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
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
#![feature(box_into_raw_non_null)]
#![allow(dead_code)]
#![feature(map_get_key_value)]

//! [X-fast Trie](https://en.wikipedia.org/wiki/X-fast_trie) is a bitwise trie to store a bounded domain of integers.
//!
//! Currently this version of the crate is using the nightly release of rust.

use std::collections::HashMap;
use std::ptr::NonNull;

type Node<T> = NonNull<TrieNode<T>>;
/// Nodes of the trie
#[derive(Debug)]
pub struct TrieNode<T> {
    // Node key
    key: usize,
    /// Node value
    pub value: Option<T>,
    // Level at which the node is present
    level: usize,
    // Node's right subtree
    right: Option<NonNull<TrieNode<T>>>,
    // Node's left subtree
    left: Option<NonNull<TrieNode<T>>>,
    // Node's metadata about descendant node status
    is_desc_left: bool,
    is_desc_right: bool,
}

impl<T> TrieNode<T> {
    
    /// Creates a new node of the trie with `key` and `value` and no children.
    pub fn new(key: usize, value: T, level: usize) -> Box<Self> {
        Box::new(TrieNode{
            key: key,
            value: Some(value),
            level: level,
            right: None,
            left: None,
            is_desc_right: true,
            is_desc_left: true,
        })
    }

    // constructor for internal nodes
    fn new_internal(level: usize) -> Box<Self> {
        Box::new(TrieNode{
            key: 0,
            value: None,
            level,
            right: None,
            left: None,
            is_desc_left: true,
            is_desc_right: true,
        })
    }

    // return the rightmost node for @cur_node as parent
    // @max_level: max possible height of the trie
    fn get_rightmost_node(max_level: usize, mut cur_node: *mut TrieNode<T>) -> Option<Node<T>> {
        unsafe {
            while (*cur_node).level != max_level {
                match (*cur_node).right {
                    Some(right_node) => {
                        cur_node = right_node.as_ptr();
                    }
                    None => {
                        (*cur_node).left.map(|left_node| {
                            cur_node = left_node.as_ptr();
                        });
                    }
                }
            }
            NonNull::new(cur_node as *mut TrieNode<T>)
        }
    }

    // return the leftmost node for @cur_node as parent
    // @max_level: max possible height of the trie
    fn get_leftmost_node(max_level: usize, mut cur_node: *mut TrieNode<T>) -> Option<Node<T>> {
        unsafe {
            while (*cur_node).level != max_level {
                match (*cur_node).left {
                    Some(left_node) => {
                        cur_node = left_node.as_ptr();
                    }
                    None => {
                        (*cur_node).right.map(|right_node| {
                            cur_node = right_node.as_ptr();
                        });
                    }
                }
            }
            NonNull::new(cur_node as *mut TrieNode<T>)
        }
    }
}

#[derive(Debug)]
/// A bitwise trie to store integers.
///
/// The values in a X-fast trie are stored at the leaves. An internal node is added to the trie
/// only if it has leaves in its subtree.
///
/// Each level of the trie is modelled as a hash map storing the trie nodes at that level.
///
/// The range of integers need to be specified while initializing a trie.
/// # Examples
/// ```
///     use xfast::Xfast;
///
///     let mut test_trie: Xfast<&str> = Xfast::new(31);
///     test_trie.insert_key(11, "eleven");
///     test_trie.insert_key(1, "one");
///     test_trie.insert_key(5, "five");
///     assert_eq!(test_trie.len(), 3);
///        
///     let predecessor_3 = test_trie.find_predecessor(3);
///     if predecessor_3.is_some() {
///         let predecessor_value = predecessor_3.unwrap().value.unwrap();
///         assert_eq!(predecessor_value, "one");
///     }
/// ```

pub struct Xfast<T=String> {
    nr_levels: usize,
    level_maps: Vec<HashMap<usize, NonNull<TrieNode<T>>>>,
}

impl<T> Xfast<T> {
    
    /// Creates a new Xfast Trie to store a given `range` of integers
    /// # Examples
    /// ```
    /// # #![allow(unused_mut)]
    ///     use xfast::Xfast;
    ///     
    ///     let mut test_trie: Xfast<&str> = Xfast::new(31);
    /// ```
    pub fn new(range: usize) -> Self {
        let nr_levels = Self::get_levels_count(range);
        let level_maps = Self::create_map_list(nr_levels+1);
        let mut new_trie = Xfast {
            nr_levels,
            level_maps,
        };
        // insert the root node in the trie at level 0
        let root_node = TrieNode::new_internal(0);
        let root_node = Box::into_raw_non_null(root_node);
        new_trie.level_maps[0].insert(0, root_node);
        new_trie
    }

    // levels => height of the trie
    fn get_levels_count(mut range: usize) -> usize {
        let mut levels = 0;
        while range > 0 {
            range >>= 1;
            levels += 1;
        }
        levels
    }

    // helper fn for populating a vector list of hashmaps
    fn create_map_list(nr_levels: usize) -> Vec<HashMap<usize, Node<T>>> {
        (0..nr_levels).map(|_| HashMap::new()).collect()
    }

    /// Returns the count of values stored in the trie
    /// # Examples
    /// ```
    ///     use xfast::Xfast;
    ///
    ///     let mut test_trie: Xfast<&str> = Xfast::new(31);
    ///     test_trie.insert_key(11, "eleven");
    ///     test_trie.insert_key(1, "one");
    ///     assert_eq!(test_trie.len(), 2);
    /// ```
    pub fn len(&self) -> usize {
        self.level_maps[self.nr_levels].len()
    }

    fn find_lowest_common_ancestor(&self, key: usize) -> Option<*mut TrieNode<T>> {
        let mut low = 0;
        let mut high = self.nr_levels;
        let mut ancestor_node: Option<*mut TrieNode<T>> = None;

        while high >= low {
            let mid = (low + high)/2;
            let prefix = key >> (self.nr_levels - mid);
            //check the presence of an internal node with the keyed as `prefix` in hashmap at the `mid` level 
            match self.level_maps[mid].get(&prefix) {
                Some(&value) => {
                    low = mid + 1;
                    ancestor_node = Some(value.as_ptr());
                }
                None => {
                    // prevent out of bound subtraction of a usize
                    if mid == 0 {
                        break;
                    }
                    high = mid - 1;
                }
            }
        }
        ancestor_node
    }

    /// Returns the smallest node more than or eqaul to the node associated with `key`. In case of no such node it returns None.
    /// #Examples
    /// # Examples
    /// ```
    ///     use xfast::Xfast;
    ///
    ///     let mut test_trie: Xfast<&str> = Xfast::new(31);
    ///     test_trie.insert_key(11, "eleven");
    ///     test_trie.insert_key(1, "one");
    ///     test_trie.insert_key(5, "five");
    ///     assert_eq!(test_trie.len(), 3);
    ///     
    ///     if let Some(successor_3) = test_trie.find_successor(3) {
    ///         let successor_value = successor_3.value.unwrap();
    ///         assert_eq!(successor_value, "five");
    ///     }
    ///     let successor_14 = test_trie.find_successor(14);
    ///         assert!(successor_14.is_none());
    /// ```
    pub fn find_successor(&self, key: usize) -> Option<&TrieNode<T>> {
        // find the lowest common ancestor- a node which shares maximum common prefix with the key
        let successor_node: Option<*mut TrieNode<T>> = self.find_lowest_common_ancestor(key);
        if let Some(node) = successor_node {
            unsafe {
                // successor of a key already present is the key itself
                if (*node).level == (self.nr_levels) {
                    return Some(&(*node));
                }

                //right subtree of an internal node can have the successor
                let mut updated_node = None;
                if (key >> (self.nr_levels - (*node).level -1 ) & 1) != 0 {
                    (*node).right.map(|right_node| {
                        updated_node = Some(right_node.as_ptr());
                    });
                }
                else {
                    //left subtree of the internal node has the successor
                    (*node).left.map(|left_node| {
                        updated_node = Some(left_node.as_ptr());
                    });
                }
                                
                // in case the key of the successor node (leaf node) above calculated has lower key than the currently searched key
                // navigate using the right and left pointer of the leaf node to find the smallest node which has a key >= the key being searched
                if !updated_node.is_none() && (*updated_node.unwrap()).key < key {
                    let mut temp_node = None;
                    (*updated_node.unwrap()).right.map(|right_node| {
                        temp_node = Some(&(*right_node.as_ptr()));
                    });
                    return temp_node;
                }
                if !updated_node.is_none() {
                    return Some(&(*updated_node.unwrap()));
                }
                return None;
            }
        }
        None
    }

    /// Returns the largest node less that or eqaul to the node with `key`. In case of no such node it returns None.
    /// #Examples
    /// # Examples
    /// ```
    ///     use xfast::Xfast;
    ///
    ///     let mut test_trie: Xfast<&str> = Xfast::new(31);
    ///     test_trie.insert_key(11, "eleven");
    ///     test_trie.insert_key(1, "one");
    ///     test_trie.insert_key(5, "five");
    ///     assert_eq!(test_trie.len(), 3);
    ///        
    ///     if let Some(predecessor_3) = test_trie.find_predecessor(3) {
    ///         let predecessor_value = predecessor_3.value.unwrap();
    ///         assert_eq!(predecessor_value, "one");
    ///     }
    ///
    ///     let predecessor_0 = test_trie.find_predecessor(0);
    ///         assert!(predecessor_0.is_none());
    /// ```
    pub fn find_predecessor(&self, key: usize) -> Option<&TrieNode<T>> {
        // find the lowest common ancestor- a node which shares maximum common prefix with the key
        let predecessor_node: Option<*mut TrieNode<T>> = self.find_lowest_common_ancestor(key);
        if let Some(node) = predecessor_node {
            unsafe {
                // predecessor of a key already present is the key itself
                if (*node).level == (self.nr_levels) {
                    return Some(&(*node));
                }

                let mut updated_node = None;
                if (key >> (self.nr_levels - (*node).level -1) & 1) != 0 {
                    (*node).right.map(|right_node| {
                        updated_node = Some(right_node.as_ptr());
                    });
                }
                else {
                    (*node).left.map(|left_node| {
                        updated_node = Some(left_node.as_ptr());
                    });
                }

                if !updated_node.is_none() && (*updated_node.unwrap()).key > key {
                    let mut temp_node = None;
                    (*updated_node.unwrap()).left.map(|left_node| {
                        temp_node = Some(&(*left_node.as_ptr()));
                    });
                    return temp_node;
                }
                if !updated_node.is_none() {
                return Some(&(*updated_node.unwrap()));
                }
                return None;
                }
            }
        None
    }

    fn populate_internal_nodes(&mut self, key: usize) {
        let mut level = 1;
        let max_levels = self.nr_levels;
        while level < max_levels {
            let prefix = key >> (max_levels - level);
            if let None = self.level_maps[level].get(&prefix) {
                let temp_node = TrieNode::new_internal(level);
                let temp_node = Box::into_raw_non_null(temp_node);
                self.level_maps[level].insert(prefix, temp_node);
                // add to the right child if the bit is 1 at that index else make it the left child
                if (prefix & 1) != 0 {
                    let temp_prefix = prefix >> 1;
                    self.level_maps[level-1].get(&temp_prefix).map(|&value| unsafe{
                        (*value.as_ptr()).right = Some(temp_node);
                        (*value.as_ptr()).is_desc_right = false;
                    });
                }
                else {
                    let temp_prefix = prefix >> 1;
                    self.level_maps[level-1].get(&temp_prefix).map(|&value| unsafe{
                        (*value.as_ptr()).left = Some(temp_node);
                        (*value.as_ptr()).is_desc_left = false;
                    }); 
                }
            }
            level += 1;
        }
    }

    fn update_descendant_ptr(&mut self, key: usize) {
        let mut prefix = key;
        let mut level = self.nr_levels - 1;

        while level > 0 {
            prefix = prefix >> 1;
            // find an internal node prefixed as `prefix` at `level` in the level_map
            self.level_maps[level].get(&prefix).map(|&value| unsafe {
                //check if this node has a left child
                match (*value.as_ptr()).left {
                    //the internal node doesn't have a left child
                    None => {
                        //An internal node is inserted in a trie only when it has one its children
                        //Therefore, this node has a right child which is used to find its descendant ptr
                        (*value.as_ptr()).right.map(|right_node| {
                            (*value.as_ptr()).left = TrieNode::get_leftmost_node(self.nr_levels, right_node.as_ptr());
                            (*value.as_ptr()).is_desc_left = true;
                        });
                    },
                    // Left child is present
                    Some(left_ptr) => {
                        //this internal node can have a right child or not
                        match (*value.as_ptr()).right {
                            // the right child is not present
                            None => {
                                (*value.as_ptr()).right = TrieNode::get_rightmost_node(self.nr_levels, left_ptr.as_ptr());
                                (*value.as_ptr()).is_desc_right = true;
                            }
                            // right child is also present
                            Some(right_ptr)=> {
                                // if any of the left or the right child is associated with a descendant pointer then update with the latest descendant pointer. 
                                // At any given instance only one descendant ptr can be present
                                if (*value.as_ptr()).is_desc_right {
                                    (*value.as_ptr()).right = TrieNode::get_rightmost_node(self.nr_levels, left_ptr.as_ptr());
                                }
                                else if (*value.as_ptr()).is_desc_left {
                                    (*value.as_ptr()).left = TrieNode::get_leftmost_node(self.nr_levels, right_ptr.as_ptr());
                                }
                            }
                        }
                    }
                }
            });
            level -= 1;
        }

        // update the descendant ptr for the root node
        self.level_maps[0].get(&0).map(|&value| unsafe {
            let is_left_descendant = (*value.as_ptr()).is_desc_left;
            let is_right_descendant = (*value.as_ptr()).is_desc_right;
            if is_left_descendant {
                (*value.as_ptr()).right.map(|right_node| {
                    (*value.as_ptr()).left = TrieNode::get_leftmost_node(self.nr_levels, right_node.as_ptr());
                });
            }
            if is_right_descendant {
                (*value.as_ptr()).left.map(|left_node| {
                    (*value.as_ptr()).right = TrieNode::get_rightmost_node(self.nr_levels, left_node.as_ptr());
                });
            }
        });
    }

    /// Insert `key` and `value` into the trie
    /// # Examples
    /// ```
    ///     use xfast::Xfast;
    ///
    ///     let mut test_trie: Xfast<&str> = Xfast::new(31);
    ///     test_trie.insert_key(11, "eleven");
    /// ```
    pub fn insert_key(&mut self, key: usize, value: T) {
        //create a new node with key and val
        let new_node = TrieNode::new(key, value, self.nr_levels);
        let new_node = Some(Box::into_raw_non_null(new_node));
        //find predecessor and successor for the new node
        let predecessor = self.find_predecessor(key);
        let successor = self.find_successor(key);
        
        //update the right and left pointers of the new node to refer to its successors and predecessors resp.
        //update the right ptr in the predecessor ,and left ptr in the successor with the new_node.
        predecessor.map(|pred_node| unsafe{
            //FIXME
            let pred_node = &(*pred_node) as *const TrieNode<T> as *mut TrieNode<T>;
            new_node.map(|node| {
                (*node.as_ptr()).right = (*pred_node).right;
                (*node.as_ptr()).left = NonNull::new(pred_node);
            });
            (*pred_node).right = new_node;
        });

        successor.map(|suc_node| unsafe{
            let suc_node = &(*suc_node) as *const TrieNode<T> as *mut TrieNode<T>;
            new_node.map(|node| {
                (*node.as_ptr()).left = (*suc_node).left;
                (*node.as_ptr()).right = NonNull::new(suc_node);
            });
            (*suc_node).left = new_node;
        });

        //populate intermediate iternal nodes on the path down the new_node
        self.populate_internal_nodes(key);
        
        //insert the new_node at the last level and update the ptr of its parent node using the prefix bit
        self.level_maps[self.nr_levels].insert(key, new_node.unwrap());
        let temp_key = key >> 1;
        self.level_maps[self.nr_levels-1].get(&temp_key).map(|&value| unsafe {
            if (key & 1) != 0 {
                (*value.as_ptr()).right= new_node;
                (*value.as_ptr()).is_desc_right = false;
            }
            else {
                (*value.as_ptr()).left = new_node;
                (*value.as_ptr()).is_desc_left = false;
            }
        });

        // update descendant ptrs
        self.update_descendant_ptr(key);
    }

    fn delete_internal_node(&mut self, key: usize) {
        let mut level = self.nr_levels-1;
        let mut prefix = key;
        let mut child_prefix = key;

        while level > 0 {
            prefix = prefix >> 1;
            if let Some(internal_node) = self.level_maps[level].get(&prefix) {
                unsafe {
                    //check if it has a descendant node
                    if (child_prefix &1) == 1 {
                        //check left node
                        if !(*internal_node.as_ptr()).is_desc_left {
                            break;
                        }
                    }
                    else if !(*internal_node.as_ptr()).is_desc_right {
                            break;
                    }
                }
            }
                    
            let parent_prefix = prefix >> 1;
            self.level_maps[level-1].get(&parent_prefix).map(|parent_node| unsafe{
                //node present in right subtree
                if (prefix & 1) != 0 {
                    (*parent_node.as_ptr()).right = None;
                    (*parent_node.as_ptr()).is_desc_right = true;
                }
                else {
                    (*parent_node.as_ptr()).left = None;
                    (*parent_node.as_ptr()).is_desc_left = true;
                }
            });
            self.level_maps[level].remove(&prefix);
            child_prefix = child_prefix>>1;
            level -= 1;
        }
    }

    /// Delete a key from the trie. If the node doesn't exist it returns None else retuns the deleted   `TrieNode` wrapped in a `NonNull` struct.
    /// # Examples
    ///  ```
    ///     use xfast::Xfast;
    ///
    ///     let mut test_trie: Xfast<&str> = Xfast::new(31);
    ///     test_trie.insert_key(11, "eleven");
    ///     test_trie.insert_key(1, "one");
    ///     test_trie.insert_key(5, "five");
    ///     assert_eq!(test_trie.len(), 3);
    ///        
    ///     test_trie.delete_key(5);
    ///     assert_eq!(test_trie.len(), 2);
    ///     assert!(test_trie.delete_key(2).is_none());
    ///     assert_eq!(test_trie.len(), 2);
    /// ```
    pub fn delete_key(&mut self, key: usize) -> Option<Node<T>>{
        //find the key in the lowest level
        let deleted_node = self.find_key_as_non_null(key);
        if deleted_node.is_none() {
            return None;
        }

        let deleted_node = deleted_node.unwrap();
        
        self.level_maps[self.nr_levels-1].get(&(key>>1)).map(|internal_node| unsafe{
            if (key &1) == 1 {
                (*internal_node.as_ptr()).right = None;
                (*internal_node.as_ptr()).is_desc_right = true;
            }
            else {
                (*internal_node.as_ptr()).left = None;
                (*internal_node.as_ptr()).is_desc_left = true;
            }
        });
        
        self.delete_internal_node(key);
        unsafe {
            let predecessor_node = (*deleted_node.as_ptr()).left;
            let successor_node = (*deleted_node.as_ptr()).right;
            
            if !predecessor_node.is_none() {
                (*predecessor_node.unwrap().as_ptr()).right = successor_node;
            }
            if !successor_node.is_none() {

                (*successor_node.unwrap().as_ptr()).left = predecessor_node;
            }
        }
        let deleted_node = self.level_maps[self.nr_levels].remove(&key);
        self.update_descendant_ptr(key);
        deleted_node
    }

    fn find_key_as_non_null(&self, key: usize) -> Option<Node<T>> {
        self.level_maps[self.nr_levels].get(&key).map(|&value| {
            value
        })
    }

    /// Find a key in the trie
    /// # Examples
    ///  ```
    ///     use xfast::Xfast;
    ///
    ///     let mut test_trie: Xfast<&str> = Xfast::new(31);
    ///     test_trie.insert_key(11, "eleven");
    ///     test_trie.insert_key(1, "one");
    ///     if let Some(node_1) = test_trie.find_key(1) {
    ///         // all the leaf nodes values have non trivial values and assert is_some. 
    ///         // So unwrapping will not panic
    ///         assert_eq!(node_1.value.unwrap(), "one");
    ///     }
    /// ```
    pub fn find_key(&self, key: usize) -> Option<&TrieNode<T>> {
        self.level_maps[self.nr_levels].get(&key).map(|&value| unsafe {
            &(*value.as_ptr())
        })
    }

    /// Returns an iterator around all the key-TrieNode pairs stored in the trie.
    /// # Examples
    /// ```
    ///     use xfast::Xfast;
    ///
    ///     let mut test_trie: Xfast<&str> = Xfast::new(31);
    ///     test_trie.insert_key(11, "eleven");
    ///     test_trie.insert_key(1, "one");
    ///     test_trie.insert_key(19, "nineteen");
    ///     for (key, node) in test_trie.iter() {
    ///         println!("key: {} value: {:?}", key, node);
    ///     }
    /// ```
    pub fn iter(&self) -> XfastIter<T> {
        let leaf_map = &self.level_maps[self.nr_levels];
        let mut keys: Vec<usize> = vec!();
        
        for &cur_key in leaf_map.keys() {
            keys.push(cur_key);
        }

        XfastIter {
            leaf_map,
            keys,
            index: 0,
        }
    }

    /// Returns a mutable iterator around all the key-TrieNode pairs stored in the trie.
    /// # Examples
    /// ```
    ///     use xfast::Xfast;
    ///
    ///     let mut test_trie: Xfast<&str> = Xfast::new(31);
    ///     test_trie.insert_key(11, "eleven");
    ///     test_trie.insert_key(1, "one");
    ///     test_trie.insert_key(19, "nineteen");
    ///     for (key, node) in test_trie.iter_mut() {
    ///         if key % 2 == 1 {
    ///             node.value = Some("updated_odd");    
    ///         }
    ///     }
    ///
    ///     if let Some(node_1) = test_trie.find_key(1) {
    ///         assert_eq!(node_1.value.unwrap(), "updated_odd");
    ///     }
    /// ```
    pub fn iter_mut(&mut self) -> XfastIterMut<T> {
        let leaf_map = &self.level_maps[self.nr_levels];
        let mut keys: Vec<usize> = vec!();
        
        for &cur_key in leaf_map.keys() {
            keys.push(cur_key);
        }

        XfastIterMut {
            leaf_map,
            keys,
            index: 0,
        }
    }
}

/// Iterator around the Xfast key and value (TrieNode) pairs

pub struct XfastIter<'a, T> {
    leaf_map: &'a HashMap<usize, Node<T>>,
    keys: Vec<usize>,
    index: usize,
}

impl<'a, T> Iterator for XfastIter<'a, T> {
    type Item = (&'a usize, &'a TrieNode<T>);

    fn next(&mut self) -> Option<Self::Item> {
        if self.index < self.leaf_map.len() {
            let key = self.keys[self.index];
            self.index += 1;
            let kv_pair = self.leaf_map.get_key_value(&key);
            kv_pair.map(|(key, value)| unsafe{
                let value = value.as_ref();
                (key, value)
            })
        }
        else {
            None
        }
    }
}

/// Mutable Iterator around the Xfast key and value (TrieNode) pairs
pub struct XfastIterMut<'a, T> {
    leaf_map: &'a HashMap<usize, Node<T>>,
    keys: Vec<usize>,
    index: usize,
}

impl<'a, T> Iterator for XfastIterMut<'a, T> {
    type Item = (&'a usize, &'a mut TrieNode<T>);

    fn next(&mut self) -> Option<Self::Item> {
        if self.index < self.leaf_map.len() {
            let key = self.keys[self.index];
            self.index += 1;
            let kv_pair = self.leaf_map.get_key_value(&key);
            kv_pair.map(|(key, value)| unsafe{
                let value = &mut (*value.as_ptr());
                (key, value)
            })
        }
        else {
            None
        }
    }
}

impl<'a, T> IntoIterator for &'a Xfast<T> {
    type Item = (&'a usize, &'a TrieNode<T>);
    type IntoIter = XfastIter<'a, T>;
    fn into_iter(self) -> XfastIter<'a, T> {
        self.iter()
    }
}



mod test{
    use super::Xfast;

    fn init()  -> Xfast<String> {
        let mut test_trie: Xfast<String> = Xfast::new(31);
        test_trie.insert_key(11, String::from("eleven"));
        test_trie.insert_key(1, String::from("one"));
        test_trie.insert_key(18, String::from("eighteen"));
        test_trie.insert_key(5, String::from("five"));
        test_trie
    }

    #[test]
    fn successor() -> Result<(), String> {
        let test_trie = init();
        if let Some(successor) = test_trie.find_successor(7) {
            if successor.key == 11 {
                return Ok(())
            }
        }
        Err(String::from("Successor of 7 is wrong"))
    }

    #[test]
    fn none_successor() -> Result<(), String> {
        let test_trie = init();
        if test_trie.find_successor(19).is_none() {
            Ok(())
        }
        else {
            Err(String::from("Successor of 19 is wrong"))
        }
    }

    #[test]
    fn predecessor() -> Result<(), String> {
        let test_trie = init();
        if let Some(predecessor) = test_trie.find_predecessor(8) {
            if predecessor.key == 5 {
                return Ok(())
            }
        }
        Err(String::from("Predecessor of 8 is wrong"))
    }

    #[test]
    fn none_predecessor() -> Result<(), String> {
        let test_trie = init();
        if test_trie.find_predecessor(0).is_none() {
            Ok(())
        }
        else {
            Err(String::from("Predecessor of 1 is wrong"))
        }
    }

    #[test]
    fn find_key_present() -> Result<(), String> {
        let test_trie = init();
        if let Some(value) = test_trie.find_key(11) {
            if value.key == 11 {
                    return Ok(());
            }
        }
        Err(String::from("Key should have been present"))
    }

    #[test]
    fn find_key_not_present() -> Result<(), String> {
        let test_trie = init();
        if test_trie.find_key(7).is_none() {
            return Ok(());
        }
        Err(String::from("Key should not have been present"))
    }

    #[test]
    fn delete_node() -> Result<(), String> {
        let mut test_trie = init();
        test_trie.delete_key(18);
        if test_trie.find_key(18).is_none() {
            Ok(())
        }
        else {
            Err(String::from("Key should have been deleted"))
        }   
    }

    #[test]
    fn successor_after_del() -> Result<(), String> {
        let mut test_trie = init();
        test_trie.delete_key(18);
        if test_trie.find_successor(18).is_none() {
            Ok(())
        }
        else {
            Err(String::from("Successor of 18 is wrong"))
        }
    }

    #[test]
    fn predecessor_after_del() -> Result<(), String> {
        let mut test_trie = init();
        test_trie.delete_key(18);
        if let Some(predecessor) = test_trie.find_predecessor(18) {
            if predecessor.key == 11 {
                return Ok(());
            }
        }
        Err(String::from("Successor of 18 is wrong"))
    }

    #[test]
    fn deleting_non_existent() -> Result<(), String> {
        let mut test_trie = init();
        if test_trie.delete_key(19).is_none() {
            Ok(())
        }
        else {
            Err(String::from("The deleted node didn't exist!!"))
        }
    }
}