows().map(|(left, right)| {
             <span class="macro">assert!</span>(
                 left.end() &lt; right.start(),
                 <span class="string">&quot;overlapping or adjacent ranges detected&quot;
             </span>);
             <span class="kw-2">*</span>left.end() + <span class="number">1</span>..=<span class="kw-2">*</span>right.start() - <span class="number">1
         </span>});
         covered_space.extend(between_blanks);

         <span class="comment">// end of the blanks
         </span><span class="kw">if let </span><span class="prelude-val">Some</span>(last_blank_end) = <span class="self">self</span>.blanks.last().map(RangeInclusive::end) {
             <span class="kw">if </span><span class="kw-2">*</span>last_blank_end != u128::MAX {
                 covered_space.push(last_blank_end + <span class="number">1</span>..=u128::MAX);
             }
         }

         <span class="kw">if </span>covered_space.is_empty() {
             covered_space.push(<span class="number">0</span>..=<span class="number">0</span>); <span class="comment">// empty data case
         </span>};

         <span class="kw">let </span><span class="kw-2">mut </span>compact_start: u64 = <span class="number">1</span>; <span class="comment">// 0 is reserved for `null`
         </span><span class="kw">let </span><span class="kw-2">mut </span>ranges_mapping: Vec&lt;RangeMapping&gt; = Vec::with_capacity(covered_space.len());
         <span class="kw">for </span>cov <span class="kw">in </span>covered_space {
             <span class="kw">let </span>range_mapping = <span class="kw">super</span>::RangeMapping {
                 value_range: cov,
                 compact_start,
             };
             <span class="kw">let </span>covered_range_len = range_mapping.range_length();
             ranges_mapping.push(range_mapping);
             compact_start += covered_range_len <span class="kw">as </span>u64;
         }
         <span class="comment">// println!(&quot;num ranges {}&quot;, ranges_mapping.len());
         </span>CompactSpace { ranges_mapping }
     }
 }

 <span class="attribute">#[cfg(test)]
 </span><span class="kw">mod </span>tests {
     <span class="kw">use super</span>::<span class="kw-2">*</span>;

     <span class="attribute">#[test]
     </span><span class="kw">fn </span>test_binary_heap_pop_order() {
         <span class="kw">let </span><span class="kw-2">mut </span>blanks: BinaryHeap&lt;BlankRange&gt; = BinaryHeap::new();
         blanks.push((<span class="number">0</span>..=<span class="number">10</span>).try_into().unwrap());
         blanks.push((<span class="number">100</span>..=<span class="number">200</span>).try_into().unwrap());
         blanks.push((<span class="number">100</span>..=<span class="number">110</span>).try_into().unwrap());
         <span class="macro">assert_eq!</span>(blanks.pop().unwrap().blank_size(), <span class="number">101</span>);
         <span class="macro">assert_eq!</span>(blanks.pop().unwrap().blank_size(), <span class="number">11</span>);
     }
 }
 </code></pre></div>
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