2020-12-16

# Day 16: Ticket Translation

Description:
As you're walking to yet another connecting flight, you realize that one of the legs of your re-routed trip coming up is on a high-speed train. However, the train ticket you were given is in a language you don't understand. You should probably figure out what it says before you get to the train station after the next flight.

Unfortunately, you can't actually read the words on the ticket. You can, however, read the numbers, and so you figure out the fields these tickets must have and the valid ranges for values in those fields.

You collect the rules for ticket fields, the numbers on your ticket, and the numbers on other nearby tickets for the same train service (via the airport security cameras) together into a single document you can reference (your puzzle input).

The rules for ticket fields specify a list of fields that exist somewhere on the ticket and the valid ranges of values for each field. For example, a rule like class: 1-3 or 5-7 means that one of the fields in every ticket is named class and can be any value in the ranges 1-3 or 5-7 (inclusive, such that 3 and 5 are both valid in this field, but 4 is not).

Each ticket is represented by a single line of comma-separated values. The values are the numbers on the ticket in the order they appear; every ticket has the same format. For example, consider this ticket:

.--------------------------------------------------------.
| ????: 101 ?????: 102 ??????????: 103 ???: 104 |
| |
| ??: 301 ??: 302 ???????: 303 ??????? |
| ??: 401 ??: 402 ???? ????: 403 ????????? |
'--------------------------------------------------------'

Here, ? represents text in a language you don't understand. This ticket might be represented as 101,102,103,104,301,302,303,401,402,403; of course, the actual train tickets you're looking at are much more complicated. In any case, you've extracted just the numbers in such a way that the first number is always the same specific field, the second number is always a different specific field, and so on - you just don't know what each position actually means!

Start by determining which tickets are completely invalid; these are tickets that contain values which aren't valid for any field. Ignore your ticket for now.

For example, suppose you have the following notes:

class: 1-3 or 5-7
row: 6-11 or 33-44
seat: 13-40 or 45-50

7,1,14

nearby tickets:
7,3,47
40,4,50
55,2,20
38,6,12

It doesn't matter which position corresponds to which field; you can identify invalid nearby tickets by considering only whether tickets contain values that are not valid for any field. In this example, the values on the first nearby ticket are all valid for at least one field. This is not true of the other three nearby tickets: the values 4, 55, and 12 are are not valid for any field. Adding together all of the invalid values produces your ticket scanning error rate: 4 + 55 + 12 = 71.

Consider the validity of the nearby tickets you scanned. What is your ticket scanning error rate?

--- Part Two ---

Now that you've identified which tickets contain invalid values, discard those tickets entirely. Use the remaining valid tickets to determine which field is which.

Using the valid ranges for each field, determine what order the fields appear on the tickets. The order is consistent between all tickets: if seat is the third field, it is the third field on every ticket, including your ticket.

For example, suppose you have the following notes:

class: 0-1 or 4-19
row: 0-5 or 8-19
seat: 0-13 or 16-19

11,12,13

nearby tickets:
3,9,18
15,1,5
5,14,9

Based on the nearby tickets in the above example, the first position must be row, the second position must be class, and the third position must be seat; you can conclude that in your ticket, class is 12, row is 11, and seat is 13.

Once you work out which field is which, look for the six fields on your ticket that start with the word departure. What do you get if you multiply those six values together?

Input:
departure location: 42-322 or 347-954
departure station: 49-533 or 555-966
departure platform: 28-86 or 101-974
departure track: 50-150 or 156-950
departure date: 30-117 or 129-957
departure time: 31-660 or 678-951
arrival location: 26-482 or 504-959
arrival station: 29-207 or 220-971
arrival platform: 28-805 or 829-964
arrival track: 48-377 or 401-964
class: 28-138 or 145-959
duration: 33-182 or 205-966
price: 25-437 or 449-962
route: 41-403 or 428-968
row: 33-867 or 880-960
seat: 40-921 or 930-955
train: 47-721 or 732-955
type: 33-243 or 265-964
wagon: 31-756 or 768-973
zone: 50-690 or 713-967

67,107,59,79,53,131,61,101,71,73,137,109,157,113,173,103,83,167,149,163

nearby tickets:
179,948,890,368,224,849,508,533,931,918,864,792,592,356,895,62,540,744,902,559
363,432,890,266,55,794,624,60,732,756,325,508,167,70,593,477,906,865,572,889
682,482,782,319,82,269,837,205,638,509,316,885,66,240,144,105,181,370,565,366
231,859,362,313,941,210,434,105,801,354,137,524,908,237,578,778,80,837,181,241
148,106,604,76,746,568,625,682,713,619,987,802,783,741,625,376,888,619,133,359
765,834,830,713,638,621,55,858,682,740,283,648,148,641,319,934,58,635,178,934
520,582,467,608,63,205,562,705,608,463,638,347,855,920,167,565,803,833,638,240
838,829,279,69,568,685,615,306,756,716,786,606,172,886,592,792,461,234,707,741
754,457,917,896,612,509,7,633,841,780,275,364,791,562,294,908,863,111,286,598
68,932,770,61,752,852,610,357,651,838,532,915,307,459,76,620,799,878,651,504
356,474,102,588,611,602,995,354,894,889,312,173,67,781,783,461,606,434,513,569
778,160,480,229,472,888,621,231,792,177,72,529,678,166,293,309,230,147,544,157
236,401,572,927,829,580,739,243,660,863,279,470,880,312,902,624,271,316,947,529
784,77,233,793,299,915,24,221,51,920,52,651,617,750,288,361,801,680,792,793
361,771,232,452,798,784,265,514,890,457,314,275,232,151,622,742,220,307,104,898
855,289,159,521,735,505,22,585,276,637,309,296,686,231,172,641,864,370,599,846
402,179,564,797,148,460,455,266,266,157,12,272,884,355,801,230,595,66,227,720
481,656,363,273,884,642,241,224,912,765,356,772,163,61,909,242,171,512,768,134
913,840,947,298,131,682,586,567,166,780,322,571,734,608,675,560,740,803,840,57
453,734,981,585,914,577,898,855,656,586,838,231,941,70,105,786,690,169,113,915
172,227,986,904,470,558,175,403,173,635,402,178,930,308,771,104,570,904,506,292
479,432,936,942,772,205,594,518,558,652,57,170,602,253,687,172,557,646,317,945
301,284,148,886,743,468,603,603,579,782,297,313,373,578,638,207,326,832,176,636
575,364,588,768,113,571,899,55,300,692,270,686,115,321,362,510,476,78,657,781
755,273,72,940,318,155,60,779,111,604,370,320,368,156,290,479,281,571,117,831
856,477,126,584,288,751,860,734,912,227,113,900,348,949,561,935,633,653,291,899
845,894,364,78,658,829,782,66,626,454,511,609,319,834,678,507,566,912,390,846
919,733,803,474,648,471,235,457,459,474,525,512,510,896,909,866,154,353,933,292
532,571,563,105,602,305,577,572,136,596,53,910,932,921,147,299,237,218,80,461
640,625,911,846,270,655,719,85,229,895,349,241,736,102,274,739,52,778,656,922
768,795,520,349,716,78,322,366,829,744,775,741,562,629,136,134,743,458,876,904
69,589,55,778,11,241,265,650,292,850,591,563,588,686,842,515,307,575,595,866
607,235,272,451,862,61,562,372,508,776,170,455,299,836,50,549,293,431,836,462
138,781,457,733,371,351,480,372,906,204,620,841,287,431,52,317,181,856,313,689
318,713,790,747,232,220,530,274,841,946,300,855,467,99,735,311,891,176,180,370
403,276,774,116,224,626,306,566,630,145,453,170,796,334,430,587,745,318,635,589
116,163,103,680,571,565,949,835,73,800,804,462,755,482,102,130,365,161,183,582
777,56,332,906,801,634,533,848,61,684,610,920,75,625,772,236,571,466,177,678
768,834,632,783,56,434,643,624,896,311,291,715,372,122,109,163,913,511,598,910
124,629,685,714,508,110,613,64,802,314,132,600,745,172,104,569,914,849,581,310
476,561,842,624,284,70,316,308,115,640,529,708,893,313,793,631,109,458,599,628
915,352,865,831,882,75,561,933,290,224,560,885,82,910,536,221,317,435,283,606
320,832,624,221,164,129,635,518,680,805,831,755,745,781,89,888,830,305,719,220
160,291,108,58,225,786,270,356,892,282,623,363,794,514,885,164,171,468,241,13
563,845,920,76,881,772,867,374,314,453,644,555,932,307,57,773,90,801,459,863
908,611,8,365,690,602,523,358,846,319,747,117,642,51,834,570,921,308,629,290
909,168,631,802,787,354,164,940,888,864,694,294,891,790,798,837,733,610,163,654
685,403,571,851,116,666,64,746,469,904,932,864,932,830,933,617,367,365,294,750
644,935,296,772,306,681,204,80,838,322,851,713,82,579,742,861,171,276,590,508
616,482,911,783,865,355,73,66,306,853,833,463,679,303,456,889,701,148,504,308
74,838,942,755,287,73,299,299,103,268,917,107,631,508,348,401,290,831,151,75
587,129,130,690,922,77,847,732,52,746,640,466,467,358,634,621,681,678,679,105
374,864,531,910,428,896,659,180,51,793,455,651,752,547,304,647,755,473,266,298
280,843,714,592,609,850,436,288,59,481,528,649,74,295,129,715,683,125,796,229
173,222,927,61,591,83,611,270,164,362,461,599,66,837,282,451,55,350,207,149
347,117,687,235,777,584,99,101,518,275,83,563,528,718,883,636,205,168,593,54
308,72,284,243,804,476,589,73,584,932,431,949,111,640,54,347,885,701,846,948
924,374,59,570,633,646,451,468,564,466,556,361,102,591,363,239,646,526,621,575
681,894,470,903,71,631,938,528,610,352,56,174,636,84,208,524,846,165,366,557
513,898,462,903,893,238,556,799,172,720,761,478,563,286,274,838,880,73,315,56
510,54,842,300,784,596,715,854,685,635,225,799,284,688,775,653,862,766,798,158
834,281,776,287,479,841,887,464,474,85,71,518,521,853,347,128,106,596,104,305
791,843,373,456,562,805,146,592,583,66,893,631,756,182,908,872,561,234,618,777
947,207,735,464,601,872,355,67,53,770,749,511,234,281,948,620,347,654,831,893
64,101,570,656,102,361,114,904,268,850,915,639,353,109,478,169,768,892,330,799
282,4,574,180,159,231,348,849,177,854,904,311,660,579,688,105,429,746,781,60
613,166,228,745,768,687,462,785,737,52,880,862,221,468,151,267,530,170,477,596
647,865,914,603,614,587,228,589,76,895,53,732,349,871,230,366,274,628,434,480
645,509,165,533,774,54,801,852,458,401,270,656,555,605,644,150,666,798,636,588
931,896,832,61,592,281,231,865,782,233,157,238,74,899,944,847,608,431,923,302
77,102,145,302,771,463,652,75,477,60,680,480,938,556,865,642,372,684,798,334
944,269,271,618,160,473,319,274,937,223,609,678,233,937,933,129,518,266,105,762
792,847,750,620,181,862,242,937,529,785,750,884,226,84,129,756,829,302,820,180
738,738,689,793,460,730,888,370,940,147,533,645,900,113,103,223,656,721,614,607
403,465,736,57,132,511,590,685,172,513,291,586,178,604,324,748,860,683,278,847
70,773,68,167,706,652,891,890,468,165,229,945,745,364,315,54,461,233,595,740
101,860,908,657,578,462,50,54,648,927,57,745,899,781,752,688,623,112,506,908
162,112,648,891,270,752,363,182,293,293,542,309,751,829,830,240,222,896,932,366
288,636,751,795,275,399,846,507,680,55,681,130,351,935,851,897,360,531,224,111
230,109,996,586,267,804,54,220,949,832,563,921,233,606,304,80,240,601,181,358
86,277,292,476,52,778,898,107,890,374,82,289,168,912,314,21,771,843,436,318
889,460,561,354,750,165,301,355,803,387,689,146,893,610,523,577,354,468,745,532
525,436,481,847,160,594,566,453,893,839,166,508,78,842,633,135,843,748,110,199
741,893,163,906,591,589,713,378,739,946,689,613,311,308,901,778,86,297,531,864
684,303,170,635,504,433,929,605,158,222,570,896,641,587,721,238,207,860,460,80
369,277,634,227,102,605,354,884,684,294,83,766,682,107,557,639,732,569,933,470
105,559,237,459,931,755,428,829,720,653,839,831,992,679,582,163,431,609,278,919
137,358,512,399,842,800,786,660,617,52,648,916,71,626,752,685,293,790,659,586
595,847,657,613,362,834,612,834,747,645,104,6,596,282,506,732,583,737,845,224
903,179,312,678,609,120,934,597,312,473,884,224,456,467,77,858,526,452,355,620
462,609,311,78,771,930,913,433,283,840,640,559,981,609,640,682,61,575,778,228
179,17,74,783,147,403,596,905,478,628,290,520,907,774,267,625,622,912,849,372
611,511,529,745,115,681,58,765,462,163,946,948,72,575,915,234,883,587,77,937
103,775,276,170,364,363,656,178,528,689,128,643,66,173,713,274,55,72,630,891
573,918,561,158,772,450,736,600,564,914,361,617,180,207,228,154,281,473,277,745
858,643,843,136,834,132,800,348,627,403,689,307,75,286,931,294,750,200,505,227
895,630,57,288,295,319,214,162,863,784,354,733,279,646,890,111,467,572,911,562
113,53,276,583,842,323,322,747,368,617,367,462,79,367,859,301,624,293,720,612
527,308,116,430,311,848,223,530,887,563,107,471,652,105,286,881,217,518,241,286
531,402,478,526,146,296,936,942,353,289,87,719,314,804,604,606,905,646,300,74
308,626,943,737,291,520,73,76,853,613,239,164,431,271,505,113,229,328,316,177
904,379,129,945,887,145,773,66,655,916,642,784,80,162,734,855,575,279,276,719
603,518,831,626,207,135,622,800,581,310,76,938,832,837,128,617,349,360,472,792
867,478,605,603,55,802,449,362,660,646,623,515,769,636,163,771,574,547,755,719
1,75,732,453,637,353,86,746,370,130,769,648,60,348,643,531,310,131,453,892
317,60,747,516,586,475,373,604,356,860,465,590,641,764,514,690,659,563,737,567
733,939,771,893,267,200,680,221,590,792,769,61,916,653,362,360,912,855,138,916
940,855,713,85,507,601,674,652,616,283,234,238,567,613,744,627,79,593,66,848
300,114,852,911,736,110,627,8,287,459,652,746,181,849,63,734,746,558,617,156
80,401,619,636,355,912,245,166,656,919,528,623,738,163,794,744,800,844,233,474
700,150,740,785,51,178,576,112,505,115,642,735,240,101,786,578,646,506,367,521
437,472,82,114,316,942,641,101,293,86,991,476,369,429,801,360,792,888,635,458
573,721,233,568,131,720,559,980,861,592,798,180,79,83,773,749,239,312,133,590
947,883,479,657,72,303,772,129,889,864,117,149,892,899,273,465,198,510,180,147
52,476,709,451,939,831,530,53,756,171,147,582,627,376,295,719,601,175,655,790
769,103,572,732,567,984,522,274,894,160,831,370,774,294,592,655,281,525,594,311
478,508,568,241,690,851,324,633,288,890,350,614,846,568,743,135,68,572,781,771
641,227,556,316,573,306,635,300,596,930,18,647,569,596,307,480,637,80,921,162
54,587,304,884,993,934,947,469,375,638,284,772,480,401,314,289,593,347,597,743
718,797,884,364,797,356,930,121,750,797,529,743,520,313,681,566,181,658,457,113
179,557,372,911,133,224,639,620,288,181,116,853,19,375,173,511,598,933,612,243
994,781,579,887,79,829,946,616,352,750,221,377,639,523,583,733,581,598,526,229
630,610,948,278,206,361,945,990,902,510,882,372,830,458,770,838,531,62,238,867
911,619,655,721,660,105,721,854,523,686,946,770,470,283,630,343,917,52,829,138
602,567,580,350,457,223,851,558,888,556,732,85,843,168,626,708,930,146,55,458
831,178,944,106,296,626,521,688,277,602,800,282,353,436,862,817,860,311,556,82
279,602,658,282,897,783,61,566,656,173,479,432,934,357,805,250,460,451,353,854
240,165,829,775,237,241,173,658,299,429,60,189,619,113,583,768,149,265,453,782
843,137,227,702,316,569,857,797,111,779,67,70,681,376,161,770,468,114,531,482
449,881,322,453,631,462,69,734,129,474,481,433,907,316,871,232,319,360,299,915
372,565,136,720,658,894,66,891,557,624,225,381,373,910,274,795,533,777,106,931
940,891,450,105,461,58,574,682,737,322,479,719,734,52,402,285,157,377,67,22
299,916,933,801,101,801,110,453,895,748,165,103,774,558,715,374,461,746,282,539
680,178,107,911,636,656,758,638,521,150,504,619,776,168,276,221,274,582,148,313
159,205,354,517,519,239,525,601,629,586,276,277,773,735,736,311,557,783,314,378
640,74,450,563,829,77,627,607,781,120,84,477,863,270,938,743,801,754,907,639
63,560,173,194,462,746,103,683,797,239,889,515,633,862,279,642,173,644,508,402
175,854,450,804,686,847,408,164,510,372,355,575,269,633,786,274,277,471,306,512
364,433,386,755,102,881,109,885,567,111,734,592,129,451,564,436,129,349,351,457
131,591,646,650,597,476,130,938,471,687,372,524,562,103,264,634,77,148,474,781
293,288,642,931,849,933,994,352,581,373,175,741,320,935,73,319,556,136,788,949
642,791,838,369,689,363,937,80,687,840,480,596,861,589,684,625,363,623,363,123
684,515,862,719,623,297,583,570,593,67,556,797,859,476,699,558,475,753,231,107
234,882,373,647,901,173,729,660,648,515,842,625,611,117,110,936,160,275,776,947
802,360,599,353,526,164,930,836,526,223,172,904,605,896,222,314,53,911,257,845
838,599,839,276,903,889,133,653,947,688,114,897,801,998,559,936,229,169,555,897
465,606,356,370,802,748,156,860,62,103,473,278,482,832,893,995,436,654,598,616
599,129,611,770,303,843,563,751,855,587,593,515,641,647,831,301,586,660,760,81
166,361,775,377,576,575,239,76,768,465,612,750,593,471,157,680,923,239,885,458
299,716,564,504,713,527,797,533,587,605,436,235,138,107,852,791,638,403,121,593
738,505,240,569,149,918,140,656,156,318,631,848,754,278,841,911,599,70,916,55
181,690,278,569,434,838,182,453,855,653,271,597,990,941,533,774,840,746,268,103
60,60,612,752,913,592,689,469,592,686,785,768,278,916,505,656,355,606,890,19
532,355,633,480,135,493,621,157,82,902,75,135,468,302,597,435,900,287,862,901
734,781,891,65,428,740,691,71,66,177,464,558,682,352,571,60,300,571,148,601
687,372,146,464,516,109,549,738,521,135,236,59,314,229,402,918,656,137,921,629
199,453,533,356,296,905,308,629,633,911,369,459,569,587,739,367,899,233,482,112
836,778,136,478,505,657,164,858,947,526,639,273,365,366,785,745,854,398,852,74
625,939,86,243,771,117,119,517,651,66,265,643,66,310,864,310,305,626,732,849
624,621,887,467,573,761,589,612,648,883,355,432,451,515,281,67,780,601,162,465
632,240,761,881,782,593,110,856,783,900,844,52,282,634,276,836,293,271,579,895
913,720,514,743,241,434,786,929,800,920,948,179,883,607,68,903,129,481,779,512
732,642,893,625,509,310,70,319,101,904,113,373,136,132,555,988,619,734,744,587
171,929,829,85,656,884,281,744,226,229,104,844,430,276,157,228,83,866,283,273
988,133,594,175,452,162,575,678,627,606,625,512,660,436,116,842,582,300,635,594
167,461,194,884,357,206,55,77,858,369,802,745,887,779,305,613,576,789,600,170
562,461,429,275,636,589,651,106,55,526,989,581,920,577,798,373,429,773,464,772
917,858,606,288,733,356,284,234,865,476,925,919,804,227,507,55,914,301,567,149
269,685,521,56,850,310,364,609,296,15,67,646,52,513,350,241,458,652,745,85
782,163,352,242,610,560,380,106,659,284,312,898,180,896,289,475,62,835,897,117
690,791,780,133,910,598,85,595,834,83,373,238,450,580,907,761,783,785,855,741
638,279,348,782,749,71,891,586,353,105,867,565,354,924,310,562,930,680,911,243
59,947,70,859,865,116,648,326,794,941,845,169,241,898,775,786,917,315,280,566
913,522,166,790,361,453,848,146,604,354,162,101,844,456,772,914,997,163,907,898
308,934,175,804,775,166,352,55,833,343,368,860,457,948,862,288,62,841,229,181
636,605,591,687,376,911,782,461,101,721,402,449,615,269,146,777,71,838,347,672
921,510,530,428,461,139,904,105,862,679,322,579,858,283,453,301,897,52,402,589
747,605,634,584,67,715,886,278,570,524,299,721,308,890,300,607,231,478,90,902
348,681,631,358,830,635,228,468,105,717,768,908,300,750,224,515,110,642,867,696
171,477,284,508,117,72,681,568,896,841,77,846,555,355,721,591,296,668,308,113
268,936,936,932,318,274,582,517,849,635,282,168,858,678,932,280,760,804,357,714
232,921,859,456,505,361,678,645,467,79,153,302,353,915,313,449,932,949,801,130
838,532,913,116,529,905,612,575,236,947,567,533,520,171,765,569,829,883,942,364
242,569,522,578,597,570,457,314,133,274,301,775,910,644,168,209,138,558,173,297
883,511,297,366,114,595,299,642,77,52,54,840,284,661,318,282,278,591,647,641
17,840,847,220,347,304,177,720,840,840,653,946,376,181,481,629,633,172,365,680
222,945,839,160,678,353,299,587,476,532,743,101,477,936,316,204,402,225,790,519
226,479,62,617,159,66,785,588,990,521,156,361,685,656,754,769,482,930,913,167
769,109,753,747,226,705,274,844,85,609,148,316,52,181,689,632,612,595,307,931
558,805,88,106,372,754,222,756,838,475,471,844,482,884,299,769,232,589,802,789
683,305,744,451,531,718,307,276,146,886,525,802,233,395,622,775,302,935,889,61
294,612,573,524,365,108,562,289,76,134,743,321,58,771,718,294,271,938,729,787
739,559,237,794,278,178,575,464,568,916,436,929,352,859,619,794,582,361,769,745
382,131,862,356,525,286,457,886,718,241,456,180,312,173,295,581,179,616,57,375
592,226,740,276,351,837,518,224,478,403,610,462,69,354,789,367,982,178,804,481
773,582,310,684,656,450,687,145,532,937,752,901,280,206,748,300,945,235,986,134
436,944,296,581,685,228,321,847,363,133,605,934,156,842,116,388,464,275,137,145
451,584,105,933,621,922,618,316,732,568,679,229,307,591,363,920,223,577,106,454
678,732,376,372,457,910,155,476,835,753,656,54,294,829,432,312,312,853,521,130
303,685,543,471,851,451,910,573,354,558,687,372,753,78,746,372,657,753,348,168
646,115,224,891,800,788,237,565,900,602,51,165,179,653,656,769,303,926,80,780
736,354,768,585,796,919,612,309,743,163,357,892,616,628,83,88,60,751,714,103
229,615,842,772,775,620,859,90,920,294,643,921,740,277,916,577,839,107,600,746
931,177,590,462,558,89,353,476,640,930,779,575,591,719,307,167,527,403,846,429
921,795,51,303,596,720,741,720,571,649,572,67,366,350,935,925,900,521,431,772
505,467,561,609,678,611,601,220,104,915,269,864,169,778,580,847,654,364,899,991
592,600,432,64,450,801,353,592,645,714,228,754,929,287,862,578,560,506,451,846
179,621,178,606,366,896,844,363,611,220,618,277,367,243,455,916,127,738,888,866
63,520,291,785,932,777,788,801,295,788,301,717,655,362,844,265,584,718,798,993
51,294,348,111,935,640,633,639,533,936,138,224,166,228,358,113,205,92,436,377
900,916,160,865,515,537,803,679,589,149,282,528,349,82,136,451,750,130,507,114
741,948,278,604,848,355,750,506,741,175,780,850,232,361,785,228,848,556,219,936
76,805,451,286,832,565,774,943,515,317,626,719,473,678,114,21,504,890,471,852
525,734,932,681,715,461,612,179,613,633,738,838,560,208,942,564,637,300,789,432
805,74,620,838,559,555,82,845,50,0,784,681,368,897,906,636,508,600,163,137
431,86,792,55,61,466,825,467,652,60,377,581,747,159,530,347,131,682,237,626
53,350,632,838,601,374,606,891,831,164,781,453,5,583,63,273,558,522,585,598
54,755,629,312,530,420,641,831,628,574,310,626,358,476,463,150,130,688,268,531
737,800,859,157,685,365,604,312,907,313,783,513,533,230,648,472,884,509,672,720
713,349,241,457,106,449,474,885,79,481,721,233,936,831,913,772,381,946,57,832
931,362,944,482,930,374,650,654,942,890,676,83,355,117,377,747,508,717,243,931
172,116,843,274,220,836,837,360,645,295,138,772,302,179,51,362,464,80,515,986
569,83,658,159,842,359,114,156,911,756,398,848,286,583,629,749,455,776,456,69
641,900,180,352,608,620,948,117,309,639,190,891,894,319,294,651,860,310,638,532
631,937,274,907,150,0,773,526,733,794,476,275,113,169,311,863,795,358,403,516
508,780,181,603,846,802,231,472,513,109,649,239,680,679,389,916,437,512,401,285
148,402,303,591,639,826,630,683,243,633,686,473,940,295,743,280,475,163,573,291
518,690,62,115,351,795,555,854,322,740,627,68,641,171,646,639,20,159,181,72
86,321,166,790,853,175,310,513,80,133,771,658,629,707,789,914,174,292,574,375
224,455,524,315,364,589,582,101,743,159,166,647,304,316,455,19,647,562,170,745
51,55,105,306,517,906,830,319,638,233,940,520,277,470,810,638,634,428,657,933
656,172,638,571,145,249,101,831,234,454,114,848,269,402,627,65,749,371,901,932
718,82,527,376,180,592,630,132,280,850,910,528,279,224,922,857,430,746,716,133
78,631,173,228,365,888,733,774,741,298,771,830,358,167,198,690,348,901,798,241
883,238,402,796,740,103,919,194,294,355,634,579,586,69,56,270,746,63,74,589
285,946,777,514,132,627,648,179,619,235,432,606,830,193,171,909,720,682,581,784
271,111,644,883,895,583,227,270,773,921,291,321,371,303,559,667,352,529,320,457
716,364,112,449,227,618,797,747,573,802,588,304,801,679,169,788,742,856,987,797
507,310,480,146,451,793,769,720,738,164,753,172,459,936,67,516,287,468,734,88
579,291,240,163,906,509,138,79,556,60,605,851,655,296,86,437,916,153,298,910
401,505,599,652,588,161,877,782,530,882,623,362,805,851,748,135,842,59,508,308
895,691,751,57,156,841,932,520,146,366,714,890,561,772,636,367,716,111,296,625
690,359,853,775,7,57,53,222,279,590,70,321,660,71,585,643,782,72,920,111
597,753,166,563,180,512,68,794,861,510,718,308,525,979,848,862,689,376,565,271
355,845,802,234,472,920,174,62,945,889,715,110,721,900,917,948,866,461,140,787

``````use crate::common::AdventOfCodeDay;

#[derive(Debug,Clone)]
pub struct Day16 {
rules: Vec<Rule>,
ticket: RawTicketData,
nearby: Vec<RawTicketData>,
}

#[derive(Debug,Clone)]
struct Rule {
name: String,
ranges: Vec<(i32, i32)>,
}

impl Rule {
fn matches(&self, dat: i32) -> bool {
return self.ranges.iter().any(|(lower, upper)| dat >= *lower && dat <= *upper);
}
}

#[derive(Debug,Clone)]
struct RawTicketData {
fields: Vec<i32>,
}

impl Day16 {
pub fn new() -> Self {
let input_bytes = include_bytes!("../res/16_input.txt");
let input_str = String::from_utf8_lossy(input_bytes);

let lines = input_str
.lines()
.map(|p| String::from(p))
.collect::<Vec<String>>();

let mut i = 0;

let mut rules: Vec<Rule> = Vec::new();
loop {
let line = lines[i].clone();
if line == "" { i+=1; i+=1; break; }

let s1 = line.split(": ").collect::<Vec<&str>>();
let name = s1[0].to_owned();

let s2 = s1[1].split(" or ").collect::<Vec<&str>>();

let s21 = s2[0].split('-').collect::<Vec<&str>>();
let range1 = (s21[0].parse::<i32>().unwrap(), s21[1].parse::<i32>().unwrap());

let s22 = s2[1].split('-').collect::<Vec<&str>>();
let range2 = (s22[0].parse::<i32>().unwrap(), s22[1].parse::<i32>().unwrap());

rules.push(Rule {
name: name,
ranges: vec![ range1, range2 ],
});

i+=1;
}

let myticket = RawTicketData {
fields: lines[i].split(',').map(|p| p.parse::<i32>().unwrap()).collect(),
};
i+=1;

i+=1;
i+=1;

let mut nearbytickets: Vec<RawTicketData> = Vec::new();
while i < lines.len() {

nearbytickets.push(RawTicketData {
fields: lines[i].split(',').map(|p| p.parse::<i32>().unwrap()).collect(),
});

i+=1;
}

Self {
rules: rules,
ticket: myticket,
nearby: nearbytickets,
}
}
}

return self.nearby
.iter()
.flat_map(|p| p.fields.iter())
.filter(|f| self.rules.iter().all(|r| !r.matches(**f)))
.sum::<i32>()
.to_string();
}

let valid = self.nearby
.iter()
.filter(|p| p.fields.iter().all(|f| self.rules.iter().any(|r| r.matches(*f))))
.map(|p| p.clone())
.collect::<Vec<RawTicketData>>();

let mut candidates: Vec<(Rule, Vec<usize>)>;
candidates = self.rules
.iter()
.map(|rule| (rule.clone(), (0..self.ticket.fields.len())
.filter(|i| rule.matches(self.ticket.fields[*i]))
.filter(|i| valid.iter().all(|d| rule.matches(d.fields[*i]) ) )
.map(|p| p.clone())
.collect::<Vec<usize>>()))
.collect::<Vec<(Rule, Vec<usize>)>>();

verboseln!();
if is_verbose!() { for c in &candidates { verboseln!("{}: {:?}", c.0.name, c.1); } }
verboseln!();

while candidates.iter().any(|c| c.1.len() != 1) {

let rm = candidates.iter()
.filter(|c| c.1.len() == 1)
.flat_map(|p| p.1.iter())
.filter(|p| candidates.iter().filter(|c| c.1.contains(p)).count() > 1)
.map(|p|p.clone())
.collect::<Vec<usize>>();

// Field {rm} is teh single candidate of a rule and so it can not be a candidate for any other rule
verboseln!("Remove {:?}", rm);
for c in candidates.iter_mut().filter(|c| c.1.len() > 1) { c.1.retain(|v| !rm.contains(v) ); }

let unique = (0..self.ticket.fields.len())
.filter(|i| candidates.iter().filter(|c| c.1.contains(i)).count() == 1)
.filter(|i| candidates.iter().filter(|c| c.1.contains(i) && c.1.len() > 1).count() == 1)
.map(|p|p.clone())
.collect::<Vec<usize>>();

// Field {uniq} only appears in one rule and so it must be the candidate for that rule
verboseln!("Clean {:?}", unique);
for ui in &unique {
for c in candidates.iter_mut().filter(|c| c.1.contains(ui)) { c.1.retain(|v| v == ui ); }
}
}

verboseln!();
if is_verbose!() { for c in &candidates { verboseln!("{}: {:?} => {}", c.0.name, c.1, self.ticket.fields[c.1[0]]); } }
verboseln!();

return candidates.iter()
.filter(|c| c.0.name.starts_with("departure"))
.map(|c| c.1[0])
.map(|i| self.ticket.fields[i])
.map(|v| v as u128)
.fold(1, |a,b| a*b)
.to_string();
}
}``````
Result Part 1: 29019
Result Part 2: 517827547723

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