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
// # Definition
// NatNums are defined by:
// 0 = {}
// n = (n-1) U {n-1} 
// or an easier but kinda wrong definition:
// n = {{}, {n-1}}
//
// ## examples:
//
// 0 = {}
// NatNum::Zero
// 1 = { {} }
// NatNum::Mult([NatNum::Zero])
// 2 = { {}, { {} } }
// NatNum::Mult([NatNum::Zero, NatNum::Mult([NatNum::Zero])])
// 3 = { {}, { {} }, { {}, { {} } } }
// NatNum::Mult([NatNum::Zero, NatNum::Mult([NatNum::Zero]), NatNum::Mult([NatNum::Zero, NatNum::Mult([NatNum::Zero])])
//
// TODO: maybe change Vec<NatNum> to an array when const generics hit stable, to avoid heap allocations and potential runtime costs.
//
#[derive(PartialEq, Debug, Clone)]
pub enum NatNum {
    Zero,
    Mult(Vec<NatNum>),
}

impl NatNum {
    pub fn to_number(&self) -> u32 {
        match self {
            NatNum::Zero => return 0,
            NatNum::Mult(nat_num) => return simple_nat_to_num(nat_num),
        }
    }

    /// a recursive adder for two NatNumbers / Nat Trees
    pub fn add_rec(&self, other: &NatNum) -> NatNum {
        // check if one of the numbers represents 0, if so return the other.
        // if both are 0 num2 is always returned but this doesn't matter.
        match &self {
            NatNum::Zero => return other.clone(),
            NatNum::Mult(tree1) => {
                match other {
                    NatNum::Zero => return self.clone(),
                    NatNum::Mult(tree2) => {
                        // compare the 'size' of both trees (their actual value)
                        // to do the cheaper computation
                        if tree1.len() >= tree2.len() {
                            let mut tree_data = tree1.clone();
                            recursive_nat_tree_increment(&mut tree_data, tree2.len() as u32);
                            return NatNum::Mult(tree_data)
                        } else {
                            let mut tree_data = tree2.clone();
                            recursive_nat_tree_increment(&mut tree_data, tree1.len() as u32);
                            return NatNum::Mult(tree_data)
                        }
                    }
                }
            }
        }
    }

    // TODO: Write a Tree to Number parser.
    pub fn to_number_checked(&self) -> u32 {
        unimplemented!()
    }

    pub fn to_string(&self) -> String {
        match self {
            NatNum::Zero => String::from("{}"),
            NatNum::Mult(tree) => {
                let mut graph = String::from("{}\n");
                recursive_nat_tree_to_string_simple(tree, &mut graph, 0);
                graph
            }
        }
    }
}

impl From<u32> for NatNum {
    fn from(num: u32) -> NatNum {
        if num == 0 {
            return NatNum::Zero
        }
        let mut nat_num_data: Vec<NatNum> = Vec::new();
        populate_nat_tree(&mut nat_num_data, num);
        let nat_num = NatNum::Mult(nat_num_data);

        nat_num
    }
}


/// returns the count of the elements
/// doesn't check the 'correctness of the tree' / 'Wohlfundierung'
fn simple_nat_to_num(num: &Vec<NatNum>) -> u32 {
    return num.len() as u32;
}


/// recursively populates a vector with a tree like structure of NatNumbers
/// curr: remaining iterations for each tree / subtree
/// it works by subtracting -1 from 'curr' in each iteration
/// than it looks for these cases:
/// curr = 0 => stop iteration e.g tree is fully populated
/// curr = 1 => Add a NatNum::Zero
/// curr = _ => Add a new subtree and recursively populates it (same function)
fn populate_nat_tree(tree: &mut Vec<NatNum>, curr: u32) {
    match curr {
        0 => return,
        1 => {
            tree.insert(0,NatNum::Zero);
            populate_nat_tree(tree, curr - 1);
        },
        _ => {
            let mut sub_tree_data = Vec::new();
            populate_nat_tree(&mut sub_tree_data, curr - 1);
            let sub_tree = NatNum::Mult(sub_tree_data);
            tree.insert(0,sub_tree);
            populate_nat_tree(tree, curr - 1)
        },
    }
}

// copies itself and pushes itself into itself as a new subtree 
fn recursive_nat_tree_increment(tree: &mut Vec<NatNum>, rem: u32) {
    if rem == 0 {
        return;
    }
    let new_subtree = tree.clone();
    let end_num = NatNum::Mult(new_subtree);
    tree.push(end_num);
    recursive_nat_tree_increment(tree, rem - 1)
}

// creates a string from the tree with intonations for each Subtree
// tree: vector of a natnum
// graph: String that should be manipulated
// level: current subtree level, used for intonation
fn recursive_nat_tree_to_string_simple(tree: &Vec<NatNum>, graph: &mut String, level: u32) {
    for x in tree {
        match x {
            NatNum::Zero => {
                graph.push_str(&format!("{}{{}}\n", simple_graph_intonation(level)));
            }
            NatNum::Mult(subtree) => {
                graph.push_str(&format!("{}{{}}\n", simple_graph_intonation(level)));
                recursive_nat_tree_to_string_simple(subtree, graph, level + 1)
            }
        }
    }
}

// example:
//
// |-> {}
// |-> {}
// |   |-> {}
fn simple_graph_intonation(level: u32) -> String {
    let mut intonation = String::new();
    intonation.push_str("|");
    for _ in 0..level {
        intonation.push_str("  |");
    }
    intonation.push_str("->");
    intonation
}

// TESTS
#[cfg(test)]
mod test {
    use super::*;

    #[test]
    fn create_zero() {
        let num = NatNum::Zero;
        assert_eq!(num.to_number(), 0);
    }

    #[test]
    fn create_one() {
        let num = NatNum::Mult(vec![NatNum::Zero]);
        assert_eq!(num.to_number(), 1)
    }

    #[test]
    fn create_two() {
        let num = NatNum::Mult(vec![NatNum::Zero, NatNum::Mult(vec![NatNum::Zero])]);
        assert_eq!(num.to_number(), 2)
    }

    #[test]
    #[rustfmt::skip]
    fn create_three() {
        let num = NatNum::Mult(vec![
            NatNum::Zero,
            NatNum::Mult(vec![
                NatNum::Zero
                ]),
            NatNum::Mult(vec![
                NatNum::Zero,
                NatNum::Mult(vec![
                    NatNum::Zero
                    ])
                ]),
            ]);

        assert_eq!(num.to_number(), 3)
    }

    #[test]
    fn from_zero() {
        let num = NatNum::from(0);
        assert_eq!(num, NatNum::Zero);
        assert_eq!(num.to_number(), 0);
    }

    #[test]
    fn from_one() {
        let num = NatNum::from(1);
        assert_eq!(num, NatNum::Mult(vec![NatNum::Zero]));
        assert_eq!(num.to_number(), 1);
    }

    #[test]
    #[rustfmt::skip]
    fn from_two() {
        let num = NatNum::from(2);
        assert_eq!(num, NatNum::Mult(vec![
            NatNum::Zero,
            NatNum::Mult(vec![
                NatNum::Zero
                ])
            ]));
        assert_eq!(num.to_number(), 2);
    }

    #[test]
    #[rustfmt::skip]
    fn from_three() {
        let num = NatNum::from(3);
        assert_eq!(num, NatNum::Mult(vec![
            NatNum::Zero,
            NatNum::Mult(vec![
                NatNum::Zero
                ]),
            NatNum::Mult(vec![
                NatNum::Zero,
                NatNum::Mult(vec![
                    NatNum::Zero
                    ])
            ])
        ]));
    }

    #[test]
    #[rustfmt::skip]
    fn from_four() {
        let num = NatNum::from(4);
        assert_eq!(num, NatNum::Mult(vec![
            NatNum::Zero,
            NatNum::Mult(vec![
                NatNum::Zero
                ]),
            NatNum::Mult(vec![
                NatNum::Zero,
                NatNum::Mult(vec![
                    NatNum::Zero
                    ])
            ]),
            NatNum::Mult(vec![
                NatNum::Zero,
                NatNum::Mult(vec![
                    NatNum::Zero
                    ]),
                NatNum::Mult(vec![
                    NatNum::Zero,
                    NatNum::Mult(vec![
                        NatNum::Zero
                        ])
                ])
            ])
        ]));
    }

    #[test]
    fn add_zeros() {
        let num1 = NatNum::from(0);
        let num2 = NatNum::from(0);
        let num3 = NatNum::from(2);

        assert_eq!(num1.add_rec(&num2), NatNum::from(0));
        assert_eq!(num1.add_rec(&num3), NatNum::from(2));
        assert_eq!(num3.add_rec(&num1), NatNum::from(2));
    }

    #[test]
    fn add_non_zero() {
        let num1 = NatNum::from(1);
        let num2 = NatNum::from(2);
        let num3 = NatNum::from(3);

        assert_eq!(num1.add_rec(&num2), NatNum::from(3));
        assert_eq!(num2.add_rec(&num2), NatNum::from(4));
        assert_eq!(num3.add_rec(&num2), NatNum::from(5));
    }
    
    #[test]
    fn prints() {
        let num0 = NatNum::from(0);
        let num1 = NatNum::from(1);
        let num4 = NatNum::from(4);
        assert_eq!(num0.to_string(), "{}");
        assert_eq!(num1.to_string(), "{}\n|->{}\n");
        assert_eq!(num4.to_string(), "{}\n|->{}\n|->{}\n|  |->{}\n|->{}\n|  |->{}\n|  |->{}\n|  |  |->{}\n|->{}\n|  |->{}\n|  |->{}\n|  |  |->{}\n|  |->{}\n|  |  |->{}\n|  |  |->{}\n|  |  |  |->{}\n");
        
    }
}