1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
use std::{
    cmp::{min, Ordering},
    fmt::Debug,
    mem,
};

pub(crate) use crate::op_set::OpSetMetadata;
use crate::query::{ChangeVisibility, Index, QueryResult, TreeQuery};
use crate::types::Op;
pub const B: usize = 16;

#[derive(Clone, Debug)]
pub(crate) struct OpTreeNode {
    pub(crate) children: Vec<OpTreeNode>,
    pub(crate) elements: Vec<usize>,
    pub(crate) index: Index,
    pub(crate) length: usize,
}

impl OpTreeNode {
    pub(crate) fn new() -> Self {
        Self {
            elements: Vec::new(),
            children: Vec::new(),
            index: Default::default(),
            length: 0,
        }
    }

    fn search_element<'a, 'b: 'a, Q>(
        &'b self,
        query: &mut Q,
        m: &OpSetMetadata,
        ops: &'a [Op],
        index: usize,
    ) -> bool
    where
        Q: TreeQuery<'a>,
    {
        if let Some(e) = self.elements.get(index) {
            if query.query_element_with_metadata(&ops[*e], m) == QueryResult::Finish {
                return true;
            }
        }
        false
    }

    pub(crate) fn search<'a, 'b: 'a, Q>(
        &'b self,
        query: &mut Q,
        m: &OpSetMetadata,
        ops: &'a [Op],
        mut skip: Option<usize>,
    ) -> bool
    where
        Q: TreeQuery<'a>,
    {
        if self.is_leaf() {
            for e in self.elements.iter().skip(skip.unwrap_or(0)) {
                if query.query_element_with_metadata(&ops[*e], m) == QueryResult::Finish {
                    return true;
                }
            }
            false
        } else {
            for (child_index, child) in self.children.iter().enumerate() {
                match skip {
                    Some(n) if n > child.len() => {
                        skip = Some(n - child.len() - 1);
                    }
                    Some(n) if n == child.len() => {
                        skip = Some(0); // important to not be None so we never call query_node again
                        if self.search_element(query, m, ops, child_index) {
                            return true;
                        }
                    }
                    Some(n) => {
                        if child.search(query, m, ops, Some(n)) {
                            return true;
                        }
                        skip = Some(0); // important to not be None so we never call query_node again
                        if self.search_element(query, m, ops, child_index) {
                            return true;
                        }
                    }
                    None => {
                        // descend and try find it
                        match query.query_node_with_metadata(child, m, ops) {
                            QueryResult::Descend => {
                                if child.search(query, m, ops, None) {
                                    return true;
                                }
                            }
                            QueryResult::Finish => return true,
                            QueryResult::Next => (),
                            QueryResult::Skip(_) => panic!("had skip from non-root node"),
                        }
                        if self.search_element(query, m, ops, child_index) {
                            return true;
                        }
                    }
                }
            }
            false
        }
    }

    pub(crate) fn len(&self) -> usize {
        self.length
    }

    fn reindex(&mut self, ops: &[Op]) {
        let mut index = Index::new();
        for c in &self.children {
            index.merge(&c.index);
        }
        for i in &self.elements {
            index.insert(&ops[*i]);
        }
        self.index = index
    }

    pub(crate) fn is_leaf(&self) -> bool {
        self.children.is_empty()
    }

    pub(crate) fn is_full(&self) -> bool {
        self.elements.len() >= 2 * B - 1
    }

    /// Returns the child index and the given index adjusted for the cumulative index before that
    /// child.
    fn find_child_index(&self, index: usize) -> (usize, usize) {
        let mut cumulative_len = 0;
        for (child_index, child) in self.children.iter().enumerate() {
            if cumulative_len + child.len() >= index {
                return (child_index, index - cumulative_len);
            } else {
                cumulative_len += child.len() + 1;
            }
        }
        panic!("index {} not found in node with len {}", index, self.len())
    }

    pub(crate) fn insert_into_non_full_node(&mut self, index: usize, element: usize, ops: &[Op]) {
        assert!(!self.is_full());

        self.index.insert(&ops[element]);

        if self.is_leaf() {
            self.length += 1;
            self.elements.insert(index, element);
        } else {
            let (child_index, sub_index) = self.find_child_index(index);
            let child = &mut self.children[child_index];

            if child.is_full() {
                self.split_child(child_index, ops);

                // child structure has changed so we need to find the index again
                let (child_index, sub_index) = self.find_child_index(index);
                let child = &mut self.children[child_index];
                child.insert_into_non_full_node(sub_index, element, ops);
            } else {
                child.insert_into_non_full_node(sub_index, element, ops);
            }
            self.length += 1;
        }
    }

    // A utility function to split the child `full_child_index` of this node
    // Note that `full_child_index` must be full when this function is called.
    pub(crate) fn split_child(&mut self, full_child_index: usize, ops: &[Op]) {
        let original_len_self = self.len();

        let full_child = &mut self.children[full_child_index];

        // Create a new node which is going to store (B-1) keys
        // of the full child.
        let mut successor_sibling = OpTreeNode::new();

        let original_len = full_child.len();
        assert!(full_child.is_full());

        successor_sibling.elements = full_child.elements.split_off(B);

        if !full_child.is_leaf() {
            successor_sibling.children = full_child.children.split_off(B);
        }

        let middle = full_child.elements.pop().unwrap();

        full_child.length =
            full_child.elements.len() + full_child.children.iter().map(|c| c.len()).sum::<usize>();

        successor_sibling.length = successor_sibling.elements.len()
            + successor_sibling
                .children
                .iter()
                .map(|c| c.len())
                .sum::<usize>();

        let z_len = successor_sibling.len();

        let full_child_len = full_child.len();

        full_child.reindex(ops);
        successor_sibling.reindex(ops);

        self.children
            .insert(full_child_index + 1, successor_sibling);

        self.elements.insert(full_child_index, middle);

        assert_eq!(full_child_len + z_len + 1, original_len, "{:#?}", self);

        assert_eq!(original_len_self, self.len());
    }

    fn remove_from_leaf(&mut self, index: usize) -> usize {
        self.length -= 1;
        self.elements.remove(index)
    }

    fn remove_element_from_non_leaf(
        &mut self,
        index: usize,
        element_index: usize,
        ops: &[Op],
    ) -> usize {
        self.length -= 1;
        if self.children[element_index].elements.len() >= B {
            let total_index = self.cumulative_index(element_index);
            // recursively delete index - 1 in predecessor_node
            let predecessor = self.children[element_index].remove(index - 1 - total_index, ops);
            // replace element with that one
            mem::replace(&mut self.elements[element_index], predecessor)
        } else if self.children[element_index + 1].elements.len() >= B {
            // recursively delete index + 1 in successor_node
            let total_index = self.cumulative_index(element_index + 1);
            let successor = self.children[element_index + 1].remove(index + 1 - total_index, ops);
            // replace element with that one
            mem::replace(&mut self.elements[element_index], successor)
        } else {
            let middle_element = self.elements.remove(element_index);
            let successor_child = self.children.remove(element_index + 1);
            self.children[element_index].merge(middle_element, successor_child, ops);

            let total_index = self.cumulative_index(element_index);
            self.children[element_index].remove(index - total_index, ops)
        }
    }

    fn cumulative_index(&self, child_index: usize) -> usize {
        self.children[0..child_index]
            .iter()
            .map(|c| c.len() + 1)
            .sum()
    }

    fn remove_from_internal_child(
        &mut self,
        index: usize,
        mut child_index: usize,
        ops: &[Op],
    ) -> usize {
        if self.children[child_index].elements.len() < B
            && if child_index > 0 {
                self.children[child_index - 1].elements.len() < B
            } else {
                true
            }
            && if child_index + 1 < self.children.len() {
                self.children[child_index + 1].elements.len() < B
            } else {
                true
            }
        {
            // if the child and its immediate siblings have B-1 elements merge the child
            // with one sibling, moving an element from this node into the new merged node
            // to be the median

            if child_index > 0 {
                let middle = self.elements.remove(child_index - 1);

                // use the predessor sibling
                let successor = self.children.remove(child_index);
                child_index -= 1;

                self.children[child_index].merge(middle, successor, ops);
            } else {
                let middle = self.elements.remove(child_index);

                // use the sucessor sibling
                let successor = self.children.remove(child_index + 1);

                self.children[child_index].merge(middle, successor, ops);
            }
        } else if self.children[child_index].elements.len() < B {
            if child_index > 0
                && self
                    .children
                    .get(child_index - 1)
                    .map_or(false, |c| c.elements.len() >= B)
            {
                let last_element = self.children[child_index - 1].elements.pop().unwrap();
                assert!(!self.children[child_index - 1].elements.is_empty());
                self.children[child_index - 1].length -= 1;
                self.children[child_index - 1]
                    .index
                    .remove(&ops[last_element]);

                let parent_element =
                    mem::replace(&mut self.elements[child_index - 1], last_element);

                self.children[child_index]
                    .index
                    .insert(&ops[parent_element]);
                self.children[child_index]
                    .elements
                    .insert(0, parent_element);
                self.children[child_index].length += 1;

                if let Some(last_child) = self.children[child_index - 1].children.pop() {
                    self.children[child_index - 1].length -= last_child.len();
                    self.children[child_index - 1].reindex(ops);
                    self.children[child_index].length += last_child.len();
                    self.children[child_index].children.insert(0, last_child);
                    self.children[child_index].reindex(ops);
                }
            } else if self
                .children
                .get(child_index + 1)
                .map_or(false, |c| c.elements.len() >= B)
            {
                let first_element = self.children[child_index + 1].elements.remove(0);
                self.children[child_index + 1]
                    .index
                    .remove(&ops[first_element]);
                self.children[child_index + 1].length -= 1;

                assert!(!self.children[child_index + 1].elements.is_empty());

                let parent_element = mem::replace(&mut self.elements[child_index], first_element);

                self.children[child_index].length += 1;
                self.children[child_index]
                    .index
                    .insert(&ops[parent_element]);
                self.children[child_index].elements.push(parent_element);

                if !self.children[child_index + 1].is_leaf() {
                    let first_child = self.children[child_index + 1].children.remove(0);
                    self.children[child_index + 1].length -= first_child.len();
                    self.children[child_index + 1].reindex(ops);
                    self.children[child_index].length += first_child.len();

                    self.children[child_index].children.push(first_child);
                    self.children[child_index].reindex(ops);
                }
            }
        }
        self.length -= 1;
        let total_index = self.cumulative_index(child_index);
        self.children[child_index].remove(index - total_index, ops)
    }

    pub(crate) fn check(&self) -> usize {
        let l = self.elements.len() + self.children.iter().map(|c| c.check()).sum::<usize>();
        assert_eq!(self.len(), l, "{:#?}", self);

        l
    }

    pub(crate) fn remove(&mut self, index: usize, ops: &[Op]) -> usize {
        let original_len = self.len();
        if self.is_leaf() {
            let v = self.remove_from_leaf(index);
            self.index.remove(&ops[v]);
            assert_eq!(original_len, self.len() + 1);
            debug_assert_eq!(self.check(), self.len());
            v
        } else {
            let mut total_index = 0;
            for (child_index, child) in self.children.iter().enumerate() {
                match (total_index + child.len()).cmp(&index) {
                    Ordering::Less => {
                        // should be later on in the loop
                        total_index += child.len() + 1;
                        continue;
                    }
                    Ordering::Equal => {
                        let v = self.remove_element_from_non_leaf(
                            index,
                            min(child_index, self.elements.len() - 1),
                            ops,
                        );
                        self.index.remove(&ops[v]);
                        assert_eq!(original_len, self.len() + 1);
                        debug_assert_eq!(self.check(), self.len());
                        return v;
                    }
                    Ordering::Greater => {
                        let v = self.remove_from_internal_child(index, child_index, ops);
                        self.index.remove(&ops[v]);
                        assert_eq!(original_len, self.len() + 1);
                        debug_assert_eq!(self.check(), self.len());
                        return v;
                    }
                }
            }
            panic!(
                "index not found to remove {} {} {} {}",
                index,
                total_index,
                self.len(),
                self.check()
            );
        }
    }

    fn merge(&mut self, middle: usize, successor_sibling: OpTreeNode, ops: &[Op]) {
        self.index.insert(&ops[middle]);
        self.index.merge(&successor_sibling.index);
        self.elements.push(middle);
        self.elements.extend(successor_sibling.elements);
        self.children.extend(successor_sibling.children);
        self.length += successor_sibling.length + 1;
        assert!(self.is_full());
    }

    /// Update the operation at the given index using the provided function.
    ///
    /// This handles updating the indices after the update.
    pub(crate) fn update<'a>(
        &mut self,
        index: usize,
        vis: ChangeVisibility<'a>,
    ) -> ChangeVisibility<'a> {
        if self.is_leaf() {
            self.index.change_vis(vis)
        } else {
            let mut cumulative_len = 0;
            let len = self.len();
            for (_child_index, child) in self.children.iter_mut().enumerate() {
                match (cumulative_len + child.len()).cmp(&index) {
                    Ordering::Less => {
                        cumulative_len += child.len() + 1;
                    }
                    Ordering::Equal => {
                        return self.index.change_vis(vis);
                    }
                    Ordering::Greater => {
                        let vis = child.update(index - cumulative_len, vis);
                        return self.index.change_vis(vis);
                    }
                }
            }
            panic!("Invalid index to set: {} but len was {}", index, len)
        }
    }

    pub(crate) fn last(&self) -> usize {
        if self.is_leaf() {
            // node is never empty so this is safe
            *self.elements.last().unwrap()
        } else {
            // if not a leaf then there is always at least one child
            self.children.last().unwrap().last()
        }
    }

    pub(crate) fn get(&self, index: usize) -> Option<usize> {
        if self.is_leaf() {
            return self.elements.get(index).copied();
        } else {
            let mut cumulative_len = 0;
            for (child_index, child) in self.children.iter().enumerate() {
                match (cumulative_len + child.len()).cmp(&index) {
                    Ordering::Less => {
                        cumulative_len += child.len() + 1;
                    }
                    Ordering::Equal => return self.elements.get(child_index).copied(),
                    Ordering::Greater => {
                        return child.get(index - cumulative_len);
                    }
                }
            }
        }
        None
    }
}