Encoding Error
2020-12-09
Day 09: Encoding Error
--- Day 9: Encoding Error ---
With your neighbor happily enjoying their video game, you turn your attention to an open data port on the little screen in the seat in front of you.
Though the port is non-standard, you manage to connect it to your computer through the clever use of several paperclips. Upon connection, the port outputs a series of numbers (your puzzle input).
The data appears to be encrypted with the eXchange-Masking Addition System (XMAS) which, conveniently for you, is an old cypher with an important weakness.
XMAS starts by transmitting a preamble of 25 numbers. After that, each number you receive should be the sum of any two of the 25 immediately previous numbers. The two numbers will have different values, and there might be more than one such pair.
For example, suppose your preamble consists of the numbers 1 through 25 in a random order. To be valid, the next number must be the sum of two of those numbers:
26 would be a valid next number, as it could be 1 plus 25 (or many other pairs, like 2 and 24).
49 would be a valid next number, as it is the sum of 24 and 25.
100 would not be valid; no two of the previous 25 numbers sum to 100.
50 would also not be valid; although 25 appears in the previous 25 numbers, the two numbers in the pair must be different.
Suppose the 26th number is 45, and the first number (no longer an option, as it is more than 25 numbers ago) was 20. Now, for the next number to be valid, there needs to be some pair of numbers among 1-19, 21-25, or 45 that add up to it:
26 would still be a valid next number, as 1 and 25 are still within the previous 25 numbers.
65 would not be valid, as no two of the available numbers sum to it.
64 and 66 would both be valid, as they are the result of 19+45 and 21+45 respectively.
Here is a larger example which only considers the previous 5 numbers (and has a preamble of length 5):
35
20
15
25
47
40
62
55
65
95
102
117
150
182
127
219
299
277
309
576
In this example, after the 5-number preamble, almost every number is the sum of two of the previous 5 numbers; the only number that does not follow this rule is 127.
The first step of attacking the weakness in the XMAS data is to find the first number in the list (after the preamble) which is not the sum of two of the 25 numbers before it. What is the first number that does not have this property?
--- Part Two ---
The final step in breaking the XMAS encryption relies on the invalid number you just found: you must find a contiguous set of at least two numbers in your list which sum to the invalid number from step 1.
Again consider the above example:
35
20
15
25
47
40
62
55
65
95
102
117
150
182
127
219
299
277
309
576
In this list, adding up all of the numbers from 15 through 40 produces the invalid number from step 1, 127. (Of course, the contiguous set of numbers in your actual list might be much longer.)
To find the encryption weakness, add together the smallest and largest number in this contiguous range; in this example, these are 15 and 47, producing 62.
What is the encryption weakness in your XMAS-encrypted list of numbers?
With your neighbor happily enjoying their video game, you turn your attention to an open data port on the little screen in the seat in front of you.
Though the port is non-standard, you manage to connect it to your computer through the clever use of several paperclips. Upon connection, the port outputs a series of numbers (your puzzle input).
The data appears to be encrypted with the eXchange-Masking Addition System (XMAS) which, conveniently for you, is an old cypher with an important weakness.
XMAS starts by transmitting a preamble of 25 numbers. After that, each number you receive should be the sum of any two of the 25 immediately previous numbers. The two numbers will have different values, and there might be more than one such pair.
For example, suppose your preamble consists of the numbers 1 through 25 in a random order. To be valid, the next number must be the sum of two of those numbers:
26 would be a valid next number, as it could be 1 plus 25 (or many other pairs, like 2 and 24).
49 would be a valid next number, as it is the sum of 24 and 25.
100 would not be valid; no two of the previous 25 numbers sum to 100.
50 would also not be valid; although 25 appears in the previous 25 numbers, the two numbers in the pair must be different.
Suppose the 26th number is 45, and the first number (no longer an option, as it is more than 25 numbers ago) was 20. Now, for the next number to be valid, there needs to be some pair of numbers among 1-19, 21-25, or 45 that add up to it:
26 would still be a valid next number, as 1 and 25 are still within the previous 25 numbers.
65 would not be valid, as no two of the available numbers sum to it.
64 and 66 would both be valid, as they are the result of 19+45 and 21+45 respectively.
Here is a larger example which only considers the previous 5 numbers (and has a preamble of length 5):
35
20
15
25
47
40
62
55
65
95
102
117
150
182
127
219
299
277
309
576
In this example, after the 5-number preamble, almost every number is the sum of two of the previous 5 numbers; the only number that does not follow this rule is 127.
The first step of attacking the weakness in the XMAS data is to find the first number in the list (after the preamble) which is not the sum of two of the 25 numbers before it. What is the first number that does not have this property?
--- Part Two ---
The final step in breaking the XMAS encryption relies on the invalid number you just found: you must find a contiguous set of at least two numbers in your list which sum to the invalid number from step 1.
Again consider the above example:
35
20
15
25
47
40
62
55
65
95
102
117
150
182
127
219
299
277
309
576
In this list, adding up all of the numbers from 15 through 40 produces the invalid number from step 1, 127. (Of course, the contiguous set of numbers in your actual list might be much longer.)
To find the encryption weakness, add together the smallest and largest number in this contiguous range; in this example, these are 15 and 47, producing 62.
What is the encryption weakness in your XMAS-encrypted list of numbers?
Input:
50
32
17
18
6
12
24
43
14
40
15
25
19
22
44
41
30
21
7
31
35
38
28
46
1
34
64
13
27
29
8
57
20
9
10
26
11
15
12
75
16
37
73
14
25
39
17
18
19
21
30
38
22
42
23
24
27
32
91
83
98
26
28
29
47
53
33
55
31
41
35
36
37
44
43
67
45
73
72
56
100
59
70
86
54
95
57
60
62
74
107
76
66
68
71
81
79
99
87
151
114
104
166
110
155
113
111
116
178
117
125
119
180
128
134
182
137
283
187
150
196
183
197
191
306
280
405
223
221
224
297
235
504
236
267
330
247
271
494
320
324
287
333
371
341
459
374
471
412
456
444
511
522
518
460
558
610
795
483
571
612
644
591
607
611
835
1088
793
834
715
786
1344
856
872
900
1093
1029
943
1738
1178
1041
1384
1054
1074
1235
1198
1202
1322
1218
1326
2247
1627
1571
2135
1587
1729
1728
1843
2629
3519
2328
1972
1984
2095
2115
2128
2256
2252
2272
2400
3450
3618
2540
2789
2913
3158
3198
3315
3712
3559
3457
4067
4240
4351
3956
4761
4079
6856
4210
4243
5286
4508
4652
7850
11300
9396
6772
5329
6655
6071
11806
7438
6874
7016
7769
7413
13179
8035
8307
11623
14068
10734
12012
8718
10579
9160
11424
15932
15473
13098
16176
11400
11984
18147
13087
13890
14454
15592
19435
15182
20319
16342
16753
22786
21805
17878
29927
20560
19297
34209
20584
22824
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43384
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23384
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26438
57838
26977
33060
29636
40079
31524
34479
61884
33095
34631
37175
44855
38438
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42121
43408
43968
47311
47871
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62925
49822
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72917
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100581
131461
91279
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97693
106435
123120
147892
118573
115114
179352
126075
132193
132345
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144782
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251217
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212807
221549
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263355
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32
17
18
6
12
24
43
14
40
15
25
19
22
44
41
30
21
7
31
35
38
28
46
1
34
64
13
27
29
8
57
20
9
10
26
11
15
12
75
16
37
73
14
25
39
17
18
19
21
30
38
22
42
23
24
27
32
91
83
98
26
28
29
47
53
33
55
31
41
35
36
37
44
43
67
45
73
72
56
100
59
70
86
54
95
57
60
62
74
107
76
66
68
71
81
79
99
87
151
114
104
166
110
155
113
111
116
178
117
125
119
180
128
134
182
137
283
187
150
196
183
197
191
306
280
405
223
221
224
297
235
504
236
267
330
247
271
494
320
324
287
333
371
341
459
374
471
412
456
444
511
522
518
460
558
610
795
483
571
612
644
591
607
611
835
1088
793
834
715
786
1344
856
872
900
1093
1029
943
1738
1178
1041
1384
1054
1074
1235
1198
1202
1322
1218
1326
2247
1627
1571
2135
1587
1729
1728
1843
2629
3519
2328
1972
1984
2095
2115
2128
2256
2252
2272
2400
3450
3618
2540
2789
2913
3158
3198
3315
3712
3559
3457
4067
4240
4351
3956
4761
4079
6856
4210
4243
5286
4508
4652
7850
11300
9396
6772
5329
6655
6071
11806
7438
6874
7016
7769
7413
13179
8035
8307
11623
14068
10734
12012
8718
10579
9160
11424
15932
15473
13098
16176
11400
11984
18147
13087
13890
14454
15592
19435
15182
20319
16342
16753
22786
21805
17878
29927
20560
19297
34209
20584
22824
28326
43384
44502
23384
24487
26438
57838
26977
33060
29636
40079
31524
34479
61884
33095
34631
37175
44855
38438
39857
39881
42121
43408
43968
47311
47871
76379
62925
49822
74848
60072
56613
58501
72917
109474
86089
64619
67574
67726
72976
71806
98510
78295
79738
81978
116685
100581
131461
91279
95182
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use crate::common::AdventOfCodeDay;
use std::collections::HashSet;
pub struct Day09 {
input: Vec<u64>,
}
impl Day09 {
pub fn new() -> Self {
let input_bytes = include_bytes!("../res/09_input.txt");
let input_str = String::from_utf8_lossy(input_bytes);
let data = input_str
.lines()
.map(|p| p.parse::<u64>().unwrap())
.collect::<Vec<u64>>();
Self {
input: data
}
}
fn all_combinations(data: Vec<&u64>) -> HashSet<u64> {
let mut hs: HashSet<u64> = HashSet::new();
for i1 in 0..24 {
for i2 in (i1+1)..25 {
hs.insert(data[i1] + data[i2]);
}
}
return hs;
}
fn find_invalid(&self) -> u64 {
for i in 25..self.input.len() {
let comb = Day09::all_combinations(self.input.iter().skip(i-25).take(25).collect());
if !comb.contains(&self.input[i]) {
return self.input[i];
}
}
panic!();
}
}
impl AdventOfCodeDay for Day09 {
fn task_1(&self) -> String {
return self.find_invalid().to_string();
}
fn task_2(&self) -> String {
let target = self.find_invalid();
let mut sum = self.input[0];
let mut idx1 = 0; //inclusive
let mut idx2 = 0; //inclusive
loop {
if sum == target {
verboseln!("[{}..{}] [[{:?}]] = {} ({})",
idx1,
idx2,
self.input.iter().skip(idx1).take(idx2-idx1+1).collect::<Vec<&u64>>(),
self.input.iter().skip(idx1).take(idx2-idx1+1).sum::<u64>(),
target);
return (self.input.iter().skip(idx1).take(idx2-idx1+1).min().unwrap() + self.input.iter().skip(idx1).take(idx2-idx1+1).max().unwrap()).to_string();
} else if sum < target {
idx2 += 1;
sum += self.input[idx2];
} else if sum > target {
sum -= self.input[idx1];
idx1 += 1;
}
verboseln!("[{}..{}] = {}", idx1, idx2, sum);
}
}
}Result Part 1: 69316178
Result Part 2: 9351526